Middle School Science Quiz: Systems Acting At Distance

20 questions · exam conditions

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Systems Acting At DistanceQuestion 1 of 20

A magnet attracts a steel paper clip from a distance of $5\,\text{cm}$ . The clip starts at rest, not touching the magnet, and then moves toward the magnet through the air gap. Which statement is correct about the work done by the magnetic force and the clip's energy?

The magnetic force does no work because the clip is not touching the magnet.

The magnetic force does positive work, so the clip's kinetic energy increases as it moves toward the magnet.

The magnetic force does negative work, so the clip's kinetic energy increases as it moves toward the magnet.

Only contact forces can change kinetic energy, so the clip's kinetic energy stays zero.

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Middle School Science Quiz

Middle School Science Quiz: Systems Acting At Distance

Practice Systems Acting At Distance in Middle School Science with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Systems Acting At Distance, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Science.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

The magnetic force does no work because the clip is not touching the magnet.
The magnetic force does positive work, so the clip's kinetic energy increases as it moves toward the magnet. (correct answer)
The magnetic force does negative work, so the clip's kinetic energy increases as it moves toward the magnet.
Only contact forces can change kinetic energy, so the clip's kinetic energy stays zero.

Explanation: This question tests understanding that non-contact forces (gravity, electric, magnetic) can do work over distances, changing potential energy even when objects aren't touching. Work is defined as force applied over distance (W = F×d, or W = mgh for lifting against gravity), and non-contact forces like gravity, electric forces, and magnetic forces can do work because they act across space without requiring contact: when you lift a book from floor to shelf, Earth's gravitational force (pulling downward at distance—book not touching Earth) acts over the 2 m height you lift through, and you do work W = mgh against this force, storing the work as gravitational potential energy (PE = mgh gained). When the magnet attracts the steel paper clip across the 5 cm air gap, the magnetic force pulls the clip toward the magnet, and since the clip moves in the direction of the magnetic force (both toward magnet), the magnetic force does positive work on the clip. This positive work by the magnetic force converts magnetic potential energy (stored in the separated configuration) into kinetic energy, causing the clip to accelerate from rest and gain speed as it approaches the magnet—demonstrating that magnetic fields can transmit force and do work across empty space without physical contact. Choice B is correct because it properly recognizes magnetic force does positive work (force and motion in same direction) which increases the clip's kinetic energy. Choice A incorrectly claims no work when the clip clearly moves through distance under magnetic force, Choice C incorrectly states negative work when force and motion are in same direction (both toward magnet), and Choice D falsely claims only contact forces can change KE when magnetic force clearly accelerates the clip across the gap. Work by non-contact forces demonstrates energy transfer without contact: gravitational force does work as objects rise or fall (lift: work against gravity → PE increases, fall: work by gravity → PE decreases, KE increases), electric forces do work as charges move in field (against force: PE increases, by force: PE decreases), and magnetic forces do work as magnets or magnetic materials move in magnetic fields (apart against attraction: PE increases, together by attraction: PE decreases)—all occurring across gaps without physical contact because fields extend through space allowing forces to act at distance.

Question 2

A $1\,\text{kg}$ object is lifted straight up at constant speed from $h=0\,\text{m}$ to $h=3\,\text{m}$ . Gravity pulls downward during the entire motion even though the object is not touching Earth. What is the work done by gravity on the object during the lift? (Use $g\approx 10\,\text{m/s}^2$ .)

$+30\,\text{J}$
$-30\,\text{J}$ (correct answer)
$0\,\text{J}$ because gravity is non-contact
$-3\,\text{J}$

Explanation: This question tests understanding that non-contact forces (gravity, electric, magnetic) can do work over distances, changing potential energy even when objects aren't touching. Work is defined as force applied over distance (W = F×d, or W = mgh for lifting against gravity), and non-contact forces like gravity, electric forces, and magnetic forces can do work because they act across space without requiring contact: when you lift a book from floor to shelf, Earth's gravitational force (pulling downward at distance—book not touching Earth) acts over the 2 m height you lift through, and you do work W = mgh against this force, storing the work as gravitational potential energy (PE = mgh gained). When a 1 kg object is lifted from h=0 to h=3 m, gravity exerts a downward force F = mg = 1×10 = 10 N throughout the motion, while the object moves upward 3 m (opposite to gravity's direction). Since force and displacement are in opposite directions (gravity pulls down, object moves up), gravity does negative work: W = -F×d = -10 N × 3 m = -30 J (or W = -mgh = -1×10×3 = -30 J). This negative work by gravity corresponds to the positive work (+30 J) done by the lifter against gravity, and represents the 30 J of energy transferred from the lifter to gravitational PE storage. Choice B is correct because it properly calculates gravity's negative work as W = -mgh = -30 J. Choice A (+30 J) has the wrong sign (that's the lifter's work, not gravity's), Choice C (0 J) incorrectly claims no work because of non-contact when gravity clearly acts over distance, and Choice D (-3 J) appears to forget the factor of g (using just -1×3). Work by non-contact forces demonstrates energy transfer without contact: gravitational force does work as objects rise or fall (lift: work against gravity → PE increases, fall: work by gravity → PE decreases, KE increases), electric forces do work as charges move in field (against force: PE increases, by force: PE decreases), and magnetic forces do work as magnets or magnetic materials move in magnetic fields (apart against attraction: PE increases, together by attraction: PE decreases)—all occurring across gaps without physical contact because fields extend through space allowing forces to act at distance.

Question 3

A student raises a $2\,\text{kg}$ box straight upward $2\,\text{m}$ at constant speed. Gravity pulls downward (non-contact). Which statement about the work done by gravity on the box during the lift is correct? (Use $g\approx 10\,\text{m/s}^2$ .)

