- A skateboarder rolls down a ramp from a higher platform to a lower level. As the skateboarder goes down, their speed increases. What happens to the skateboarder's kinetic energy, and why?
Answer: It increases, because gravitational potential energy is converted into kinetic energy as gravity does positive work along the motion.
This question tests understanding of what causes kinetic energy to change—specifically, that work done by forces or energy conversions cause KE to increase, decrease, or remain constant. Kinetic energy changes are governed by the work-energy relationship and energy conservation: (1) KE increases when positive work is done (force in direction of motion: engine accelerating car, force forward while car moves forward, does positive work increasing KE from 0 to ½mv²), or when other energy converts to KE (falling object: PE → KE, chemical from fuel → KE in engine); (2) KE decreases when negative work is done (force opposite to motion: friction on sliding object, force backward while object moves forward, does negative work removing KE and converting to thermal), or when KE converts to other forms (rising ball: KE → PE, collision: KE → thermal/sound/deformation); and (3) KE stays constant when no net work is done (balanced forces: F_net=0 so no acceleration, speed constant means KE constant), or when motion is perpendicular to force (satellite orbit: gravity pulls inward perpendicular to velocity, no work, KE unchanged). A skateboarder rolling down a ramp speeds up, so kinetic energy increases from KE_initial (slow at top) to KE_final (fast at bottom)—this KE increase results from gravitational potential energy converting to kinetic energy as gravity does positive work: skateboarder starts high (large PE = mgh), ends low (smaller PE), and lost PE becomes gained KE; gravity pulls downward, skateboarder moves downward along ramp (component of motion in gravity's direction), so gravity does positive work W = mgh (where h is vertical drop), increasing KE by exactly the PE lost. The energy conversion: PE_initial + KE_initial = PE_final + KE_final (conservation of mechanical energy), with PE decreasing by mgh and KE increasing by same amount mgh, so ΔKE = -ΔPE = mgh (what PE loses, KE gains), explaining speed increase from energy transformation. Choice B is correct because it accurately explains KE increase using positive work and energy conversion: gravitational potential energy is converted into kinetic energy as gravity does positive work along the motion (gravity has component along ramp doing positive work). Choice A reverses the energy conversion by claiming PE increases while going downward, when PE = mgh decreases as height h decreases; choice C incorrectly states gravity is perpendicular to motion down ramp, when gravity has a component along the ramp doing work; choice D falsely claims friction adds energy, when friction would actually remove energy by doing negative work. Explaining KE changes systematically: (1) observe motion: speeding up (KE increasing), slowing down (KE decreasing), or constant speed (KE constant), (2) identify forces: what forces act? in what directions relative to motion?, (3) determine net work: forces in motion direction do positive work (add KE), forces opposing motion do negative work (remove KE), perpendicular forces do zero work (don't change KE), balanced forces: W_net=0 (KE constant), (4) apply work-energy: W_net = ΔKE (work equals energy change), (5) check energy conversions: if work doesn't fully explain, look for conversions (PE ↔ KE, chemical → KE, KE → thermal), and (6) verify conservation: energy source for KE increase? (work input, PE decreasing, chemical burning), energy destination for KE decrease? (work output, PE increasing, thermal from friction)—all energy accounted. Common scenarios: (1) free fall: KE increases (PE → KE, gravity does positive work accelerating downward), (2) thrown upward: KE decreases then increases (KE → PE going up as gravity does negative work, PE → KE coming down as gravity does positive work), (3) braking: KE decreases (friction does negative work, KE → thermal in brakes), (4) horizontal surface no friction: KE constant (no forces doing work, speed constant by Newton's First Law), (5) engine accelerating: KE increases (chemical energy → thermal → mechanical work → KE, engine does positive work).
- A skateboarder is coasting in a straight line on a smooth, level surface at a steady 5 m/s. The skateboarder does not push, and the speed stays the same. What happens to the skateboarder's kinetic energy, and why?
Answer: It stays constant because the speed is constant, so KE=21mv2 does not change (no net work changes the speed).
This question tests understanding of what causes kinetic energy to change—specifically, that work done by forces or energy conversions cause KE to increase, decrease, or remain constant. Kinetic energy changes are governed by the work-energy relationship and energy conservation: (1) KE increases when positive work is done (force in direction of motion: engine accelerating car, force forward while car moves forward, does positive work increasing KE from 0 to ½mv²), or when other energy converts to KE (falling object: PE → KE, chemical from fuel → KE in engine); (2) KE decreases when negative work is done (force opposite to motion: friction on sliding object, force backward while object moves forward, does negative work removing KE and converting to thermal), or when KE converts to other forms (rising ball: KE → PE, collision: KE → thermal/sound/deformation); and (3) KE stays constant when no net work is done (balanced forces: F_net=0 so no acceleration, speed constant means KE constant), or when motion is perpendicular to force (satellite orbit: gravity pulls inward perpendicular to velocity, no work, KE unchanged). A skateboarder coasting at constant 5 m/s on a smooth, level surface (no pushing) has constant kinetic energy KE = ½m(5²) = 12.5m J throughout—KE doesn't change because speed doesn't change (constant v means constant v² means constant ½mv²), and speed stays constant because net force is zero: on smooth surface, friction is negligible, gravity downward balanced by normal force upward, no horizontal forces (F_net=0), so no acceleration (a=0 from F=ma with F=0), meaning velocity constant (no Δv), meaning KE constant (no ΔKE). The work-energy perspective: net work equals zero (no forces doing work in direction of motion: no friction, gravity perpendicular so W_gravity=0), so no net work means no KE change (W_net = ΔKE = 0), explaining constant energy despite motion (no unbalanced forces, no net work, no energy change). Choice C is correct because it properly identifies zero net work or balanced forces for constant KE. Choice D is wrong because it misidentifies forces: claims friction is the only force and does zero work, but on smooth surface friction is negligible (not acting significantly), and even if small, it would do negative work slowing it slightly, but question states speed stays the same, implying no friction. Explaining KE changes systematically: (1) observe motion: speeding up (KE increasing), slowing down (KE decreasing), or constant speed (KE constant), (2) identify forces: what forces act? in what directions relative to motion?, (3) determine net work: forces in motion direction do positive work (add KE), forces opposing motion do negative work (remove KE), perpendicular forces do zero work (don't change KE), balanced forces: W_net=0 (KE constant), (4) apply work-energy: W_net = ΔKE (work equals energy change), (5) check energy conversions: if work doesn't fully explain, look for conversions (PE ↔ KE, chemical → KE, KE → thermal), and (6) verify conservation: energy source for KE increase? (work input, PE decreasing, chemical burning), energy destination for KE decrease? (work output, PE increasing, thermal from friction)—all energy accounted. Common scenarios: (1) free fall: KE increases (PE → KE, gravity does positive work accelerating downward), (2) thrown upward: KE decreases then increases (KE → PE going up as gravity does negative work, PE → KE coming down as gravity does positive work), (3) braking: KE decreases (friction does negative work, KE → thermal in brakes), (4) horizontal surface no friction: KE constant (no forces doing work, speed constant by Newton's First Law), (5) engine accelerating: KE increases (chemical energy → thermal → mechanical work → KE, engine does positive work). - A student pulls a wagon on level ground with a steady forward pull, but the wagon moves at a constant speed (it does not speed up). What does this tell you about the wagon's kinetic energy and the net work on it?
Answer: The kinetic energy stays constant, so the net work is zero (the forward pull is balanced by friction/drag).
