Physics Quiz: Model Energy Transfer Between Objects

What this quiz covers

This quiz focuses on Model Energy Transfer Between Objects, giving you a quick way to practice the rules, question types, and explanations that matter most for Physics.

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.

Question 1

1. It is converted mainly into thermal energy and sound energy (and deformation) in the carts during the collision. (correct answer)
2. It is converted into additional gravitational PE_g because the carts are moving forward.
3. It is destroyed because inelastic collisions do not conserve energy.
4. All of the initial KE is transferred to the 2.0 kg cart as KE, so total KE stays the same.

Explanation: This question tests understanding of energy transfer and energy transformations between objects in a system. Energy exists in multiple forms including kinetic energy (energy of motion, KE = ½mv²), gravitational potential energy (energy due to position, PE = mgh), elastic potential energy (stored in springs, PE = ½kx²), and thermal energy (internal energy related to temperature). Before the collision, the total kinetic energy is KE_initial = ½ × 1.0 kg × (6.0 m/s)² + ½ × 2.0 kg × 0² = 18 J. After the inelastic collision, the kinetic energy is KE_final = ½ × (1.0 + 2.0) kg × (2.0 m/s)² = 6 J, which is less than KE_initial; the missing 12 J was not destroyed but rather converted to thermal energy (heating the objects), sound energy, and deformation energy—this is characteristic of inelastic collisions. Choice A is correct because it properly applies conservation of energy showing E_initial = E_final by identifying where the lost mechanical energy went to non-mechanical forms. Choice C is a tempting distractor that violates conservation of energy by suggesting energy is destroyed, when actually energy only transforms from one form to another or transfers between objects. When analyzing energy transfers: (1) identify all energy forms present initially and finally, (2) apply conservation of energy (E_initial = E_final), (3) account for all energy forms including those dissipated to thermal/sound if mechanical energy decreases, and (4) remember energy can transform and transfer but never disappear. To check if energy is conserved: sum all energy forms at the initial state, sum all energy forms at the final state (including thermal if friction or inelastic collision), and verify the totals are equal—if not, identify what energy form you missed in your accounting.

Question 2

1. At the lowest point, KE is maximum and is slightly less than the initial PE_g because some energy is transformed to thermal and sound. (correct answer)
2. At the lowest point, PE_g is maximum because the bob is moving fastest there.
3. At the lowest point, total energy is greater than at the release point because gravity adds energy.
4. At the lowest point, KE must be zero because PE_g has been used up.

Explanation: This question tests understanding of energy transfer and energy transformations between objects in a system. The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another or transferred between objects, so the total energy in an isolated system remains constant. In this scenario, as the bob falls, its height changes from 1.5 m to 0 m, causing gravitational potential energy to decrease by ΔPE = mgh = (0.80 kg)(10 m/s²)(1.5 m) = 12 J, but with small air resistance, some energy converts to thermal and sound. By conservation of energy, the KE at the bottom is slightly less than 12 J, showing that PE transforms mostly into KE with some dissipation. Choice A is correct because it accurately compares energy states at different positions or times. Choice C violates conservation of energy by suggesting energy is created, when actually energy only transforms from one form to another or transfers between objects. When analyzing energy transfers: (1) identify all energy forms present initially and finally, (2) apply conservation of energy (E_initial = E_final), (3) account for all energy forms including those dissipated to thermal/sound if mechanical energy decreases, and (4) remember energy can transform and transfer but never disappear. To check if energy is conserved: sum all energy forms at the initial state, sum all energy forms at the final state (including thermal if friction or inelastic collision), and verify the totals are equal—if not, identify what energy form you missed in your accounting.

Question 3

1. PE_g decreases and becomes KE because the sled is slowing down.
2. KE decreases and is transformed mainly into thermal energy in the sled and snow. (correct answer)
3. KE decreases because energy is destroyed by friction.
4. Thermal energy decreases and becomes KE because friction provides a forward push.