Gravity does $+40\,\text{J}$ of work because the box moved upward.
Gravity does $-40\,\text{J}$ of work because the force is downward while the motion is upward. (correct answer)
Gravity does $0\,\text{J}$ of work because gravity is non-contact.
Gravity does $-20\,\text{J}$ of work because only mass matters, not distance.

Explanation: This question tests understanding that non-contact forces (gravity, electric, magnetic) can do work over distances, changing potential energy even when objects aren't touching. Work is defined as force applied over distance (W = F×d), and non-contact forces like gravity, electric forces, and magnetic forces can do work because they act across space without requiring contact: when you lift objects, Earth's gravitational force does work (negative work opposing the motion) even though the object never touches Earth. When lifting a 2 kg box upward 2 m at constant speed, gravitational force F = mg = 2×10 = 20 N points downward while displacement d = 2 m points upward (opposite directions), so gravity's work is W = F·d·cos(180°) = 20×2×(-1) = -40 J; the negative sign indicates gravity does negative work (opposes motion), which equals the negative of the work you do against gravity (+40 J), and represents the increase in gravitational PE. Choice B is correct because it accurately states gravity does -40 J of work, correctly recognizing that when force (downward) and displacement (upward) are opposite, work is negative: W = -mgh = -2×10×2 = -40 J. Choice A (+40 J) has wrong sign (gravity opposes upward motion, so does negative work), Choice C (0 J) incorrectly claims no work because gravity is non-contact (gravity clearly does work at distance), and Choice D (-20 J) calculates incorrectly (seems to forget height in W = mgh). Work by non-contact forces demonstrates energy transfer without contact: gravity does negative work during lifting (force opposes motion), which corresponds to the positive work you must do against gravity, storing energy as increased PE. Understanding work signs is crucial: gravity does negative work when objects move up against it (your positive work stores PE) and positive work when objects fall with it (gravity's positive work releases PE as KE).

Question 4

A $1.5\,\text{kg}$ ball is held at a height of $4\,\text{m}$ above the ground and then released. Gravity acts at a distance. About how much work does gravity do on the ball while it falls $4\,\text{m}$ ? (Use $g\approx 10\,\text{m/s}^2$ .)

$-60\,\text{J}$
$+6\,\text{J}$
$+60\,\text{J}$ (correct answer)
$+15\,\text{J}$

Explanation: This question tests understanding that non-contact forces (gravity, electric, magnetic) can do work over distances, changing potential energy even when objects aren't touching. Work is defined as force applied over distance (W = F×d, or W = mgh for gravity), and non-contact forces like gravity, electric forces, and magnetic forces can do work because they act across space without requiring contact: when objects fall, Earth's gravitational force (pulling downward at distance) acts over the distance fallen, and gravity does positive work W = mgh on the falling object. When a 1.5 kg ball falls 4 m, gravitational force (F = mg = 1.5×10 = 15 N pulling down) acts in the direction of motion (ball moving down), so gravity does positive work W = F×d = 15 N × 4 m = 60 J (or directly: W = mgh = 1.5×10×4 = 60 J); this positive work by gravity decreases gravitational PE by 60 J and increases kinetic energy by 60 J (ball speeds up), demonstrating that gravity's work converts PE to KE during the fall. Choice C is correct because it correctly calculates gravity's work as +60 J using W = mgh = 1.5×10×4 = 60 J, with positive sign because force and displacement are in same direction (both downward). Choice A (-60 J) has wrong sign (gravity does positive work when objects fall in its direction), Choice B (+6 J) calculates incorrectly (appears to forget factor of g), and Choice D (+15 J) seems to use just mg without multiplying by height. Work by non-contact forces demonstrates energy transfer without contact: gravitational force does positive work as objects fall (force and motion both downward), converting 60 J of gravitational PE to 60 J of KE without any contact between Earth and ball. Understanding that forces can do work at distance is essential: gravity continuously does work throughout the 4 m fall, transferring energy from the gravitational field (PE) to the ball's motion (KE).

Question 5

A student lifts the same $4\,\text{kg}$ backpack from the floor to two different shelves at constant speed. Shelf 1 is $1\,\text{m}$ high and Shelf 2 is $3\,\text{m}$ high. Gravity (a non-contact force) pulls downward. How does the work done against gravity compare for the two lifts?

The work is the same because the backpack's mass is the same.
The work to Shelf 2 is 3 times the work to Shelf 1 because the height is 3 times as large. (correct answer)
The work to Shelf 2 is $\tfrac{1}{3}$ the work to Shelf 1 because the backpack moves slower.
No work is done against gravity because gravity is non-contact.

Explanation: This question tests understanding that non-contact forces (gravity, electric, magnetic) can do work over distances, changing potential energy even when objects aren't touching. Work is defined as force applied over distance (W = F×d, or W = mgh for lifting against gravity), and non-contact forces like gravity, electric forces, and magnetic forces can do work because they act across space without requiring contact: when you lift objects to different heights, Earth's gravitational force (pulling downward at distance) acts over the height you lift through, and you do work W = mgh against this force, with work proportional to height. Lifting a 4 kg backpack from floor to Shelf 1 (1 m high) requires work W₁ = mgh₁ = 4×10×1 = 40 J against gravity, while lifting the same backpack to Shelf 2 (3 m high) requires work W₂ = mgh₂ = 4×10×3 = 120 J; comparing these: W₂/W₁ = 120/40 = 3, so the work to Shelf 2 is exactly 3 times the work to Shelf 1 because height is 3 times larger (work is directly proportional to height for same mass). Choice B is correct because it accurately states that work to Shelf 2 is 3 times work to Shelf 1 due to the 3× height difference, recognizing that work against gravity W = mgh is directly proportional to height. Choice A incorrectly claims work is the same (ignoring height difference), Choice C wrongly suggests less work for greater height (speed doesn't affect work calculation, only force and distance matter), and Choice D incorrectly states no work is done against gravity (gravity clearly does negative work as object rises, requiring positive work input). Work by non-contact forces demonstrates energy transfer without contact: gravitational force acts at distance throughout both lifts, and the work done (40 J vs 120 J) is stored as gravitational potential energy at each height. Understanding that forces can do work at distance is essential: the 3× height requires 3× work against the same gravitational force, demonstrating that work depends on distance moved against the force, not on contact between objects.