This question tests understanding of what causes kinetic energy to change—specifically, that work done by forces or energy conversions cause KE to increase, decrease, or remain constant. Kinetic energy changes are governed by the work-energy relationship and energy conservation: (1) KE increases when positive work is done (force in direction of motion: engine accelerating car, force forward while car moves forward, does positive work increasing KE from 0 to ½mv²), or when other energy converts to KE (falling object: PE → KE, chemical from fuel → KE in engine); (2) KE decreases when negative work is done (force opposite to motion: friction on sliding object, force backward while object moves forward, does negative work removing KE and converting to thermal), or when KE converts to other forms (rising ball: KE → PE, collision: KE → thermal/sound/deformation); and (3) KE stays constant when no net work is done (balanced forces: F_net=0 so no acceleration, speed constant means KE constant), or when motion is perpendicular to force (satellite orbit: gravity pulls inward perpendicular to velocity, no work, KE unchanged). A wagon pulled with steady forward force but moving at constant speed (no speeding up) has constant kinetic energy KE = ½mv² throughout—KE doesn't change because speed doesn't change (constant v means constant KE), and speed stays constant because net force is zero: student's forward pull exactly balances friction/drag backward (balanced forces: F_net=0), so no acceleration (a=0), meaning velocity constant (no Δv), meaning KE constant (no ΔKE). The work-energy perspective: net work equals zero (positive work from pull exactly cancels negative work from friction: W_pull + W_friction = 0), so no net work means no KE change (W_net = ΔKE = 0), explaining constant energy despite forces acting (forces balanced, no net work, no energy change). Choice C is correct because it properly identifies zero net work or balanced forces for constant KE. Choice D is wrong because it confuses net work: claims net work positive because force applied, but if speed constant, net work must be zero (positive work balanced by negative work from friction, otherwise would accelerate and KE increase). Explaining KE changes systematically: (1) observe motion: speeding up (KE increasing), slowing down (KE decreasing), or constant speed (KE constant), (2) identify forces: what forces act? in what directions relative to motion?, (3) determine net work: forces in motion direction do positive work (add KE), forces opposing motion do negative work (remove KE), perpendicular forces do zero work (don't change KE), balanced forces: W_net=0 (KE constant), (4) apply work-energy: W_net = ΔKE (work equals energy change), (5) check energy conversions: if work doesn't fully explain, look for conversions (PE ↔ KE, chemical → KE, KE → thermal), and (6) verify conservation: energy source for KE increase? (work input, PE decreasing, chemical burning), energy destination for KE decrease? (work output, PE increasing, thermal from friction)—all energy accounted. Common scenarios: (1) free fall: KE increases (PE → KE, gravity does positive work accelerating downward), (2) thrown upward: KE decreases then increases (KE → PE going up as gravity does negative work, PE → KE coming down as gravity does positive work), (3) braking: KE decreases (friction does negative work, KE → thermal in brakes), (4) horizontal surface no friction: KE constant (no forces doing work, speed constant by Newton's First Law), (5) engine accelerating: KE increases (chemical energy → thermal → mechanical work → KE, engine does positive work).
- A student pushes a toy cart forward across the floor for 2 seconds, and the cart speeds up. Then the student stops pushing, and the cart continues but gradually slows due to friction. During which part is the cart's kinetic energy increasing, and what causes that increase?
Answer: It increases while the student is pushing, because the applied force does positive work on the cart and increases its speed.
This question tests understanding of what causes kinetic energy to change—specifically, that work done by forces or energy conversions cause KE to increase, decrease, or remain constant. Kinetic energy changes are governed by the work-energy relationship and energy conservation: (1) KE increases when positive work is done (force in direction of motion: engine accelerating car, force forward while car moves forward, does positive work increasing KE from 0 to ½mv²), or when other energy converts to KE (falling object: PE → KE, chemical from fuel → KE in engine); (2) KE decreases when negative work is done (force opposite to motion: friction on sliding object, force backward while object moves forward, does negative work removing KE and converting to thermal), or when KE converts to other forms (rising ball: KE → PE, collision: KE → thermal/sound/deformation); and (3) KE stays constant when no net work is done (balanced forces: F_net=0 so no acceleration, speed constant means KE constant), or when motion is perpendicular to force (satellite orbit: gravity pulls inward perpendicular to velocity, no work, KE unchanged). During the pushing phase, the cart speeds up so kinetic energy increases from low initial KE to higher final KE—this KE increase results from the student doing positive work on the cart: student applies forward force (push), cart moves forward (same direction as force), and work = force × distance is positive (force and displacement aligned), with this work equal to the KE gained; after pushing stops, friction does negative work (force backward, motion forward), causing KE to decrease as cart slows. The energy flow: while pushing, student's chemical energy (muscles) → mechanical work → cart's KE (increasing); after pushing, cart's KE → thermal energy via friction (decreasing KE, warming floor/wheels). Choice A is correct because it accurately explains KE increase during the correct phase: it increases while the student is pushing, because the applied force does positive work on the cart and increases its speed. Choice B wrongly claims KE increases after pushing stops, when friction actually does negative work decreasing KE; choice C incorrectly states friction increases KE, when friction always does negative work removing KE; choice D falsely claims KE cannot change unless mass changes, contradicting KE = ½mv² where v changes while m stays constant. Explaining KE changes systematically: (1) observe motion: speeding up (KE increasing), slowing down (KE decreasing), or constant speed (KE constant), (2) identify forces: what forces act? in what directions relative to motion?, (3) determine net work: forces in motion direction do positive work (add KE), forces opposing motion do negative work (remove KE), perpendicular forces do zero work (don't change KE), balanced forces: W_net=0 (KE constant), (4) apply work-energy: W_net = ΔKE (work equals energy change), (5) check energy conversions: if work doesn't fully explain, look for conversions (PE ↔ KE, chemical → KE, KE → thermal), and (6) verify conservation: energy source for KE increase? (work input, PE decreasing, chemical burning), energy destination for KE decrease? (work output, PE increasing, thermal from friction)—all energy accounted. Understanding causes of KE changes helps: predict motion (if force forward, object will speed up increasing KE), explain energy (where did KE come from? work or conversion; where did it go? work or conversion), design systems (want high KE? apply large force over distance doing lots of work; want to reduce KE? use friction or convert to other form), and reason about safety (high-speed objects have large KE requiring large work/distance to stop—why speed limits matter, why braking distances long at high speeds).
- A student throws a ball straight upward. Right after it leaves the student's hand, it is moving upward quickly. As it rises, it slows down until it momentarily stops at the top. Why does the ball's kinetic energy decrease while it is rising?
Answer: The ball's kinetic energy decreases because gravity acts opposite the ball's upward motion, doing negative work and converting kinetic energy into gravitational potential energy.
This question tests understanding of what causes kinetic energy to change—specifically, that work done by forces or energy conversions cause KE to increase, decrease, or remain constant. Kinetic energy changes are governed by the work-energy relationship and energy conservation: (1) KE increases when positive work is done (force in direction of motion: engine accelerating car, force forward while car moves forward, does positive work increasing KE from 0 to ½mv²), or when other energy converts to KE (falling object: PE → KE, chemical from fuel → KE in engine); (2) KE decreases when negative work is done (force opposite to motion: friction on sliding object, force backward while object moves forward, does negative work removing KE and converting to thermal), or when KE converts to other forms (rising ball: KE → PE, collision: KE → thermal/sound/deformation); and (3) KE stays constant when no net work is done (balanced forces: F_net=0 so no acceleration, speed constant means KE constant), or when motion is perpendicular to force (satellite orbit: gravity pulls inward perpendicular to velocity, no work, KE unchanged). For KE decreasing: As the ball rises and slows down, say from 10 m/s (KE_initial = ½m(10²) = 50m J) to 0 m/s at the top (KE_final = 0), losing all its kinetic energy—this KE decrease occurs because gravity does negative work: gravity force acts downward (opposite to ball's upward motion), and as ball rises distance h upward, gravity does work W = -mg×h (negative because force opposes displacement), removing kinetic energy which converts to gravitational potential energy (ball gains PE = mgh). Choice B is correct because it correctly cites negative work or energy conversion from KE for KE decrease. Choice A is wrong because it reverses work direction: claims gravity does work in the same direction speeding it up, when gravity actually opposes upward motion doing negative work to slow it down. Explaining KE changes systematically: (1) observe motion: speeding up (KE increasing), slowing down (KE decreasing), or constant speed (KE constant), (2) identify forces: what forces act? in what directions relative to motion?, (3) determine net work: forces in motion direction do positive work (add KE), forces opposing motion do negative work (remove KE), perpendicular forces do zero work (don't change KE), balanced forces: W_net=0 (KE constant), (4) apply work-energy: W_net = ΔKE (work equals energy change), (5) check energy conversions: if work doesn't fully explain, look for conversions (PE ↔ KE, chemical → KE, KE → thermal), and (6) verify conservation: energy source for KE increase? (work input, PE decreasing, chemical burning), energy destination for KE decrease? (work output, PE increasing, thermal from friction)—all energy accounted. Common scenarios: (1) free fall: KE increases (PE → KE, gravity does positive work accelerating downward), (2) thrown upward: KE decreases then increases (KE → PE going up as gravity does negative work, PE → KE coming down as gravity does positive work), (3) braking: KE decreases (friction does negative work, KE → thermal in brakes), (4) horizontal surface no friction: KE constant (no forces doing work, speed constant by Newton's First Law), (5) engine accelerating: KE increases (chemical energy → thermal → mechanical work → KE, engine does positive work).