Explanation: This question tests understanding of energy transfer and energy transformations between objects in a system. Energy transformations occur when energy changes from one form to another, such as gravitational potential energy converting to kinetic energy as an object falls, or kinetic energy converting to thermal energy due to friction. As the sled moves on the rough patch, friction does negative work, converting kinetic energy to thermal energy; initial KE = ½(4.0 kg)(5.0 m/s)² = 50 J, final KE = ½(4.0 kg)(1.0 m/s)² = 2 J, so ΔKE = -48 J becomes thermal. The sled does not change height, so no PE_g involvement. Choice B is correct because it correctly identifies where the lost mechanical energy went. Choice C violates conservation of energy by suggesting energy is destroyed, when actually energy only transforms from one form to another or transfers between objects. When analyzing energy transfers: (1) identify all energy forms present initially and finally, (2) apply conservation of energy (E_initial = E_final), (3) account for all energy forms including those dissipated to thermal/sound if mechanical energy decreases, and (4) remember energy can transform and transfer but never disappear. Key energy transformations to recognize: falling objects convert PE → KE, rising objects convert KE → PE, friction converts KE → thermal, collisions redistribute KE and often convert some to thermal/sound, and springs alternate between elastic PE and KE.

Question 4

1. $W = \Delta \text{PE}_g$ because pushing only changes gravitational potential energy.
2. $W = \text{KE}_f$ because friction cannot change energy, only speed.
3. $W = \text{KE}_f + E_{\text{thermal}}$ where $W = Fd$ is the energy transferred to the crate–floor system. (correct answer)
4. $W = \text{KE}_f - E_{\text{thermal}}$ because thermal energy must be subtracted from the total.

Explanation: This question tests understanding of energy transfer and energy transformations between objects in a system. The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another or transferred between objects, so the total energy in an isolated system remains constant. As the crate moves 3.0 m under applied force, work W = Fd = (40 N)(3.0 m) = 120 J is done, transferring energy to the object as kinetic energy. However, if friction is present, work by friction converts some kinetic energy to thermal energy, warming the surfaces; here, KE_f = ½(5.0 kg)(4.0 m/s)² = 40 J, so E_thermal = 120 J - 40 J = 80 J. Choice C is correct because it properly applies conservation of energy showing E_initial = E_final. Choice D uses the wrong energy formula by subtracting thermal energy incorrectly, leading to an incorrect energy value. When analyzing energy transfers: (1) identify all energy forms present initially and finally, (2) apply conservation of energy (E_initial = E_final), (3) account for all energy forms including those dissipated to thermal/sound if mechanical energy decreases, and (4) remember energy can transform and transfer but never disappear. Key energy transformations to recognize: falling objects convert PE → KE, rising objects convert KE → PE, friction converts KE → thermal, collisions redistribute KE and often convert some to thermal/sound, and springs alternate between elastic PE and KE.

Question 5

1. Most of the initial KE of puck 1 is transferred to KE of puck 2, with negligible conversion to other forms. (correct answer)
2. The initial KE of puck 1 is converted into PE_g of puck 2.
3. The initial KE of puck 1 is destroyed because puck 1 stops moving.
4. Thermal energy flows from puck 2 to puck 1, causing puck 1 to stop.

Explanation: This question tests understanding of energy transfer and energy transformations between objects in a system. The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another or transferred between objects, so the total energy in an isolated system remains constant. Before the collision, the total kinetic energy is KE_initial = ½(0.20 kg)(8.0 m/s)² + ½(0.20 kg)(0)² = 6.4 J. After the elastic collision, KE_final = ½(0.20 kg)(0)² + ½(0.20 kg)(8.0 m/s)² = 6.4 J, showing full transfer of KE from puck 1 to puck 2 with no dissipation since it's elastic and frictionless. Choice A is correct because it accurately describes the energy transformation from KE of one object to KE of another. Choice C violates conservation of energy by suggesting energy is destroyed, when actually energy only transforms from one form to another or transfers between objects. When analyzing energy transfers: (1) identify all energy forms present initially and finally, (2) apply conservation of energy (E_initial = E_final), (3) account for all energy forms including those dissipated to thermal/sound if mechanical energy decreases, and (4) remember energy can transform and transfer but never disappear. Common mistake: assuming energy is lost when mechanical energy decreases—energy is never lost, only converted to less obvious forms like thermal energy (which spreads out and can't easily be recovered for mechanical work).

Question 6

1. KE of the moving cart transfers to the other cart as KE, and some KE transforms to thermal energy and sound energy. (correct answer)
2. Gravitational potential energy transfers from the moving cart to the stationary cart, increasing the total mechanical energy.
3. Thermal energy transfers from the stationary cart to the moving cart, causing both carts to speed up.
4. KE is destroyed during the collision, so the total energy of the system decreases.