Question 6

A ball is released from rest and falls straight down $5\,\text{m}$ (no contact with Earth; gravity acts at a distance). Ignoring air resistance, which statement best describes the energy change as the ball falls?

Gravitational potential energy decreases and kinetic energy increases. (correct answer)
Gravitational potential energy increases and kinetic energy decreases.
Both gravitational potential energy and kinetic energy increase.
No work is done because the ball is not touching Earth.

Explanation: This question tests understanding that non-contact forces (gravity, electric, magnetic) can do work over distances, changing potential energy even when objects aren't touching. Work is defined as force applied over distance (W = F×d, or W = mgh for lifting against gravity), and non-contact forces like gravity, electric forces, and magnetic forces can do work because they act across space without requiring contact: when a ball falls, Earth's gravitational force (pulling downward at distance—ball not touching Earth) acts over the 5 m height it falls through, and gravity does work W = mgh on the ball, converting gravitational potential energy to kinetic energy. When the ball falls from rest down 5 m, gravitational force (pulling down) acts in the direction of motion (ball moving down), so gravity does positive work W = mgh (force and displacement in same direction: both downward); this positive work by gravity decreases gravitational PE (PE drops by mgh as height decreases) and increases kinetic energy (KE increases from 0 to mgh as ball speeds up during fall), demonstrating work-energy theorem: work done by gravity equals KE gained, and showing that PE is released as KE through gravity's work over the 5 m distance. Choice A is correct because it accurately explains that gravitational potential energy decreases (ball loses height, PE = mgh decreases) and kinetic energy increases (ball speeds up from rest, gaining KE) as gravity does positive work during the fall. Choice B reverses the energy changes (PE can't increase while falling), Choice C claims both energies increase (violates conservation—total mechanical energy stays constant), and Choice D incorrectly states no work is done because the ball isn't touching Earth (gravity clearly does work at a distance, as proven by the ball's acceleration and energy changes). Work by non-contact forces demonstrates energy transfer without contact: gravitational force does work as objects rise or fall (lift: work against gravity → PE increases, fall: work by gravity → PE decreases, KE increases), occurring across gaps without physical contact because gravity's field extends through space allowing force to act at distance. Understanding that forces can do work at distance is essential: as the ball falls 5 m, gravity continuously does work converting PE to KE, demonstrating that non-contact forces can transfer energy just as effectively as contact forces.

Question 7

Two bar magnets are held $20\,\text{cm}$ apart with opposite poles facing, so they attract across a visible air gap (no touching). When magnet B is released, it moves toward magnet A and speeds up. Which statement is correct about work and energy?

The magnetic force does work on magnet B, so magnetic potential energy decreases and kinetic energy increases. (correct answer)
No work is done because magnets must touch to pull each other.
The magnetic force does negative work, so kinetic energy decreases as they get closer.
Magnetic potential energy increases as the magnets move closer together.

Explanation: This question tests understanding that non-contact forces (gravity, electric, magnetic) can do work over distances, changing potential energy even when objects aren't touching. Work is defined as force applied over distance (W = F×d), and non-contact forces like gravity, electric forces, and magnetic forces can do work because they act across space without requiring contact: when opposite magnetic poles attract across a gap, the magnetic force can do work on moving magnets, converting magnetic potential energy to kinetic energy as they approach. When magnet B is released and moves toward magnet A due to magnetic attraction, the magnetic force (pulling B toward A) acts in the direction of motion (B moving toward A), so the magnetic force does positive work on magnet B; this positive work by the magnetic force decreases magnetic PE (magnets closer together have less magnetic PE when attracting) and increases kinetic energy (magnet B speeds up), demonstrating work-energy theorem: work done by magnetic force equals KE gained, showing that magnetic PE is released as KE through the magnetic force's work over the distance. Choice A is correct because it accurately states that the magnetic force does work on magnet B (force and motion in same direction), magnetic potential energy decreases (attracting magnets have less PE when closer), and kinetic energy increases (magnet speeds up). Choice B incorrectly claims magnets must touch to pull each other (magnetic forces clearly act at distance through fields), Choice C wrongly states negative work (force and motion are in same direction, so work is positive), and Choice D incorrectly claims PE increases (PE decreases when attracting objects move together). Work by non-contact forces demonstrates energy transfer without contact: magnetic forces do work as magnets move in fields (apart against attraction: PE increases, together by attraction: PE decreases converting to KE), all occurring across gaps without physical contact because magnetic fields extend through space. Understanding that forces can do work at distance is essential: as magnet B approaches A, the magnetic force continuously does positive work converting magnetic PE to KE, proving non-contact forces transfer energy effectively across gaps.

Question 8

A satellite moves in an elliptical orbit around Earth. Gravity (a non-contact force) always pulls the satellite toward Earth. When the satellite moves closer to Earth, it speeds up. What best explains this change in speed in terms of work and energy?