- A ball is thrown straight up and later falls back down. Ignoring air resistance, compare the ball's kinetic energy at two moments: (1) on the way up at a height of 2 m, and (2) on the way down at the same height of 2 m. What is true about the kinetic energy at these two moments?
Answer: The kinetic energy is the same at both moments because at the same height the speed is the same (energy shifts between KE and gravitational potential energy).
This question tests understanding of what causes kinetic energy to change—specifically, that work done by forces or energy conversions cause KE to increase, decrease, or remain constant. Kinetic energy changes are governed by the work-energy relationship and energy conservation: (1) KE increases when positive work is done (force in direction of motion: engine accelerating car, force forward while car moves forward, does positive work increasing KE from 0 to ½mv²), or when other energy converts to KE (falling object: PE → KE, chemical from fuel → KE in engine); (2) KE decreases when negative work is done (force opposite to motion: friction on sliding object, force backward while object moves forward, does negative work removing KE and converting to thermal), or when KE converts to other forms (rising ball: KE → PE, collision: KE → thermal/sound/deformation); and (3) KE stays constant when no net work is done (balanced forces: F_net=0 so no acceleration, speed constant means KE constant), or when motion is perpendicular to force (satellite orbit: gravity pulls inward perpendicular to velocity, no work, KE unchanged). For a ball thrown up and falling back, ignoring air resistance, at 2 m height on way up and way down, KE is the same—on way up at 2 m, speed v satisfies ½mv² + mg(2) = total E (initial KE + PE=0 at ground), on way down at 2 m, speed is same v (symmetry: gravity conservative, path reversible, so same height means same speed, same KE=½mv²). Conservation of energy explains: total mechanical energy constant (no dissipation), so at same height PE same (mg h= mg(2)), thus KE same (total E - PE = KE, same for both), with energy shifting KE → PE up, PE → KE down, but equal at equal heights. Choice C is correct because it properly identifies that at same height, speed same, KE same due to energy conservation between KE and PE. Choice B is wrong because it violates conservation: claims gravity adds extra energy on way down, but gravity doesn't create energy (conservative force), KE on down equals KE on up at same height (no extra). Explaining KE changes systematically: (1) observe motion: speeding up (KE increasing), slowing down (KE decreasing), or constant speed (KE constant), (2) identify forces: what forces act? in what directions relative to motion?, (3) determine net work: forces in motion direction do positive work (add KE), forces opposing motion do negative work (remove KE), perpendicular forces do zero work (don't change KE), balanced forces: W_net=0 (KE constant), (4) apply work-energy: W_net = ΔKE (work equals energy change), (5) check energy conversions: if work doesn't fully explain, look for conversions (PE ↔ KE, chemical → KE, KE → thermal), and (6) verify conservation: energy source for KE increase? (work input, PE decreasing, chemical burning), energy destination for KE decrease? (work output, PE increasing, thermal from friction)—all energy accounted. Common scenarios: (1) free fall: KE increases (PE → KE, gravity does positive work accelerating downward), (2) thrown upward: KE decreases then increases (KE → PE going up as gravity does negative work, PE → KE coming down as gravity does positive work), (3) braking: KE decreases (friction does negative work, KE → thermal in brakes), (4) horizontal surface no friction: KE constant (no forces doing work, speed constant by Newton's First Law), (5) engine accelerating: KE increases (chemical energy → thermal → mechanical work → KE, engine does positive work).
- A ball rolls down a ramp from rest. Halfway down, it is moving faster than it was at the top. What is the best explanation for how the ball's kinetic energy changes as it rolls downward?
Answer: Kinetic energy increases because gravitational potential energy is converted into kinetic energy, making the ball speed up.
This question tests understanding of what causes kinetic energy to change—specifically, that work done by forces or energy conversions cause KE to increase, decrease, or remain constant. Kinetic energy changes are governed by the work-energy relationship and energy conservation: (1) KE increases when positive work is done (force in direction of motion: engine accelerating car, force forward while car moves forward, does positive work increasing KE from 0 to ½mv²), or when other energy converts to KE (falling object: PE → KE, chemical from fuel → KE in engine); (2) KE decreases when negative work is done (force opposite to motion: friction on sliding object, force backward while object moves forward, does negative work removing KE and converting to thermal), or when KE converts to other forms (rising ball: KE → PE, collision: KE → thermal/sound/deformation); and (3) KE stays constant when no net work is done (balanced forces: F_net=0 so no acceleration, speed constant means KE constant), or when motion is perpendicular to force (satellite orbit: gravity pulls inward perpendicular to velocity, no work, KE unchanged). For a ball rolling down a ramp from rest, halfway down it speeds up (KE increases from 0 to ½mv²)—this KE increase results from gravity doing positive work: component of gravity force along ramp acts downward along motion, ball moves down ramp distance d, work = (mg sinθ) × d (positive, force and displacement same direction), with this work equal to KE gained (W = ΔKE). The energy source is gravitational potential energy (PE decreases as height drops), converting PE → KE, so conservation: ΔPE = -mgΔh = ΔKE = ½mv² (lost PE becomes gained KE, ignoring friction). Choice B is correct because it accurately explains KE increase using positive work or energy conversion to KE from PE. Choice A is wrong because it misidentifies energy conversion: states KE → PE when falling (actually PE → KE), and claims KE decreases as ball goes down, contradicting speeding up means KE increases. Explaining KE changes systematically: (1) observe motion: speeding up (KE increasing), slowing down (KE decreasing), or constant speed (KE constant), (2) identify forces: what forces act? in what directions relative to motion?, (3) determine net work: forces in motion direction do positive work (add KE), forces opposing motion do negative work (remove KE), perpendicular forces do zero work (don't change KE), balanced forces: W_net=0 (KE constant), (4) apply work-energy: W_net = ΔKE (work equals energy change), (5) check energy conversions: if work doesn't fully explain, look for conversions (PE ↔ KE, chemical → KE, KE → thermal), and (6) verify conservation: energy source for KE increase? (work input, PE decreasing, chemical burning), energy destination for KE decrease? (work output, PE increasing, thermal from friction)—all energy accounted. Common scenarios: (1) free fall: KE increases (PE → KE, gravity does positive work accelerating downward), (2) thrown upward: KE decreases then increases (KE → PE going up as gravity does negative work, PE → KE coming down as gravity does positive work), (3) braking: KE decreases (friction does negative work, KE → thermal in brakes), (4) horizontal surface no friction: KE constant (no forces doing work, speed constant by Newton's First Law), (5) engine accelerating: KE increases (chemical energy → thermal → mechanical work → KE, engine does positive work).
- A puck slides on nearly frictionless ice at a constant speed in a straight line. No one is pushing it. What happens to the puck's kinetic energy, and what is the best reason?
Answer: It stays constant because there is (approximately) no net force doing work on the puck, so its speed and KE stay the same.
