Physics Quiz
Practice Model Energy Transfer Computationally in Physics with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.
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A 10kg crate starts from rest at the top of a frictionless hill of height 12m. It slides down to the bottom, then travels across a rough horizontal floor where the kinetic friction force is constant at 40N for 15m, and then goes up a frictionless ramp. Using g=10m/s2, what maximum vertical height above the bottom does the crate reach on the ramp? (Track energy through: initial gravitational PE → KE at bottom → thermal from friction → final gravitational PE.)
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A 10kg crate starts from rest at the top of a frictionless hill of height 12m. It slides down to the bottom, then travels across a rough horizontal floor where the kinetic friction force is constant at 40N for 15m, and then goes up a frictionless ramp. Using g=10m/s2, what maximum vertical height above the bottom does the crate reach on the ramp? (Track energy through: initial gravitational PE → KE at bottom → thermal from friction → final gravitational PE.)
Explanation: This question tests understanding of computationally modeling energy transfers by calculating energy values at multiple stages and tracking transformations through a process. Energy conservation requires that total energy (including all forms: kinetic, potential, thermal) remains constant throughout the process: E_total = KE + PE_g + PE_spring + E_thermal = constant, which allows us to calculate unknown energies or velocities at any stage by knowing the energy distribution at another stage and accounting for all transformations between them. Using conservation from initial (height h₀=12 m, at rest: v=0) to final (height h, v=0 on ramp), we write mgh₀ = fd + mgh (accounting for friction work over d=15 m with f=40 N), solving for h = h₀ - fd/(mg) =12 - (4015)/(1010) =12 - 600/100 =6 m. Choice A is correct because it accurately applies conservation E_i = E_f to solve for unknown, including thermal from friction. Choice B is wrong because it omits thermal energy from friction work, violating conservation when mechanical energy decreases. Computational modeling strategy: (1) identify all energy forms at each stage (KE, PE_g, PE_spring, thermal), (2) calculate each form using appropriate formulas (remember ½ in KE and PE_spring), (3) sum for total energy at that stage, (4) verify E_total same at all stages (conservation), (5) if solving for unknown, use E_stage1 = E_stage2 with known values to isolate unknown. Common errors: forgetting ½ factors, omitting thermal when friction present, using wrong height reference for PE (define h=0 clearly), not accounting for all forces' work.
A 10kg crate slides down a frictionless ramp from a vertical height of 6.0m, then crosses a rough horizontal floor where the friction force is 40N. The crate comes to rest on the rough floor. Using g=10m/s2, how far does it slide on the rough floor before stopping?
Energy tracking: initial PEg → KE at bottom → thermal energy from friction until KE=0.
Explanation: This problem involves modeling energy transfers computationally from gravitational potential to thermal energy. Energy conservation tells us that initial PE_g equals the thermal energy dissipated by friction. Initially, PE_g = mgh = 10 × 10 × 6.0 = 600 J. This energy converts to kinetic at the bottom, then to thermal energy as friction does work: W_friction = fd. Since the crate stops, all 600 J becomes thermal energy: 40 × d = 600. Solving for d: d = 600/40 = 15 m. A common mistake is using the wrong formula for work or forgetting that all initial energy must be dissipated for the crate to stop.
A 6kg cart starts from rest at the top of a 12m hill (take g=10m/s2). It rolls down a frictionless track to the bottom, then crosses a rough horizontal section of length 8m where the friction force is constant at 30N, and then climbs a frictionless ramp. At the highest point it reaches on the ramp, its speed is momentarily zero. Using energy conservation including thermal energy from friction, what maximum vertical height above the bottom does the cart reach on the ramp?
(Track: Stage 1 top → Stage 2 bottom → Stage 3 after rough patch → Stage 4 highest point.)
Explanation: This problem involves modeling energy transfers computationally through multiple stages of motion. Energy conservation states that E_total = KE + PE + E_thermal remains constant throughout. Initially at the top (Stage 1), the cart has PE = mgh = 6×10×12 = 720 J and KE = 0. At the bottom (Stage 2), all this converts to KE = 720 J. Crossing the rough section creates thermal energy E_thermal = fd = 30×8 = 240 J, leaving KE = 480 J at Stage 3. At the highest point on the ramp (Stage 4), KE = 0 and all remaining energy is PE = mgh_final = 480 J, giving h_final = 480/(6×10) = 8 m. A common error is forgetting to subtract the thermal energy, which would incorrectly give 12 m height.
A 1.5kg ball is dropped from rest from a height of 18m (use g=10m/s2). It hits the ground and rebounds. During the collision with the ground, 60J of mechanical energy is converted to thermal/sound energy. Immediately after the bounce, the ball moves upward.