Gravity does work on the satellite as it moves inward, decreasing gravitational potential energy and increasing kinetic energy. (correct answer)
The satellite speeds up because its mass increases closer to Earth.
No work is done because space is empty, so energy cannot change.
Gravity does work that increases gravitational potential energy and decreases kinetic energy.

Explanation: This question tests understanding that non-contact forces (gravity, electric, magnetic) can do work over distances, changing potential energy even when objects aren't touching. Work is defined as force applied over distance (W = F×d, or W = mgh for lifting against gravity), and non-contact forces like gravity, electric forces, and magnetic forces can do work because they act across space without requiring contact: when you lift a book from floor to shelf, Earth's gravitational force (pulling downward at distance—book not touching Earth) acts over the 2 m height you lift through, and you do work W = mgh against this force, storing the work as gravitational potential energy (PE = mgh gained). When a satellite in elliptical orbit moves closer to Earth, gravitational force (always pointing toward Earth's center) has a component in the direction of motion (satellite moving inward), so gravity does positive work on the satellite. This positive work by gravity decreases gravitational PE (satellite loses height/distance from Earth) and, by conservation of energy, increases kinetic energy (satellite speeds up), demonstrating the continuous exchange between PE and KE in orbital motion—all occurring across the vacuum of space without any contact, proving that gravitational fields transmit force and energy across empty space. Choice A is correct because it properly recognizes gravity does positive work when satellite moves inward (force component along motion), decreasing PE and increasing KE to conserve total energy. Choice B incorrectly attributes speed change to mass increase (mass is constant), Choice C claims no work in empty space when gravity clearly acts through vacuum, and Choice D reverses the energy changes (PE decreases, not increases, when moving closer). Work by non-contact forces demonstrates energy transfer without contact: gravitational force does work as objects rise or fall (lift: work against gravity → PE increases, fall: work by gravity → PE decreases, KE increases), electric forces do work as charges move in field (against force: PE increases, by force: PE decreases), and magnetic forces do work as magnets or magnetic materials move in magnetic fields (apart against attraction: PE increases, together by attraction: PE decreases)—all occurring across gaps without physical contact because fields extend through space allowing forces to act at distance.

Question 9

Magnet A is held fixed on a table. Magnet B is placed $20\,\text{cm}$ away and then released so it can slide toward Magnet A. The magnets do not touch at first; there is a visible gap between them. As Magnet B moves toward Magnet A, which statement best describes the work done and the energy change?

Magnetic force does negative work, so magnetic potential energy increases and Magnet B slows down.
Magnetic force does positive work, so magnetic potential energy decreases and Magnet B speeds up. (correct answer)
No work is done because magnets are not touching, so energy cannot change.
Gravity does the work, so gravitational potential energy decreases as the magnets move closer.

Explanation: This question tests understanding that non-contact forces (gravity, electric, magnetic) can do work over distances, changing potential energy even when objects aren't touching. Work is defined as force applied over distance (W = F×d, or W = mgh for lifting against gravity), and non-contact forces like gravity, electric forces, and magnetic forces can do work because they act across space without requiring contact: when you lift a book from floor to shelf, Earth's gravitational force (pulling downward at distance—book not touching Earth) acts over the 2 m height you lift through, and you do work W = mgh against this force, storing the work as gravitational potential energy (PE = mgh gained). When Magnet B moves toward fixed Magnet A due to magnetic attraction, the magnetic force (pulling B toward A) acts in the direction of motion (B moving toward A), so the magnetic force does positive work on Magnet B. This positive work by the magnetic force decreases magnetic potential energy (PE drops as magnets get closer—like gravitational PE dropping as objects fall) and increases kinetic energy (Magnet B speeds up as it slides toward A), demonstrating that the magnetic PE stored in the separated configuration is released as KE through the magnetic force's work over the distance—all without contact, as magnetic fields act through the air gap. Choice B is correct because it properly recognizes magnetic force does positive work (force and motion same direction) decreasing PE and increasing KE. Choice A incorrectly states negative work when force and motion are in same direction (toward each other), Choice C claims no work done when object clearly moved through distance by force, and Choice D incorrectly attributes the work to gravity when horizontal magnetic attraction is the relevant force. Work by non-contact forces demonstrates energy transfer without contact: gravitational force does work as objects rise or fall (lift: work against gravity → PE increases, fall: work by gravity → PE decreases, KE increases), electric forces do work as charges move in field (against force: PE increases, by force: PE decreases), and magnetic forces do work as magnets or magnetic materials move in magnetic fields (apart against attraction: PE increases, together by attraction: PE decreases)—all occurring across gaps without physical contact because fields extend through space allowing forces to act at distance.

Question 10

A $2\,\text{kg}$ ball is held at a height of $5\,\text{m}$ above the ground and then released. Gravity (a non-contact force) pulls the ball downward as it falls through the $5\,\text{m}$ gap. Ignoring air resistance, what energy change happens because gravity does work on the ball while it falls?

Gravitational potential energy decreases and kinetic energy increases. (correct answer)
Gravitational potential energy increases and kinetic energy increases.
Gravitational potential energy increases and kinetic energy decreases.
Both gravitational potential energy and kinetic energy stay the same because there is no contact.