This question tests understanding of what causes kinetic energy to change—specifically, that work done by forces or energy conversions cause KE to increase, decrease, or remain constant. Kinetic energy changes are governed by the work-energy relationship and energy conservation: (1) KE increases when positive work is done (force in direction of motion: engine accelerating car, force forward while car moves forward, does positive work increasing KE from 0 to ½mv²), or when other energy converts to KE (falling object: PE → KE, chemical from fuel → KE in engine); (2) KE decreases when negative work is done (force opposite to motion: friction on sliding object, force backward while object moves forward, does negative work removing KE and converting to thermal), or when KE converts to other forms (rising ball: KE → PE, collision: KE → thermal/sound/deformation); and (3) KE stays constant when no net work is done (balanced forces: F_net=0 so no acceleration, speed constant means KE constant), or when motion is perpendicular to force (satellite orbit: gravity pulls inward perpendicular to velocity, no work, KE unchanged). For KE constant: A puck sliding at constant speed on nearly frictionless ice (say 4 m/s, KE = ½m(4²) = 8m J) has constant kinetic energy—KE doesn't change because speed doesn't change (constant v means constant v² means constant ½mv²), and speed stays constant because net force is approximately zero: no pushing, negligible friction (F_net ≈ 0), so no acceleration (a=0), meaning velocity constant (no Δv), meaning KE constant (no ΔKE). The work-energy perspective: net work approximately zero (negligible negative work from tiny friction: W_net ≈ 0), so no net work means no KE change (W_net = ΔKE ≈ 0), consistent with Newton's First Law (objects in motion stay in motion at constant velocity without net force). Choice B is correct because it properly identifies zero net work or balanced forces for constant KE. Choice A is wrong because it claims KE decreases without identifying energy destination or negative work, violating conservation and contradicting constant speed (constant v means constant KE). Explaining KE changes systematically: (1) observe motion: speeding up (KE increasing), slowing down (KE decreasing), or constant speed (KE constant), (2) identify forces: what forces act? in what directions relative to motion?, (3) determine net work: forces in motion direction do positive work (add KE), forces opposing motion do negative work (remove KE), perpendicular forces do zero work (don't change KE), balanced forces: W_net=0 (KE constant), (4) apply work-energy: W_net = ΔKE (work equals energy change), (5) check energy conversions: if work doesn't fully explain, look for conversions (PE ↔ KE, chemical → KE, KE → thermal), and (6) verify conservation: energy source for KE increase? (work input, PE decreasing, chemical burning), energy destination for KE decrease? (work output, PE increasing, thermal from friction)—all energy accounted. Common scenarios: (1) free fall: KE increases (PE → KE, gravity does positive work accelerating downward), (2) thrown upward: KE decreases then increases (KE → PE going up as gravity does negative work, PE → KE coming down as gravity does positive work), (3) braking: KE decreases (friction does negative work, KE → thermal in brakes), (4) horizontal surface no friction: KE constant (no forces doing work, speed constant by Newton's First Law), (5) engine accelerating: KE increases (chemical energy → thermal → mechanical work → KE, engine does positive work). - A hockey puck slides across rough ice. It starts moving quickly, but after a few seconds it is moving much more slowly and eventually stops. What best explains why the puck's kinetic energy decreases?
Answer: Friction acts opposite the puck's motion and does negative work, converting kinetic energy into thermal energy.
This question tests understanding of what causes kinetic energy to change—specifically, that work done by forces or energy conversions cause KE to increase, decrease, or remain constant. Kinetic energy changes are governed by the work-energy relationship and energy conservation: (1) KE increases when positive work is done (force in direction of motion: engine accelerating car, force forward while car moves forward, does positive work increasing KE from 0 to ½mv²), or when other energy converts to KE (falling object: PE → KE, chemical from fuel → KE in engine); (2) KE decreases when negative work is done (force opposite to motion: friction on sliding object, force backward while object moves forward, does negative work removing KE and converting to thermal), or when KE converts to other forms (rising ball: KE → PE, collision: KE → thermal/sound/deformation); and (3) KE stays constant when no net work is done (balanced forces: F_net=0 so no acceleration, speed constant means KE constant), or when motion is perpendicular to force (satellite orbit: gravity pulls inward perpendicular to velocity, no work, KE unchanged). A sliding hockey puck initially moving at 10 m/s (KE_initial = ½m(10²) = 50m J) gradually slows due to friction and stops (KE_final = 0), losing all its kinetic energy—this KE decrease occurs because friction does negative work: friction force acts backward (opposite to puck's forward motion), and as puck slides distance d forward, friction does work W = -f×d (negative because force opposes displacement), removing kinetic energy which converts to thermal energy (ice and puck warm microscopically from friction). The work-energy theorem explains: W_friction = ΔKE = 0 - 50m = -50m J (negative work equals negative KE change), and conservation requires: lost KE (50m J) = thermal energy gained (ice + puck warmer by 50m J total), so KE didn't disappear, it converted to thermal through friction's negative work. Choice B is correct because it correctly cites negative work or energy conversion from KE for KE decrease. Choice A is wrong because it reverses work direction: claims friction does positive work increasing KE, when friction always does negative work decreasing KE. Explaining KE changes systematically: (1) observe motion: speeding up (KE increasing), slowing down (KE decreasing), or constant speed (KE constant), (2) identify forces: what forces act? in what directions relative to motion?, (3) determine net work: forces in motion direction do positive work (add KE), forces opposing motion do negative work (remove KE), perpendicular forces do zero work (don't change KE), balanced forces: W_net=0 (KE constant), (4) apply work-energy: W_net = ΔKE (work equals energy change), (5) check energy conversions: if work doesn't fully explain, look for conversions (PE ↔ KE, chemical → KE, KE → thermal), and (6) verify conservation: energy source for KE increase? (work input, PE decreasing, chemical burning), energy destination for KE decrease? (work output, PE increasing, thermal from friction)—all energy accounted. Common scenarios: (1) free fall: KE increases (PE → KE, gravity does positive work accelerating downward), (2) thrown upward: KE decreases then increases (KE → PE going up as gravity does negative work, PE → KE coming down as gravity does positive work), (3) braking: KE decreases (friction does negative work, KE → thermal in brakes), (4) horizontal surface no friction: KE constant (no forces doing work, speed constant by Newton's First Law), (5) engine accelerating: KE increases (chemical energy → thermal → mechanical work → KE, engine does positive work).
- A skateboarder rolls down a ramp from a higher platform to a lower one. As the skateboarder goes down, their speed increases. What best explains the change in kinetic energy?
Answer: Kinetic energy increases because gravitational potential energy is converted into kinetic energy as the skateboarder loses height.
This question tests understanding of what causes kinetic energy to change—specifically, that work done by forces or energy conversions cause KE to increase, decrease, or remain constant. Kinetic energy changes are governed by the work-energy relationship and energy conservation: (1) KE increases when positive work is done (force in direction of motion: engine accelerating car, force forward while car moves forward, does positive work increasing KE from 0 to ½mv²), or when other energy converts to KE (falling object: PE → KE, chemical from fuel → KE in engine); (2) KE decreases when negative work is done (force opposite to motion: friction on sliding object, force backward while object moves forward, does negative work removing KE and converting to thermal), or when KE converts to other forms (rising ball: KE → PE, collision: KE → thermal/sound/deformation); and (3) KE stays constant when no net work is done (balanced forces: F_net=0 so no acceleration, speed constant means KE constant), or when motion is perpendicular to force (satellite orbit: gravity pulls inward perpendicular to velocity, no work, KE unchanged). For KE increasing: When a skateboarder rolls down a ramp from high to low, kinetic energy increases from near 0 (if starting slow) to ½mv² at bottom (v higher due to acceleration)—this KE increase results from gravity doing positive work: component of gravity along ramp acts downward along motion direction, skateboarder moves down distance along ramp, work = force_parallel × distance is positive, with this work equal to KE gained (W = ΔKE); alternatively, energy converts as PE decreases (mgh lost) to KE gained (½mv² = mgh, ignoring friction). The energy source is gravitational potential energy (higher position has more PE), converting PE → KE as height decreases, ultimately increasing KE. Choice A is correct because it accurately explains KE increase using positive work or energy conversion to KE. Choice B is wrong because it misidentifies energy conversion: states KE decreases from PE → KE, but actually PE → KE means KE increases. Explaining KE changes systematically: (1) observe motion: speeding up (KE increasing), slowing down (KE decreasing), or constant speed (KE constant), (2) identify forces: what forces act? in what directions relative to motion?, (3) determine net work: forces in motion direction do positive work (add KE), forces opposing motion do negative work (remove KE), perpendicular forces do zero work (don't change KE), balanced forces: W_net=0 (KE constant), (4) apply work-energy: W_net = ΔKE (work equals energy change), (5) check energy conversions: if work doesn't fully explain, look for conversions (PE ↔ KE, chemical → KE, KE → thermal), and (6) verify conservation: energy source for KE increase? (work input, PE decreasing, chemical burning), energy destination for KE decrease? (work output, PE increasing, thermal from friction)—all energy accounted. Common scenarios: (1) free fall: KE increases (PE → KE, gravity does positive work accelerating downward), (2) thrown upward: KE decreases then increases (KE → PE going up as gravity does negative work, PE → KE coming down as gravity does positive work), (3) braking: KE decreases (friction does negative work, KE → thermal in brakes), (4) horizontal surface no friction: KE constant (no forces doing work, speed constant by Newton's First Law), (5) engine accelerating: KE increases (chemical energy → thermal → mechanical work → KE, engine does positive work).