Explanation: This question tests understanding of energy transfer and energy transformations between objects in a system. Energy transformations occur when energy changes from one form to another, such as gravitational potential energy converting to kinetic energy as an object falls, or kinetic energy converting to thermal energy due to friction. Before the collision, the total kinetic energy is KE_initial = ½(1.5 kg)(6.0 m/s)² + 0 = 27 J. After the inelastic collision, using momentum conservation to find the final velocity (3.0 m/s for both carts together), KE_final = ½(3.0 kg)(3.0 m/s)² = 13.5 J, which is less than KE_initial. The missing energy was not destroyed but rather converted to thermal energy (heating the objects), sound energy, and deformation energy—this is characteristic of inelastic collisions. Choice A is correct because it accurately describes both the energy transfer (KE from moving cart to stationary cart) and the energy transformation (some KE converts to thermal and sound energy), accounting for the decrease in mechanical energy. Choice D violates conservation of energy by suggesting energy is destroyed, when actually energy only transforms from one form to another or transfers between objects—the 'lost' KE became thermal and sound energy. When analyzing energy transfers: (1) identify all energy forms present initially and finally, (2) apply conservation of energy (E_initial = E_final), (3) account for all energy forms including those dissipated to thermal/sound if mechanical energy decreases, and (4) remember energy can transform and transfer but never disappear. Common mistake: assuming energy is lost when mechanical energy decreases—energy is never lost, only converted to less obvious forms like thermal energy (which spreads out and can't easily be recovered for mechanical work).

Question 7

1. PE_g at the top is $50\,\text{J}$ less than KE at the bottom because the cart stops.
2. PE_g at the top equals KE at the bottom: $\text{PE}_{g,\text{top}} = \tfrac{1}{2}mv^2 = 50\,\text{J}$. (correct answer)
3. PE_g at the top is greater than KE at the bottom because potential energy increases with height.
4. KE at the bottom equals $mv^2 = 100\,\text{J}$, so PE_g at the top must be $100\,\text{J}$.

Explanation: This question tests understanding of energy transfer and energy transformations between objects in a system. The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another or transferred between objects, so the total energy in an isolated system remains constant. At the bottom of the hill, the cart has kinetic energy KE = ½mv² = ½(1.0 kg)(10 m/s)² = 50 J and zero gravitational potential energy (taking bottom as h = 0). As it rolls up the frictionless hill and comes to rest at the top, all this kinetic energy transforms into gravitational potential energy: PE_top = 50 J, with KE_top = 0. By conservation of energy on a frictionless surface, the total mechanical energy remains constant throughout. Choice B is correct because it properly applies conservation of energy, showing that the gravitational PE at the top (where v = 0) equals the KE at the bottom (where h = 0): both equal 50 J. Choice D uses the wrong kinetic energy formula (mv² instead of ½mv²), incorrectly calculating KE = (1.0 kg)(10 m/s)² = 100 J when it should be 50 J. When analyzing energy transfers: (1) identify all energy forms present initially and finally, (2) apply conservation of energy (E_initial = E_final), (3) account for all energy forms including those dissipated to thermal/sound if mechanical energy decreases, and (4) remember energy can transform and transfer but never disappear. To check if energy is conserved: sum all energy forms at the initial state, sum all energy forms at the final state (including thermal if friction or inelastic collision), and verify the totals are equal—if not, identify what energy form you missed in your accounting.

Question 8

1. All initial $\textbf{KE}$ is transferred into $\textbf{KE}$ of the combined carts; no other energy forms are involved.
2. Some initial $\textbf{KE}$ is transferred to the second cart as $\textbf{KE}$, and some is transformed into $\textbf{Thermal}$ and $\textbf{Sound}$ energy during deformation. (correct answer)
3. The collision destroys energy because the final speed is smaller than the initial speed.
4. The collision converts $\textbf{PE}_g$ into $\textbf{KE}$ because the carts are moving horizontally.