What maximum height does the ball reach after the bounce? (Assume no air resistance.)
Explanation: This problem models energy transfers computationally during a ball's bounce. Energy conservation shows E_total = KE + PE + E_thermal remains constant. Initially at height 18 m, PE = mgh = 1.5×10×18 = 270 J and KE = 0. Just before impact, all PE converts to KE = 270 J. During the collision, 60 J converts to thermal/sound energy, leaving 270 - 60 = 210 J of mechanical energy. After bounce, this energy is all KE moving upward. At maximum height after bounce, KE = 0 and PE = 210 J. Using PE = mgh: 210 = 1.5×10×h, giving h = 14 m. A common error is subtracting thermal energy from initial height rather than from total energy.
A 2kg puck is pushed along a horizontal surface for 5m by a constant applied force of 18N. A constant friction force of 6N opposes the motion. The puck starts from rest.
What is the puck’s kinetic energy after it has moved 5m? (Use work-energy: ΔKE=Wapplied+Wfriction.)
Explanation: This problem models energy transfer computationally using work-energy theorem. Energy conservation tells us that E_total = KE + E_thermal remains constant, where work changes the total energy. The applied force does work W_applied = 18×5 = 90 J, while friction does negative work W_friction = -6×5 = -30 J. The net work equals the change in kinetic energy: ΔKE = W_net = 90 - 30 = 60 J. Since the puck starts from rest (KE_i = 0), the final KE = 60 J. A common error is using only the applied work (90 J) without subtracting the friction work.
A 6kg crate starts from rest at the top of a 12m high platform (use g=10m/s2). It slides down a frictionless track to the bottom, then moves across a rough horizontal floor for 8m where the kinetic friction force is constant at 30N, and then goes up a frictionless ramp to a final point where it comes to rest.
What maximum vertical height above the floor does the crate reach on the ramp?
(Track energy: initial PEg→ bottom KE→ thermal loss on floor → final PEg.)
Explanation: This problem involves modeling energy transfers computationally through multiple stages. Energy conservation states that E_total = KE + PE + E_thermal remains constant throughout. Initially, the crate has PE = mgh = 6×10×12 = 720 J at the top. At the bottom, all this converts to KE = 720 J. On the rough floor, friction does work W_friction = -30×8 = -240 J, converting mechanical energy to thermal. The remaining mechanical energy is 720 - 240 = 480 J, which becomes PE at the final height: mgh_final = 480 J, so h_final = 480/(6×10) = 8.0 m. A common error is forgetting to subtract the thermal energy loss, which would give h = 12 m.
A 10kg crate slides down a frictionless ramp from a vertical height of 6.0m, then crosses a rough horizontal floor where the friction force is 40N. The crate comes to rest on the rough floor. Using g=10m/s2, how far does it slide on the rough floor before stopping?
Energy tracking: initial PEg → KE at bottom → thermal energy from friction until KE=0.
Explanation: This problem involves modeling energy transfers computationally from gravitational potential to thermal energy. Energy conservation tells us that initial PE_g equals the thermal energy dissipated by friction. Initially, PE_g = mgh = 10 × 10 × 6.0 = 600 J. This energy converts to kinetic at the bottom, then to thermal energy as friction does work: W_friction = fd. Since the crate stops, all 600 J becomes thermal energy: 40 × d = 600. Solving for d: d = 600/40 = 15 m. A common mistake is using the wrong formula for work or forgetting that all initial energy must be dissipated for the crate to stop.
A 5kg sled moves at 10m/s on level ground and then compresses a horizontal spring (k=200N/m). While compressing, a constant kinetic friction force of 20N acts over the compression distance. At maximum compression the sled is momentarily at rest.
Using Einitial=KE and Efinal=PEspring+Ethermal with Ethermal=fd, what is the maximum compression x of the spring?
Explanation: This problem models energy transfers computationally during spring compression with friction. Energy conservation requires E_total = KE + PE + E_thermal to remain constant. Initially, the sled has KE = ½mv² = ½×5×10² = 250 J. At maximum compression, KE = 0, PE_spring = ½kx² = ½×200×x² = 100x², and E_thermal = fd = 20x (since compression distance equals x). Setting initial energy equal to final: 250 = 100x² + 20x. Rearranging: 100x² + 20x - 250 = 0, or x² + 0.2x - 2.5 = 0. Using the quadratic formula: x = 1.5 m. A common mistake is forgetting the thermal energy term, which would give x = 1.58 m.
A 9kg cart starts from rest at height h=11m (use g=10m/s2). It rolls down a frictionless track to the bottom, then crosses a rough patch of length 6m with constant friction force 50N, and then continues on a frictionless track up to a point where its speed is measured to be 4m/s.
At that measured point, what is the cart’s height above the bottom?