- A hockey puck glides across very smooth ice at a steady speed of 10 m/s in a straight line for several seconds. During this time, its speed does not change. What can you conclude about the puck's kinetic energy, and why?
Answer: Its kinetic energy stays constant because its speed is constant, meaning net work on it is zero (no change in kinetic energy).
This question tests understanding of what causes kinetic energy to change—specifically, that work done by forces or energy conversions cause KE to increase, decrease, or remain constant. Kinetic energy changes are governed by the work-energy relationship and energy conservation: (1) KE increases when positive work is done (force in direction of motion: engine accelerating car, force forward while car moves forward, does positive work increasing KE from 0 to ½mv²), or when other energy converts to KE (falling object: PE → KE, chemical from fuel → KE in engine); (2) KE decreases when negative work is done (force opposite to motion: friction on sliding object, force backward while object moves forward, does negative work removing KE and converting to thermal), or when KE converts to other forms (rising ball: KE → PE, collision: KE → thermal/sound/deformation); and (3) KE stays constant when no net work is done (balanced forces: F_net=0 so no acceleration, speed constant means KE constant), or when motion is perpendicular to force (satellite orbit: gravity pulls inward perpendicular to velocity, no work, KE unchanged). A hockey puck gliding at constant 10 m/s on smooth ice has constant kinetic energy KE = ½m(10²) = 50m J throughout—KE doesn't change because speed doesn't change (constant v means constant v² means constant ½mv²), and speed stays constant because net force is zero: on smooth ice, friction is negligible, so no horizontal forces act (or any tiny friction exactly balances tiny air resistance), giving F_net = 0, so no acceleration (a=0 from F=ma with F=0), meaning velocity constant (no Δv), meaning KE constant (no ΔKE). The work-energy perspective: net work equals zero (no forces doing work, or positive and negative work cancel: W_net = 0), so no net work means no KE change (W_net = ΔKE = 0), explaining constant energy with no forces acting (or balanced forces, no net work, no energy change). Choice C is correct because it properly identifies that KE stays constant due to constant speed, and correctly explains this using the work-energy theorem: constant speed means no acceleration, which means net force is zero, which means net work is zero, which means no change in kinetic energy (ΔKE = W_net = 0)—this accurately connects constant motion to zero net work to constant KE. Choice A claims KE increases just because puck keeps moving forward, ignoring that constant speed means constant KE; Choice B suggests KE decreases with time even at constant speed, contradicting KE = ½mv² (constant v means constant KE); Choice D claims friction does positive work adding energy, which is wrong—friction opposes motion doing negative work, and here friction is negligible anyway. Explaining KE changes systematically: (1) observe motion: constant speed 10 m/s (KE constant), (2) identify forces: on smooth ice, friction ≈ 0, gravity and normal balance vertically, no horizontal forces (or tiny balanced forces), (3) determine net work: W_net = 0 (no forces, or balanced forces doing equal opposite work), (4) apply work-energy: W_net = 0 = ΔKE (zero work means zero energy change), (5) check energy conversions: none—KE stays as KE, no conversions occurring, and (6) verify conservation: KE constant at 50m J, no energy added or removed—perfect conservation in idealized system.
- A book is sliding across a wooden floor after being pushed. It starts off moving quickly, but it slows down and eventually stops. Which best explains why the book's kinetic energy decreases?
Answer: Friction acts opposite the motion, so it does negative work and converts some of the book's kinetic energy into thermal energy.
This question tests understanding of what causes kinetic energy to change—specifically, that work done by forces or energy conversions cause KE to increase, decrease, or remain constant. Kinetic energy changes are governed by the work-energy relationship and energy conservation: (1) KE increases when positive work is done (force in direction of motion: engine accelerating car, force forward while car moves forward, does positive work increasing KE from 0 to ½mv²), or when other energy converts to KE (falling object: PE → KE, chemical from fuel → KE in engine); (2) KE decreases when negative work is done (force opposite to motion: friction on sliding object, force backward while object moves forward, does negative work removing KE and converting to thermal), or when KE converts to other forms (rising ball: KE → PE, collision: KE → thermal/sound/deformation); and (3) KE stays constant when no net work is done (balanced forces: F_net=0 so no acceleration, speed constant means KE constant), or when motion is perpendicular to force (satellite orbit: gravity pulls inward perpendicular to velocity, no work, KE unchanged). A sliding book initially moving quickly (KE_initial = ½mv₀² where v₀ is initial speed) gradually slows due to friction and stops (KE_final = 0), losing all its kinetic energy—this KE decrease occurs because friction does negative work: friction force acts backward (opposite to book's forward motion), and as book slides distance d forward, friction does work W = -f×d (negative because force opposes displacement), removing kinetic energy which converts to thermal energy (floor and book warm microscopically from friction). The work-energy theorem explains: W_friction = ΔKE = 0 - ½mv₀² = -½mv₀² (negative work equals negative KE change), and conservation requires: lost KE (½mv₀²) = thermal energy gained (floor + book warmer by ½mv₀² total), so KE didn't disappear, it converted to thermal through friction's negative work. Choice B is correct because it correctly cites negative work and energy conversion: friction acts opposite the motion, so it does negative work and converts some of the book's kinetic energy into thermal energy. Choice A reverses work direction by claiming friction acts in same direction as motion and does positive work, when friction always opposes motion and does negative work; choice C nonsensically states KE converts into more KE; choice D falsely claims mass becomes smaller, when book's mass remains constant throughout sliding. Explaining KE changes systematically: (1) observe motion: speeding up (KE increasing), slowing down (KE decreasing), or constant speed (KE constant), (2) identify forces: what forces act? in what directions relative to motion?, (3) determine net work: forces in motion direction do positive work (add KE), forces opposing motion do negative work (remove KE), perpendicular forces do zero work (don't change KE), balanced forces: W_net=0 (KE constant), (4) apply work-energy: W_net = ΔKE (work equals energy change), (5) check energy conversions: if work doesn't fully explain, look for conversions (PE ↔ KE, chemical → KE, KE → thermal), and (6) verify conservation: energy source for KE increase? (work input, PE decreasing, chemical burning), energy destination for KE decrease? (work output, PE increasing, thermal from friction)—all energy accounted. Understanding causes of KE changes helps: predict motion (if force forward, object will speed up increasing KE), explain energy (where did KE come from? work or conversion; where did it go? work or conversion), design systems (want high KE? apply large force over distance doing lots of work; want to reduce KE? use friction or convert to other form), and reason about safety (high-speed objects have large KE requiring large work/distance to stop—why speed limits matter, why braking distances long at high speeds).
- A car starts from rest at a stoplight (v=0), then the driver presses the gas and the car speeds up to 20 m/s on a straight, level road. The car's mass stays the same. Why does the car's kinetic energy increase during this time?
Answer: Because the engine provides a forward force that does positive work on the car, increasing its speed and therefore its kinetic energy.