Explanation: This question tests understanding that non-contact forces (gravity, electric, magnetic) can do work over distances, changing potential energy even when objects aren't touching. Work is defined as force applied over distance (W = F×d, or W = mgh for lifting against gravity), and non-contact forces like gravity, electric forces, and magnetic forces can do work because they act across space without requiring contact: when you lift a book from floor to shelf, Earth's gravitational force (pulling downward at distance—book not touching Earth) acts over the 2 m height you lift through, and you do work W = mgh against this force, storing the work as gravitational potential energy (PE = mgh gained). When the 2 kg ball falls from 5 m height back to ground, gravitational force (pulling down, F = mg = 2×10 = 20 N) acts in the direction of motion (ball moving down), so gravity does positive work W = mgh = 2×10×5 = 100 J (force and displacement in same direction: both downward). This positive work by gravity decreases gravitational PE (PE drops from initial mgh = 100 J to final 0 J, losing 100 J) and increases kinetic energy (KE increases from 0 to 100 J as ball speeds up during fall), demonstrating work-energy theorem: work done by gravity (100 J) equals KE gained (100 J), and showing that the 100 J previously stored as PE is released as KE through gravity's work over the 5 m distance. Choice A is correct because it accurately explains work by gravity decreases PE and increases KE during fall. Choice B states PE increases during fall when gravity doing positive work must decrease PE, Choice C suggests KE decreases when falling objects speed up (KE increases), and Choice D claims no energy change because no contact when non-contact forces clearly do work at distance. Work by non-contact forces demonstrates energy transfer without contact: gravitational force does work as objects rise or fall (lift: work against gravity → PE increases, fall: work by gravity → PE decreases, KE increases), electric forces do work as charges move in field (against force: PE increases, by force: PE decreases), and magnetic forces do work as magnets or magnetic materials move in magnetic fields (apart against attraction: PE increases, together by attraction: PE decreases)—all occurring across gaps without physical contact because fields extend through space allowing forces to act at distance.

Question 11

A student lifts the same $2\,\text{kg}$ box against gravity to two different heights. Trial 1: lift to $1\,\text{m}$ . Trial 2: lift to $4\,\text{m}$ . The box is not touching Earth during the lift, but gravity still acts. Compared to Trial 1, how does the work the student must do against gravity in Trial 2 change? (Use $W=mgh$ .)

It is the same, because gravity is a non-contact force.
It is 2 times larger.
It is 4 times larger. (correct answer)
It is 3 times larger.

Explanation: This question tests understanding that non-contact forces (gravity, electric, magnetic) can do work over distances, changing potential energy even when objects aren't touching. Work is defined as force applied over distance (W = F×d, or W = mgh for lifting against gravity), and non-contact forces like gravity, electric forces, and magnetic forces can do work because they act across space without requiring contact: when you lift a book from floor to shelf, Earth's gravitational force (pulling downward at distance—book not touching Earth) acts over the 2 m height you lift through, and you do work W = mgh against this force, storing the work as gravitational potential energy (PE = mgh gained). Comparing work done lifting the same 2 kg box to different heights: Trial 1 requires W₁ = mgh₁ = 2×10×1 = 20 J to lift to 1 m, while Trial 2 requires W₂ = mgh₂ = 2×10×4 = 80 J to lift to 4 m. The ratio is W₂/W₁ = 80 J / 20 J = 4, showing Trial 2 requires 4 times more work because the height (and thus distance moved against gravity) is 4 times larger—work is directly proportional to height for vertical lifts against constant gravitational force. Choice C is correct because work scales linearly with height: 4× the height requires 4× the work (W = mgh, so if h increases by factor of 4, W increases by factor of 4). Choice A incorrectly suggests work is independent of height, Choice B (2 times) would be true if comparing 1 m to 2 m (not 4 m), and Choice D (3 times) doesn't match the height ratio or any clear relationship. Work by non-contact forces demonstrates energy transfer without contact: gravitational force does work as objects rise or fall (lift: work against gravity → PE increases, fall: work by gravity → PE decreases, KE increases), electric forces do work as charges move in field (against force: PE increases, by force: PE decreases), and magnetic forces do work as magnets or magnetic materials move in magnetic fields (apart against attraction: PE increases, together by attraction: PE decreases)—all occurring across gaps without physical contact because fields extend through space allowing forces to act at distance.

Question 12

A $5\,\text{kg}$ bucket is lifted straight up $2\,\text{m}$ at constant speed. Gravity pulls downward during the lift even though the bucket is not touching Earth. About how much work is done against gravity, and what happens to gravitational potential energy? (Use $g\approx 10\,\text{m/s}^2$ .)

$W=10\,\text{J}$ , and gravitational potential energy decreases.
$W=100\,\text{J}$ , and gravitational potential energy increases. (correct answer)
$W=0\,\text{J}$ , and gravitational potential energy stays the same because there is no contact.
$W=100\,\text{J}$ , and gravitational potential energy decreases.

Explanation: This question tests understanding that non-contact forces (gravity, electric, magnetic) can do work over distances, changing potential energy even when objects aren't touching. Work is defined as force applied over distance (W = F×d, or W = mgh for lifting against gravity), and non-contact forces like gravity, electric forces, and magnetic forces can do work because they act across space without requiring contact: when you lift a book from floor to shelf, Earth's gravitational force (pulling downward at distance—book not touching Earth) acts over the 2 m height you lift through, and you do work W = mgh against this force, storing the work as gravitational potential energy (PE = mgh gained). Lifting a 5 kg bucket straight up 2 m at constant speed requires work against Earth's gravitational force: gravity pulls downward with force F = mg = 5×10 = 50 N, and lifting moves the bucket upward through distance d = 2 m (opposite to gravity's direction), so work done against gravity is W = mgh = 5×10×2 = 100 J. This 100 J of work done against gravity is stored as increased gravitational potential energy (ΔPE = +100 J), representing energy that could be recovered if the bucket falls back down. Choice B is correct because it accurately calculates work against gravity as W = mgh = 100 J and correctly identifies that PE increases when work is done against gravity. Choice A (10 J) appears to forget a factor (perhaps using just 5×2), Choice C claims no work or energy change despite clear motion against force, and Choice D correctly calculates 100 J but incorrectly states PE decreases when lifting against gravity must increase PE. Work by non-contact forces demonstrates energy transfer without contact: gravitational force does work as objects rise or fall (lift: work against gravity → PE increases, fall: work by gravity → PE decreases, KE increases), electric forces do work as charges move in field (against force: PE increases, by force: PE decreases), and magnetic forces do work as magnets or magnetic materials move in magnetic fields (apart against attraction: PE increases, together by attraction: PE decreases)—all occurring across gaps without physical contact because fields extend through space allowing forces to act at distance.