Explanation: This requires modeling energy transfers computationally with multiple stages. Energy conservation states E_total = KE + PE + E_thermal remains constant. Initially, PE = 9×10×11 = 990 J. At the bottom, all converts to KE = 990 J. Crossing the rough patch, friction work W_f = -50×6 = -300 J, leaving total mechanical energy = 690 J. At the measured point, KE = ½×9×4² = 72 J, so PE = 690 - 72 = 618 J. Therefore, mgh = 618, giving h = 618/(9×10) = 6.87 m ≈ 7.0 m. A common error is forgetting to include the remaining kinetic energy.
A 1.5kg block is launched up a rough incline with initial speed 12m/s. The incline raises the block by a vertical height of 5m before the block comes to rest. Using g=10m/s2, how much energy was converted to thermal energy by friction during the trip up the incline? (Track: initial KE → gravitational PE + thermal.)
Explanation: This question tests understanding of computationally modeling energy transfers by calculating energy values at multiple stages and tracking transformations through a process. Energy conservation requires that total energy (including all forms: kinetic, potential, thermal) remains constant throughout the process: E_total = KE + PE_g + PE_spring + E_thermal = constant, which allows us to calculate unknown energies or velocities at any stage by knowing the energy distribution at another stage and accounting for all transformations between them. Tracking transformation: initial KE=½1.512²=½1.5144=108 J converts to PE_g = mgh=1.5105=75 J + E_thermal at rest, so E_thermal=108-75=33 J. Choice A is correct because it properly tracks energy transformations accounting for all forms including thermal. Choice B is wrong because it confuses initial KE calculation, using full mv² without ½ factor. Computational modeling strategy: (1) identify all energy forms at each stage (KE, PE_g, PE_spring, thermal), (2) calculate each form using appropriate formulas (remember ½ in KE and PE_spring), (3) sum for total energy at that stage, (4) verify E_total same at all stages (conservation), (5) if solving for unknown, use E_stage1 = E_stage2 with known values to isolate unknown. Common errors: forgetting ½ factors, omitting thermal when friction present, using wrong height reference for PE (define h=0 clearly), not accounting for all forces' work.
A 8kg box slides down a frictionless ramp from height 9m, then moves across a rough floor for 12m where kinetic friction is 50N, and then goes up a frictionless ramp. Using g=10m/s2, show energy tracking by finding the box’s maximum height on the final ramp.
Explanation: This question tests understanding of computationally modeling energy transfers by calculating energy values at multiple stages and tracking transformations through a process. Energy conservation requires that total energy (including all forms: kinetic, potential, thermal) remains constant throughout the process: E_total = KE + PE_g + PE_spring + E_thermal = constant, which allows us to calculate unknown energies or velocities at any stage by knowing the energy distribution at another stage and accounting for all transformations between them. Using conservation from initial (height h₀=9 m, at rest: v=0) to final (height h, v=0 on ramp), we write mgh₀ = fd + mgh (accounting for friction work over d=12 m with f=50 N), solving for h = h₀ - fd/(mg) =9 - (5012)/(810) =9 - 600/80 =9-7.5=1.5 m. Choice B is correct because it accurately applies conservation E_i = E_f to solve for unknown, including thermal from friction. Choice A is wrong because it omits thermal energy from friction work, violating conservation. Computational modeling strategy: (1) identify all energy forms at each stage (KE, PE_g, PE_spring, thermal), (2) calculate each form using appropriate formulas (remember ½ in KE and PE_spring), (3) sum for total energy at that stage, (4) verify E_total same at all stages (conservation), (5) if solving for unknown, use E_stage1 = E_stage2 with known values to isolate unknown. Common errors: forgetting ½ factors, omitting thermal when friction present, using wrong height reference for PE (define h=0 clearly), not accounting for all forces' work.
A 12kg box starts from rest at height 10m on a frictionless ramp (use g=10m/s2). At the bottom it enters a rough horizontal stretch with constant friction force 80N and eventually comes to rest on that horizontal surface.
Using energy conservation with thermal energy from friction, what distance d does the box slide on the rough horizontal surface before stopping? (Use mgh=fd.)
Explanation: This models energy transfers computationally with friction bringing motion to rest. Energy conservation states E_total = KE + PE + E_thermal remains constant throughout. Initially at height 10 m, PE = mgh = 12×10×10 = 1200 J and KE = 0. At the bottom, all PE converts to KE = 1200 J. On the rough surface, friction converts all this KE to thermal energy. Using E_thermal = fd: 1200 = 80×d, giving d = 15 m. The strategy is recognizing that all initial potential energy must equal the thermal energy generated by friction when the box stops. A common error is using the wrong mass or forgetting the factor in kinetic energy.