This question tests understanding of what causes kinetic energy to change—specifically, that work done by forces or energy conversions cause KE to increase, decrease, or remain constant. Kinetic energy changes are governed by the work-energy relationship and energy conservation: (1) KE increases when positive work is done (force in direction of motion: engine accelerating car, force forward while car moves forward, does positive work increasing KE from 0 to ½mv²), or when other energy converts to KE (falling object: PE → KE, chemical from fuel → KE in engine); (2) KE decreases when negative work is done (force opposite to motion: friction on sliding object, force backward while object moves forward, does negative work removing KE and converting to thermal), or when KE converts to other forms (rising ball: KE → PE, collision: KE → thermal/sound/deformation); and (3) KE stays constant when no net work is done (balanced forces: F_net=0 so no acceleration, speed constant means KE constant), or when motion is perpendicular to force (satellite orbit: gravity pulls inward perpendicular to velocity, no work, KE unchanged). When a car accelerates from rest to 20 m/s, kinetic energy increases from KE_initial = 0 (at rest, v=0) to KE_final = ½m(20²) = 200m J (where m is car mass)—this KE increase results from the engine doing positive work on the car: the engine applies forward force (thousands of Newtons from drivetrain), car moves forward (distance traveled while accelerating, perhaps 100 m), and work = force × distance in the direction of force is positive (force and displacement in same direction), with this work equal to the KE gained (work-energy theorem: W = ΔKE = 200m J). Choice A is correct because it accurately explains KE increase using positive work: the engine provides forward force that does positive work (force and motion in same direction), increasing the car's speed and therefore its kinetic energy. Choice B is wrong because it claims no forces act on the car, contradicting the obvious fact that acceleration requires net force (F=ma); choice C incorrectly states friction does positive work when road friction actually acts forward but doesn't do work on the car (it's the static friction that allows wheels to push, but engine does the work); choice D falsely claims mass increases, when car mass remains constant throughout acceleration. Explaining KE changes systematically: (1) observe motion: speeding up (KE increasing), slowing down (KE decreasing), or constant speed (KE constant), (2) identify forces: what forces act? in what directions relative to motion?, (3) determine net work: forces in motion direction do positive work (add KE), forces opposing motion do negative work (remove KE), perpendicular forces do zero work (don't change KE), balanced forces: W_net=0 (KE constant), (4) apply work-energy: W_net = ΔKE (work equals energy change), (5) check energy conversions: if work doesn't fully explain, look for conversions (PE ↔ KE, chemical → KE, KE → thermal), and (6) verify conservation: energy source for KE increase? (work input, PE decreasing, chemical burning), energy destination for KE decrease? (work output, PE increasing, thermal from friction)—all energy accounted. Understanding causes of KE changes helps: predict motion (if force forward, object will speed up increasing KE), explain energy (where did KE come from? work or conversion; where did it go? work or conversion), design systems (want high KE? apply large force over distance doing lots of work; want to reduce KE? use friction or convert to other form), and reason about safety (high-speed objects have large KE requiring large work/distance to stop—why speed limits matter, why braking distances long at high speeds).
- A hockey puck glides across smooth ice at a steady speed of 10 m/s in a straight line for several seconds. Its mass stays constant. What best explains why the puck's kinetic energy stays constant during this time?
Answer: The puck's kinetic energy stays constant because there is (approximately) no net force doing work on it, so its speed stays constant.
This question tests understanding of what causes kinetic energy to change—specifically, that work done by forces or energy conversions cause KE to increase, decrease, or remain constant. Kinetic energy changes are governed by the work-energy relationship and energy conservation: (1) KE increases when positive work is done (force in direction of motion: engine accelerating car, force forward while car moves forward, does positive work increasing KE from 0 to ½mv²), or when other energy converts to KE (falling object: PE → KE, chemical from fuel → KE in engine); (2) KE decreases when negative work is done (force opposite to motion: friction on sliding object, force backward while object moves forward, does negative work removing KE and converting to thermal), or when KE converts to other forms (rising ball: KE → PE, collision: KE → thermal/sound/deformation); and (3) KE stays constant when no net work is done (balanced forces: F_net=0 so no acceleration, speed constant means KE constant), or when motion is perpendicular to force (satellite orbit: gravity pulls inward perpendicular to velocity, no work, KE unchanged). A hockey puck gliding at constant 10 m/s on smooth ice has constant kinetic energy KE = ½m(10²) = 50m J throughout—KE doesn't change because speed doesn't change (constant v means constant v² means constant ½mv²), and speed stays constant because net force is approximately zero: on smooth ice, friction is negligible, gravity balanced by normal force (perpendicular to motion, do no work), so no horizontal forces means F_net ≈ 0, no acceleration (a=0 from F=ma with F=0), meaning velocity constant (no Δv), meaning KE constant (no ΔKE). The work-energy perspective: net work equals approximately zero (no significant forces doing work along motion direction: W_net ≈ 0), so no net work means no KE change (W_net = ΔKE ≈ 0), explaining constant energy with essentially no forces acting horizontally (Newton's First Law: object in motion stays in motion at constant velocity when F_net = 0). Choice A is correct because it properly identifies zero net work for constant KE: the puck's kinetic energy stays constant because there is (approximately) no net force doing work on it, so its speed stays constant. Choice B incorrectly claims friction is constantly adding energy, when smooth ice has negligible friction and any small friction would remove energy, not add it; choice C contradicts itself by claiming KE stays constant while speed increases, violating KE = ½mv² (if v increases, KE must increase); choice D falsely states gravity increases speed on level ice, when gravity acts vertically (perpendicular to horizontal motion) doing no work. Explaining KE changes systematically: (1) observe motion: speeding up (KE increasing), slowing down (KE decreasing), or constant speed (KE constant), (2) identify forces: what forces act? in what directions relative to motion?, (3) determine net work: forces in motion direction do positive work (add KE), forces opposing motion do negative work (remove KE), perpendicular forces do zero work (don't change KE), balanced forces: W_net=0 (KE constant), (4) apply work-energy: W_net = ΔKE (work equals energy change), (5) check energy conversions: if work doesn't fully explain, look for conversions (PE ↔ KE, chemical → KE, KE → thermal), and (6) verify conservation: energy source for KE increase? (work input, PE decreasing, chemical burning), energy destination for KE decrease? (work output, PE increasing, thermal from friction)—all energy accounted. Common scenarios: (1) free fall: KE increases (PE → KE, gravity does positive work accelerating downward), (2) thrown upward: KE decreases then increases (KE → PE going up as gravity does negative work, PE → KE coming down as gravity does positive work), (3) braking: KE decreases (friction does negative work, KE → thermal in brakes), (4) horizontal surface no friction: KE constant (no forces doing work, speed constant by Newton's First Law), (5) engine accelerating: KE increases (chemical energy → thermal → mechanical work → KE, engine does positive work).
- A book is pushed across a table at first, then the student stops pushing. After that, the book keeps sliding but slows down and stops. Which statement best connects the forces to the change in kinetic energy after the student stops pushing?
Answer: The net force is opposite the motion (friction), so the net work is negative and the book's kinetic energy decreases.
This question tests understanding of what causes kinetic energy to change—specifically, that work done by forces or energy conversions cause KE to increase, decrease, or remain constant. Kinetic energy changes are governed by the work-energy relationship and energy conservation: (1) KE increases when positive work is done (force in direction of motion: engine accelerating car, force forward while car moves forward, does positive work increasing KE from 0 to ½mv²), or when other energy converts to KE (falling object: PE → KE, chemical from fuel → KE in engine); (2) KE decreases when negative work is done (force opposite to motion: friction on sliding object, force backward while object moves forward, does negative work removing KE and converting to thermal), or when KE converts to other forms (rising ball: KE → PE, collision: KE → thermal/sound/deformation); and (3) KE stays constant when no net work is done (balanced forces: F_net=0 so no acceleration, speed constant means KE constant), or when motion is perpendicular to force (satellite orbit: gravity pulls inward perpendicular to velocity, no work, KE unchanged). After the student stops pushing, the book slows from initial speed to stop (KE decreases from ½mv² to 0)—this KE decrease occurs because friction does negative work: friction force acts backward (opposite to book's forward motion), and as book slides distance d forward, friction does work W = -f×d (negative because force opposes displacement), removing kinetic energy which converts to thermal energy (table and book warm from friction). The work-energy theorem explains: W_net = W_friction = ΔKE = 0 - ½mv² = -½mv² (negative net work equals negative KE change, since no other horizontal forces after pushing stops), and conservation requires: lost KE (½mv²) = thermal energy gained, so KE converts to thermal through friction's negative work. Choice A is correct because it correctly cites negative work or energy conversion from KE for KE decrease, connecting net force (friction opposite motion) to negative net work and KE decrease. Choice C is wrong because it reverses work direction: claims friction does positive work increasing KE, when friction does negative work decreasing KE (force opposes motion). Explaining KE changes systematically: (1) observe motion: speeding up (KE increasing), slowing down (KE decreasing), or constant speed (KE constant), (2) identify forces: what forces act? in what directions relative to motion?, (3) determine net work: forces in motion direction do positive work (add KE), forces opposing motion do negative work (remove KE), perpendicular forces do zero work (don't change KE), balanced forces: W_net=0 (KE constant), (4) apply work-energy: W_net = ΔKE (work equals energy change), (5) check energy conversions: if work doesn't fully explain, look for conversions (PE ↔ KE, chemical → KE, KE → thermal), and (6) verify conservation: energy source for KE increase? (work input, PE decreasing, chemical burning), energy destination for KE decrease? (work output, PE increasing, thermal from friction)—all energy accounted. Common scenarios: (1) free fall: KE increases (PE → KE, gravity does positive work accelerating downward), (2) thrown upward: KE decreases then increases (KE → PE going up as gravity does negative work, PE → KE coming down as gravity does positive work), (3) braking: KE decreases (friction does negative work, KE → thermal in brakes), (4) horizontal surface no friction: KE constant (no forces doing work, speed constant by Newton's First Law), (5) engine accelerating: KE increases (chemical energy → thermal → mechanical work → KE, engine does positive work).