Question 13

A $4\,\text{kg}$ backpack is lifted straight up from $h=1\,\text{m}$ to $h=4\,\text{m}$ . Gravity pulls down the whole time (a non-contact force). Using $g\approx 10\,\text{m/s}^2$ , how much does the backpack's gravitational potential energy change?

It decreases by $120\,\text{J}$
It increases by $120\,\text{J}$ (correct answer)
It increases by $40\,\text{J}$
It stays the same because gravity is non-contact

Explanation: This question tests understanding that non-contact forces (gravity, electric, magnetic) can do work over distances, changing potential energy even when objects aren't touching. Work is defined as force applied over distance (W = F×d, or W = mgh for lifting against gravity), and when work is done against a non-contact force like gravity, the energy is stored as potential energy: lifting the 4 kg backpack from h=1 m to h=4 m requires work against Earth's gravitational force (pulling downward at distance), and this work increases the backpack's gravitational potential energy. The change in gravitational potential energy is ΔPE = mg(h_final - h_initial) = 4×10×(4-1) = 4×10×3 = 120 J. Since the backpack is lifted upward (against gravity's downward pull), work is done against the gravitational force, and this work is stored as increased gravitational PE: initial PE = mgh₁ = 4×10×1 = 40 J, final PE = mgh₂ = 4×10×4 = 160 J, so ΔPE = 160 - 40 = 120 J increase. Choice B is correct because it properly calculates the PE increase as 120 J and correctly identifies that PE increases when work is done against gravity (lifting upward against downward gravitational force). Choice A (decreases by 120 J) has the wrong sign—PE increases when lifting against gravity, not decreases; Choice C (increases by 40 J) calculates incorrectly, perhaps using only the initial height; and Choice D (stays the same) wrongly claims gravity being non-contact prevents energy changes, when non-contact forces clearly can do work and change energy. The non-contact aspect is key: throughout the lift from 1 m to 4 m, the backpack isn't touching Earth, yet gravitational force continuously pulls downward and work must be done against it. This 120 J increase in gravitational PE represents energy stored in the gravitational field due to the backpack's higher position—energy that could be released if the backpack falls back down, demonstrating that non-contact forces enable energy storage and transfer across distances.

Question 14

A student lifts a $3\,\text{kg}$ book from the floor ( $h=0\,\text{m}$ ) to a shelf $2\,\text{m}$ high. Gravity pulls downward the whole time (a non-contact force). About how much work does the student do against gravity? (Use $g\approx 10\,\text{m/s}^2$ .)

$6\,\text{J}$
$60\,\text{J}$ (correct answer)
$600\,\text{J}$
$15\,\text{J}$

Explanation: This question tests understanding that non-contact forces (gravity, electric, magnetic) can do work over distances, changing potential energy even when objects aren't touching. Work is defined as force applied over distance (W = F×d, or W = mgh for lifting against gravity), and non-contact forces like gravity, electric forces, and magnetic forces can do work because they act across space without requiring contact: when you lift a book from floor to shelf, Earth's gravitational force (pulling downward at distance—book not touching Earth) acts over the 2 m height you lift through, and you do work W = mgh against this force, storing the work as gravitational potential energy (PE = mgh gained). Lifting a 3 kg book from floor (h=0, reference level) to a 2 m high shelf requires work against Earth's gravitational force: gravity pulls the book downward with force F = mg = 3×10 = 30 N (continuously throughout the lift, despite book not touching Earth—gravitational force acts at distance), and lifting moves the book upward through distance d = 2 m (opposite to gravitational force direction), so work done is W = F×d = 30 N × 2 m = 60 J (or directly: W = mgh = 3×10×2 = 60 J, same result). Choice B is correct because it correctly calculates work using W=mgh = 3×10×2 = 60 J, recognizing that work against gravity equals the gravitational potential energy gained. Choice A (6 J) calculates work incorrectly: appears to forget the factor of g (using just 3×2 = 6), Choice C (600 J) is off by a factor of 10 (perhaps using g=100 instead of 10), and Choice D (15 J) doesn't follow any clear formula (not mgh or any standard calculation). Work by non-contact forces demonstrates energy transfer without contact: gravitational force does work as objects rise or fall (lift: work against gravity → PE increases, fall: work by gravity → PE decreases, KE increases), and this 60 J of work done against gravity is stored as gravitational potential energy that could be recovered if the book falls back down. Understanding that forces can do work at distance (not just contact forces like friction or normal force) is essential for energy analysis: the student does 60 J of work against the non-contact gravitational force, increasing the book's gravitational potential energy by exactly 60 J.

Question 15

A $2\,\text{kg}$ rock is lifted from the ground to a ledge. In case 1 it is lifted to $1\,\text{m}$ . In case 2 it is lifted to $4\,\text{m}$ . Gravity is a non-contact force pulling downward in both cases. Using $g\approx 10\,\text{m/s}^2$ , how does the work done by the lifter against gravity in case 2 compare to case 1?