- A moving toy car hits a soft pillow and comes to a stop. Compared with just before the collision, what happens to the toy car's kinetic energy, and where does most of it go?
Answer: It decreases, mostly converting into thermal energy, sound, and deformation of the pillow and car.
This question tests understanding of what causes kinetic energy to change—specifically, that work done by forces or energy conversions cause KE to increase, decrease, or remain constant. Kinetic energy changes are governed by the work-energy relationship and energy conservation: (1) KE increases when positive work is done (force in direction of motion: engine accelerating car, force forward while car moves forward, does positive work increasing KE from 0 to ½mv²), or when other energy converts to KE (falling object: PE → KE, chemical from fuel → KE in engine); (2) KE decreases when negative work is done (force opposite to motion: friction on sliding object, force backward while object moves forward, does negative work removing KE and converting to thermal), or when KE converts to other forms (rising ball: KE → PE, collision: KE → thermal/sound/deformation); and (3) KE stays constant when no net work is done (balanced forces: F_net=0 so no acceleration, speed constant means KE constant), or when motion is perpendicular to force (satellite orbit: gravity pulls inward perpendicular to velocity, no work, KE unchanged). For a toy car hitting a soft pillow and stopping, KE decreases from ½mv² (pre-collision) to 0 (post-collision)—this KE decrease occurs because during collision, contact forces do negative work: pillow pushes back opposite to car's motion, removing KE, which converts mostly to thermal energy (heating from deformation), sound (impact noise), and deformation (pillow compresses, some elastic PE but mostly dissipated). Conservation requires: lost KE = thermal + sound + deformation energy gained, so KE didn't disappear but transformed through the collision's negative work on the car. Choice C is correct because it correctly cites energy conversion from KE for KE decrease, identifying where energy goes (thermal, sound, deformation). Choice A is wrong because it violates conservation: claims KE stays the same during collision, but car stops (v=0, KE=0), so KE decreases, energy conserved by converting to other forms, not staying as KE. Explaining KE changes systematically: (1) observe motion: speeding up (KE increasing), slowing down (KE decreasing), or constant speed (KE constant), (2) identify forces: what forces act? in what directions relative to motion?, (3) determine net work: forces in motion direction do positive work (add KE), forces opposing motion do negative work (remove KE), perpendicular forces do zero work (don't change KE), balanced forces: W_net=0 (KE constant), (4) apply work-energy: W_net = ΔKE (work equals energy change), (5) check energy conversions: if work doesn't fully explain, look for conversions (PE ↔ KE, chemical → KE, KE → thermal), and (6) verify conservation: energy source for KE increase? (work input, PE decreasing, chemical burning), energy destination for KE decrease? (work output, PE increasing, thermal from friction)—all energy accounted. Common scenarios: (1) free fall: KE increases (PE → KE, gravity does positive work accelerating downward), (2) thrown upward: KE decreases then increases (KE → PE going up as gravity does negative work, PE → KE coming down as gravity does positive work), (3) braking: KE decreases (friction does negative work, KE → thermal in brakes), (4) horizontal surface no friction: KE constant (no forces doing work, speed constant by Newton's First Law), (5) engine accelerating: KE increases (chemical energy → thermal → mechanical work → KE, engine does positive work).
- A runner is moving forward, then applies the brakes by planting their foot and slowing to a stop. During the slowing-down part, what happens to the runner's kinetic energy, and why?
Answer: It decreases because forces from the ground and friction oppose the motion, doing negative work and converting kinetic energy into other forms like thermal energy.
This question tests understanding of what causes kinetic energy to change—specifically, that work done by forces or energy conversions cause KE to increase, decrease, or remain constant. Kinetic energy changes are governed by the work-energy relationship and energy conservation: (1) KE increases when positive work is done (force in direction of motion: engine accelerating car, force forward while car moves forward, does positive work increasing KE from 0 to ½mv²), or when other energy converts to KE (falling object: PE → KE, chemical from fuel → KE in engine); (2) KE decreases when negative work is done (force opposite to motion: friction on sliding object, force backward while object moves forward, does negative work removing KE and converting to thermal), or when KE converts to other forms (rising ball: KE → PE, collision: KE → thermal/sound/deformation); and (3) KE stays constant when no net work is done (balanced forces: F_net=0 so no acceleration, speed constant means KE constant), or when motion is perpendicular to force (satellite orbit: gravity pulls inward perpendicular to velocity, no work, KE unchanged). For KE decreasing: As the runner slows from say 5 m/s (KE_initial = ½m(5²) = 12.5m J) to 0 m/s (KE_final = 0), losing KE—this decrease occurs because friction from the ground acts backward (opposite to forward motion), doing negative work: friction force opposes displacement, W = -f d, removing KE which converts to thermal energy (heat in shoes/ground) or sound. Choice B is correct because it correctly cites negative work or energy conversion from KE for KE decrease. Choice D is wrong because it misidentifies energy conversion: claims KE turns to PE on level ground, but on level ground PE doesn't change (height constant), instead KE goes to thermal. Explaining KE changes systematically: (1) observe motion: speeding up (KE increasing), slowing down (KE decreasing), or constant speed (KE constant), (2) identify forces: what forces act? in what directions relative to motion?, (3) determine net work: forces in motion direction do positive work (add KE), forces opposing motion do negative work (remove KE), perpendicular forces do zero work (don't change KE), balanced forces: W_net=0 (KE constant), (4) apply work-energy: W_net = ΔKE (work equals energy change), (5) check energy conversions: if work doesn't fully explain, look for conversions (PE ↔ KE, chemical → KE, KE → thermal), and (6) verify conservation: energy source for KE increase? (work input, PE decreasing, chemical burning), energy destination for KE decrease? (work output, PE increasing, thermal from friction)—all energy accounted. Common scenarios: (1) free fall: KE increases (PE → KE, gravity does positive work accelerating downward), (2) thrown upward: KE decreases then increases (KE → PE going up as gravity does negative work, PE → KE coming down as gravity does positive work), (3) braking: KE decreases (friction does negative work, KE → thermal in brakes), (4) horizontal surface no friction: KE constant (no forces doing work, speed constant by Newton's First Law), (5) engine accelerating: KE increases (chemical energy → thermal → mechanical work → KE, engine does positive work).
- A rubber ball rolls quickly into a thick pillow and comes to a stop. After the collision, the ball is not moving. What is the best explanation for what happened to the ball's kinetic energy?
Answer: The ball's kinetic energy decreased because some of it was converted into other forms of energy like sound, thermal energy, and deformation during the inelastic collision.
This question tests understanding of what causes kinetic energy to change—specifically, that work done by forces or energy conversions cause KE to increase, decrease, or remain constant. Kinetic energy changes are governed by the work-energy relationship and energy conservation: (1) KE increases when positive work is done (force in direction of motion: engine accelerating car, force forward while car moves forward, does positive work increasing KE from 0 to ½mv²), or when other energy converts to KE (falling object: PE → KE, chemical from fuel → KE in engine); (2) KE decreases when negative work is done (force opposite to motion: friction on sliding object, force backward while object moves forward, does negative work removing KE and converting to thermal), or when KE converts to other forms (rising ball: KE → PE, collision: KE → thermal/sound/deformation); and (3) KE stays constant when no net work is done (balanced forces: F_net=0 so no acceleration, speed constant means KE constant), or when motion is perpendicular to force (satellite orbit: gravity pulls inward perpendicular to velocity, no work, KE unchanged). A rubber ball rolling into a pillow and stopping loses all its kinetic energy from KE_initial = ½mv² to KE_final = 0—this KE decrease occurs during the inelastic collision where kinetic energy converts to other forms: the pillow does negative work on the ball (pillow pushes backward on ball while ball moves forward into it), and this work removes KE which transforms into (1) thermal energy (ball and pillow molecules vibrate more, warming slightly), (2) sound energy (thud of impact), and (3) deformation energy (pillow compresses, ball deforms temporarily). Conservation of energy requires: initial KE = thermal + sound + deformation + any remaining KE, but since ball stops, all initial KE converted to other forms (no KE remains), explaining complete energy transformation during collision. Choice C is correct because it properly identifies energy conversion during collision: the ball's kinetic energy decreased because some of it was converted into other forms of energy like sound, thermal energy, and deformation during the inelastic collision. Choice A incorrectly claims KE stayed same but was hidden in pillow, violating the definition of KE = ½mv² (stopped ball has v=0, so KE=0); choice B wrongly states KE increased when ball clearly stopped (KE went to zero); choice D falsely claims mass became zero, when ball's mass remains constant (only velocity became zero). Explaining KE changes systematically: (1) observe motion: speeding up (KE increasing), slowing down (KE decreasing), or constant speed (KE constant), (2) identify forces: what forces act? in what directions relative to motion?, (3) determine net work: forces in motion direction do positive work (add KE), forces opposing motion do negative work (remove KE), perpendicular forces do zero work (don't change KE), balanced forces: W_net=0 (KE constant), (4) apply work-energy: W_net = ΔKE (work equals energy change), (5) check energy conversions: if work doesn't fully explain, look for conversions (PE ↔ KE, chemical → KE, KE → thermal), and (6) verify conservation: energy source for KE increase? (work input, PE decreasing, chemical burning), energy destination for KE decrease? (work output, PE increasing, thermal from friction)—all energy accounted. Common scenarios: (1) free fall: KE increases (PE → KE, gravity does positive work accelerating downward), (2) thrown upward: KE decreases then increases (KE → PE going up as gravity does negative work, PE → KE coming down as gravity does positive work), (3) braking: KE decreases (friction does negative work, KE → thermal in brakes), (4) horizontal surface no friction: KE constant (no forces doing work, speed constant by Newton's First Law), (5) engine accelerating: KE increases (chemical energy → thermal → mechanical work → KE, engine does positive work).
- A bicycle rolls at a steady 10 m/s along a straight, level path. The rider keeps the speed constant for several seconds. What happens to the bicycle's kinetic energy during this time, and why?
Answer: It stays constant because the speed is constant, so KE=21mv2 does not change and the net work is zero.
This question tests understanding of what causes kinetic energy to change—specifically, that work done by forces or energy conversions cause KE to increase, decrease, or remain constant. Kinetic energy changes are governed by the work-energy relationship and energy conservation: (1) KE increases when positive work is done (force in direction of motion: engine accelerating car, force forward while car moves forward, does positive work increasing KE from 0 to ½mv²), or when other energy converts to KE (falling object: PE → KE, chemical from fuel → KE in engine); (2) KE decreases when negative work is done (force opposite to motion: friction on sliding object, force backward while object moves forward, does negative work removing KE and converting to thermal), or when KE converts to other forms (rising ball: KE → PE, collision: KE → thermal/sound/deformation); and (3) KE stays constant when no net work is done (balanced forces: F_net=0 so no acceleration, speed constant means KE constant), or when motion is perpendicular to force (satellite orbit: gravity pulls inward perpendicular to velocity, no work, KE unchanged). For KE constant: A bicycle rolling at constant 10 m/s on a level path has constant kinetic energy KE = ½m(10²) = 50m J throughout—KE doesn't change because speed doesn't change (constant v means constant v² means constant ½mv²), and speed stays constant because net force is zero: pedaling force forward (if any) exactly balances air resistance and rolling friction backward (balanced forces: F_net = 0), so no acceleration (a=0 from F=ma with F=0), meaning velocity constant (no Δv), meaning KE constant (no ΔKE). Choice B is correct because it properly identifies zero net work or balanced forces for constant KE. Choice A is wrong because it suggests KE decreases when object slows down, but here speed is constant, so KE is constant by definition. Explaining KE changes systematically: (1) observe motion: speeding up (KE increasing), slowing down (KE decreasing), or constant speed (KE constant), (2) identify forces: what forces act? in what directions relative to motion?, (3) determine net work: forces in motion direction do positive work (add KE), forces opposing motion do negative work (remove KE), perpendicular forces do zero work (don't change KE), balanced forces: W_net=0 (KE constant), (4) apply work-energy: W_net = ΔKE (work equals energy change), (5) check energy conversions: if work doesn't fully explain, look for conversions (PE ↔ KE, chemical → KE, KE → thermal), and (6) verify conservation: energy source for KE increase? (work input, PE decreasing, chemical burning), energy destination for KE decrease? (work output, PE increasing, thermal from friction)—all energy accounted. Common scenarios: (1) free fall: KE increases (PE → KE, gravity does positive work accelerating downward), (2) thrown upward: KE decreases then increases (KE → PE going up as gravity does negative work, PE → KE coming down as gravity does positive work), (3) braking: KE decreases (friction does negative work, KE → thermal in brakes), (4) horizontal surface no friction: KE constant (no forces doing work, speed constant by Newton's First Law), (5) engine accelerating: KE increases (chemical energy → thermal → mechanical work → KE, engine does positive work). - A ball is thrown straight upward. Right after it leaves the hand, it is moving fast upward. As it rises, it slows down until, at the very top of its path, its speed is momentarily zero. What causes the ball's kinetic energy to decrease while it is rising?
Answer: Gravity acts opposite the ball's motion on the way up and does negative work, converting kinetic energy into gravitational potential energy.
This question tests understanding of what causes kinetic energy to change—specifically, that work done by forces or energy conversions cause KE to increase, decrease, or remain constant. Kinetic energy changes are governed by the work-energy relationship and energy conservation: (1) KE increases when positive work is done (force in direction of motion: engine accelerating car, force forward while car moves forward, does positive work increasing KE from 0 to ½mv²), or when other energy converts to KE (falling object: PE → KE, chemical from fuel → KE in engine); (2) KE decreases when negative work is done (force opposite to motion: friction on sliding object, force backward while object moves forward, does negative work removing KE and converting to thermal), or when KE converts to other forms (rising ball: KE → PE, collision: KE → thermal/sound/deformation); and (3) KE stays constant when no net work is done (balanced forces: F_net=0 so no acceleration, speed constant means KE constant), or when motion is perpendicular to force (satellite orbit: gravity pulls inward perpendicular to velocity, no work, KE unchanged). A ball thrown upward initially has kinetic energy KE_initial = ½mv² (where v is initial upward speed), but as it rises this KE decreases to KE_top = 0 at the peak (momentarily at rest, v=0)—this KE decrease occurs because gravity does negative work: gravity pulls downward while ball moves upward (force and displacement in opposite directions), so work W = F·d·cos(180°) = -mgd (negative because cos(180°) = -1), removing kinetic energy which converts to gravitational potential energy (ball gains height h, so PE increases by mgh). The work-energy theorem explains: W_gravity = ΔKE = 0 - ½mv² = -½mv² (negative work equals negative KE change), and conservation requires: lost KE (½mv²) = gained PE (mgh), where h is maximum height reached when all KE converts to PE, so KE didn't disappear, it converted to PE through gravity's negative work. Choice B is correct because it accurately explains KE decrease using negative work and energy conversion: gravity acts opposite the ball's upward motion (force down, motion up) and does negative work, correctly identifying that this converts kinetic energy into gravitational potential energy—this properly connects cause (gravity doing negative work) to effect (KE → PE conversion). Choice A reverses work direction: claims gravity does positive work as ball rises, when gravity (downward) opposing upward motion must do negative work; Choice C suggests mass decreases as ball rises, which is false—ball's mass stays constant; Choice D claims no forces act after leaving hand, ignoring gravity which acts throughout the motion. Explaining KE changes systematically: (1) observe motion: ball slowing while rising (KE decreasing), (2) identify forces: only gravity acts (downward) after release, air resistance negligible, (3) determine net work: gravity downward while motion upward means negative work, (4) apply work-energy: W_gravity = -mgd = ΔKE < 0 (negative work removes KE), (5) check energy conversions: KE → PE as ball rises (energy transforms but total E = KE + PE stays constant), and (6) verify conservation: initial KE becomes PE at peak, then PE → KE on way down—total mechanical energy conserved.