Case 2 requires the same work because the mass is the same
Case 2 requires 2 times as much work
Case 2 requires 4 times as much work (correct answer)
Case 2 requires less work because gravity gets weaker higher up

Explanation: This question tests understanding that non-contact forces (gravity, electric, magnetic) can do work over distances, changing potential energy even when objects aren't touching. Work is defined as force applied over distance (W = F×d, or W = mgh for lifting against gravity), and work is proportional to the distance moved against the force: lifting the same 2 kg rock to different heights requires different amounts of work against Earth's gravitational force (pulling downward at distance). In case 1, lifting to h = 1 m requires work W₁ = mgh₁ = 2×10×1 = 20 J against gravity. In case 2, lifting to h = 4 m requires work W₂ = mgh₂ = 2×10×4 = 80 J against gravity. Comparing the two cases: W₂/W₁ = 80 J / 20 J = 4, so case 2 requires 4 times as much work as case 1. The work scales linearly with height because gravitational force (F = mg = 20 N) remains essentially constant over these small height changes near Earth's surface. Choice C is correct because it accurately states that case 2 requires 4 times as much work, properly recognizing that work against gravity scales linearly with height (4 m is 4 times 1 m, so work is 4 times greater). Choice A (same work) ignores the height difference; Choice B (2 times) might confuse the mass (2 kg) with the scaling factor; and Choice D (less work because gravity weakens) is incorrect because gravity's strength doesn't change appreciably over just 4 m near Earth's surface. The non-contact nature of gravity means the rock doesn't need to touch Earth for gravitational force to act and for work to be required: throughout both lifts, Earth's gravity continuously pulls downward on the rock across the distance. The 4-fold increase in work (20 J vs 80 J) translates directly to a 4-fold increase in gravitational PE gained, demonstrating that work done against non-contact forces over different distances results in proportional energy storage.

Question 16

A $2\,\text{kg}$ object is lifted straight up at constant speed from $h=0\,\text{m}$ to $h=3\,\text{m}$ . Gravity is a non-contact force pulling downward. What is the change in the object's gravitational potential energy? (Use $g\approx 10\,\text{m/s}^2$ .)

$+6\,\text{J}$
$-60\,\text{J}$
$+60\,\text{J}$ (correct answer)
$0\,\text{J}$

Explanation: This question tests understanding that non-contact forces (gravity, electric, magnetic) can do work over distances, changing potential energy even when objects aren't touching. Work is defined as force applied over distance (W = F×d, or W = mgh for lifting against gravity), and non-contact forces like gravity, electric forces, and magnetic forces can do work because they act across space without requiring contact: when you lift an object from floor to height h, Earth's gravitational force (pulling downward at distance—object not touching Earth) acts over the height h you lift through, and you do work W = mgh against this force, storing the work as gravitational potential energy (PE = mgh gained). Lifting a 2 kg object from h=0 m to h=3 m at constant speed requires work against Earth's gravitational force: the change in gravitational potential energy is ΔPE = mgh_final - mgh_initial = (2×10×3) - (2×10×0) = 60 - 0 = +60 J; this positive change means PE increased by 60 J, which equals the work done against gravity during the lift (work against force stores as PE). Choice C is correct because it correctly calculates the change in gravitational potential energy as +60 J, recognizing that lifting increases PE (positive change) by the amount of work done against gravity. Choice A (+6 J) calculates incorrectly (appears to forget factor of g), Choice B (-60 J) has the wrong sign (PE increases when lifting, not decreases), and Choice D (0 J) incorrectly suggests no energy change despite the object clearly gaining height and PE. Work by non-contact forces demonstrates energy transfer without contact: gravitational force does work as objects rise or fall (lift: work against gravity → PE increases by mgh, fall: work by gravity → PE decreases by mgh), and the +60 J change represents energy stored in the gravitational field due to the object's higher position. Understanding that forces can do work at distance (not just contact forces) is essential for energy analysis: the 60 J of work done against the non-contact gravitational force is stored as gravitational potential energy, ready to be converted back to kinetic energy if the object falls.

Question 17

A student lifts a $1.5\,\text{kg}$ water bottle upward by $2\,\text{m}$ at constant speed. During the lift, gravity pulls downward across the air gap (non-contact force). What is the work done by gravity on the bottle during the lift? Use $g\approx 10\,\text{m/s}^2$ .

$+30\,\text{J}$
$-30\,\text{J}$ (correct answer)
$+3\,\text{J}$
$-3\,\text{J}$

Explanation: This question tests understanding that non-contact forces (gravity, electric, magnetic) can do work over distances, changing potential energy even when objects aren't touching. Work is defined as W = F×d cosθ; for gravity, when lifting upward against downward force, work by gravity is negative (θ=180°, cos=-1). For the 1.5 kg bottle lifted 2 m upward at constant speed, gravity pulls downward with F=15 N, displacement upward, so W_gravity = -mg h = -1.5×10×2 = -30 J, as the non-contact force opposes the motion across the air gap. Choice B is correct because it properly calculates the negative work by gravity using W = -mgh, recognizing the sign convention for opposing force and displacement. Choice A claims +30 J, which is incorrect because it ignores the opposite directions, confusing work by gravity with work against it. Work by non-contact forces demonstrates energy transfer without contact: negative work by gravity during lift means PE increases by +30 J. Systematic analysis: (1) force (gravity, down), (2) motion (up), (3) opposite so W negative, PE increases, (4) W = -30 J, (5) energy conserved.

Question 18

A student lifts a $4\,\text{kg}$ backpack from the ground to a hook $1.5\,\text{m}$ high. Gravity pulls downward the whole time (non-contact force). About how much does the backpack's gravitational potential energy increase? (Use $g\approx 10\,\text{m/s}^2$ .)

$6\,\text{J}$
$40\,\text{J}$
$60\,\text{J}$ (correct answer)
$400\,\text{J}$

Explanation: This question tests understanding that non-contact forces (gravity, electric, magnetic) can do work over distances, changing potential energy even when objects aren't touching. Work is defined as force applied over distance (W = F×d, or W = mgh for lifting against gravity), and non-contact forces like gravity, electric forces, and magnetic forces can do work because they act across space without requiring contact: when you lift a book from floor to shelf, Earth's gravitational force (pulling downward at distance—book not touching Earth) acts over the 2 m height you lift through, and you do work W = mgh against this force, storing the work as gravitational potential energy (PE = mgh gained). Lifting a 4 kg backpack from ground (h=0) to a hook at h=1.5 m requires work against Earth's gravitational force: the increase in gravitational potential energy equals the work done against gravity, calculated as ΔPE = mgh = 4 kg × 10 m/s² × 1.5 m = 60 J. This 60 J represents the energy stored in the gravitational field due to the backpack's elevated position—energy that could be recovered if the backpack falls back down, with gravity doing 60 J of positive work to convert PE back to KE. Choice C is correct because it correctly calculates the PE increase using ΔPE = mgh = 4×10×1.5 = 60 J. Choice A (6 J) appears to forget the factor of 10 (using just 4×1.5), Choice B (40 J) seems to forget the height factor (using just 4×10), and Choice D (400 J) is off by factor of 10/1.5 ≈ 6.67, suggesting calculation error. Work by non-contact forces demonstrates energy transfer without contact: gravitational force does work as objects rise or fall (lift: work against gravity → PE increases, fall: work by gravity → PE decreases, KE increases), electric forces do work as charges move in field (against force: PE increases, by force: PE decreases), and magnetic forces do work as magnets or magnetic materials move in magnetic fields (apart against attraction: PE increases, together by attraction: PE decreases)—all occurring across gaps without physical contact because fields extend through space allowing forces to act at distance.

Question 19

A $5\,\text{kg}$ backpack is lifted from $h=0\,\text{m}$ to $h=1\,\text{m}$ , then from $h=1\,\text{m}$ to $h=3\,\text{m}$ . Gravity (non-contact) pulls downward the whole time. Ignoring air resistance, how does the work the student must do against gravity in the second lift compare to the first lift? Use $g\approx 10\,\text{m/s}^2$ .

The second lift requires the same work as the first lift because the backpack has the same mass.
The second lift requires twice as much work because the distance lifted is twice as large ( $2\,\text{m}$ vs $1\,\text{m}$ ). (correct answer)
The second lift requires half as much work because the backpack is already moving.
The second lift requires no work because gravity gets weaker after $1\,\text{m}$ .

Explanation: This question tests understanding that non-contact forces (gravity, electric, magnetic) can do work over distances, changing potential energy even when objects aren't touching. Work against gravity is W = mgh for each height change, additive for separate lifts, as gravity acts continuously. First lift (0 to 1 m): W = 5×10×1 = 50 J; second (1 to 3 m, 2 m change): W = 5×10×2 = 100 J, twice the first due to twice the height change, despite non-contact force pulling downward. Choice B is correct because it recognizes the second lift requires twice as much work against gravity due to the larger height change (2 m vs 1 m). Choice A is wrong because it claims same work, ignoring that work depends on height difference, not just mass. Work by non-contact forces demonstrates energy transfer without contact: each lift stores PE proportional to h. Systematic analysis: (1) force (gravity, down), (2) motion (up), (3) opposite, work against = mgh per segment, (4) second W=100 J > first 50 J, (5) cumulative PE increase.

Question 20

Two magnets attract across a $10\,\text{cm}$ air gap. A student slowly pulls them apart until the gap is $30\,\text{cm}$ , keeping them from snapping together. Which statement best describes what the student's work does?

The student does work against the magnetic force, increasing magnetic potential energy. (correct answer)
The student does work with the magnetic force, decreasing magnetic potential energy.
No work is possible because forces at a distance cannot transfer energy.
The magnets must touch for any potential energy to change.

Explanation: This question tests understanding that non-contact forces (gravity, electric, magnetic) can do work over distances, changing potential energy even when objects aren't touching. Work is defined as force applied over distance (W = F×d), and non-contact forces like gravity, electric forces, and magnetic forces can do work because they act across space without requiring contact: when you separate attracting magnets, the magnetic force does work (or has work done against it) even though the magnets never touch. When pulling attracting magnets from 10 cm to 30 cm separation, the magnetic force pulls them together (force points inward) while you move them apart (displacement points outward), so force and displacement are opposite; this means you do positive work against the magnetic force (like lifting against gravity), and this work is stored as increased magnetic potential energy in the magnetic field between the magnets. Choice A is correct because it accurately states the student does work against the magnetic force (force opposes the separation), increasing magnetic potential energy (energy stored in field when attracting objects are pulled apart). Choice B incorrectly says work is done "with" the force and PE decreases (you work against attraction when separating, increasing PE), Choice C wrongly claims forces at distance can't transfer energy (magnetic forces clearly do work across gaps), and Choice D incorrectly requires touching for PE changes (magnetic PE depends on separation distance, not contact). Work by non-contact forces demonstrates energy transfer without contact: magnetic forces do work as magnets move in fields (separating against attraction: work against force → PE increases, approaching by attraction: work by force → PE decreases), all occurring across air gaps. Understanding that forces can do work at distance is essential: the work done separating the magnets (against their attraction) is stored as magnetic PE that would be released if the magnets were allowed to snap back together.