Explanation: This question tests understanding of energy transfer and energy transformations between objects in a system. Energy transformations occur when energy changes from one form to another, such as gravitational potential energy converting to kinetic energy as an object falls, or kinetic energy converting to thermal energy due to friction. Before the collision, the total kinetic energy is KE_initial = ½m₁v₁² + ½m₂v₂² = ½(1.5 kg)(6.0 m/s)² + 0 = 27 J. After the inelastic collision, using momentum conservation to find final velocity v_f = 3.0 m/s, the kinetic energy is KE_final = ½(3.0 kg)(3.0 m/s)² = 13.5 J, which is less than KE_initial. The missing energy was not destroyed but rather converted to thermal energy (heating the objects), sound energy, and deformation energy—this is characteristic of inelastic collisions. Choice B is correct because it accurately describes that some kinetic energy transfers between carts while some transforms to thermal and sound energy during the collision. Choice C violates conservation of energy by suggesting energy is destroyed, when actually energy only transforms from one form to another or transfers between objects. Common mistake: assuming energy is lost when mechanical energy decreases—energy is never lost, only converted to less obvious forms like thermal energy (which spreads out and can't easily be recovered for mechanical work).

Question 9

1. $\textbf{KE}$ decreases while $\textbf{PE}_g$ increases by the same amount, so total energy stays constant. (correct answer)
2. $\textbf{KE}$ increases while $\textbf{PE}_g$ increases, so total energy increases.
3. $\textbf{PE}_g$ decreases while $\textbf{KE}$ decreases, so energy is destroyed.
4. $\textbf{PE}_g$ is transformed into $\textbf{Thermal}$ energy because there is no friction.

Explanation: This question tests understanding of energy transfer and energy transformations between objects in a system. Energy transformations occur when energy changes from one form to another, such as gravitational potential energy converting to kinetic energy as an object falls, or kinetic energy converting to thermal energy due to friction. In this scenario, as the ball rises, its speed decreases from 10 m/s toward 0 m/s at maximum height, causing kinetic energy to decrease from KE_initial = ½(0.50 kg)(10 m/s)² = 25 J to KE_final = 0 J. By conservation of energy, this decrease in KE must equal the increase in gravitational PE: ΔPE = +25 J, showing that KE transforms into PE. Choice A is correct because it accurately describes the energy transformation from kinetic energy to gravitational potential energy, with the total mechanical energy remaining constant. Choice B violates conservation of energy by suggesting both KE and PE increase, which would mean total energy increases without any external work being done. Key energy transformations to recognize: falling objects convert PE → KE, rising objects convert KE → PE, friction converts KE → thermal, collisions redistribute KE and often convert some to thermal/sound, and springs alternate between elastic PE and KE.

Question 10

1. KE \u2192 PE_g (kinetic energy increases by turning into gravitational potential energy)
2. PE_g \u2192 KE (gravitational potential energy decreases and becomes kinetic energy) (correct answer)
3. Thermal \u2192 KE (thermal energy in the air becomes kinetic energy of the ball)
4. PE_g is destroyed as the ball falls, so total energy decreases

Explanation: This question tests understanding of energy transfer and energy transformations between objects in a system. The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another or transferred between objects, so the total energy in an isolated system remains constant. In this scenario, as the ball falls from 5.0 m to the ground, its height decreases from h=5.0 m to h=0 m, causing gravitational potential energy to decrease by ΔPE = mgh = (2.0 kg)(10 m/s²)(5.0 m) = 100 J. By conservation of energy, this change must equal the increase in kinetic energy: ΔKE = ½m(v² - 0) = 100 J (since it starts from rest), showing that PE transforms into KE. Choice B is correct because it accurately describes the energy transformation from gravitational potential energy to kinetic energy. Choice D violates conservation of energy by suggesting energy is destroyed, when actually energy only transforms from one form to another or transfers between objects. When analyzing energy transfers: (1) identify all energy forms present initially and finally, (2) apply conservation of energy (E_initial = E_final), (3) account for all energy forms including those dissipated to thermal/sound if mechanical energy decreases, and (4) remember energy can transform and transfer but never disappear.

Question 11

1. PE_g decreases and is converted mostly to KE, with a small amount converted to thermal energy due to air resistance (correct answer)
2. KE decreases and is converted to PE_g as the bob moves downward
3. PE_g increases and KE increases at the same time as the bob moves downward
4. Total energy increases because gravity adds energy to the system without any decrease elsewhere

Explanation: This question tests understanding of energy transfer and energy transformations between objects in a system. The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another or transferred between objects, so the total energy in an isolated system remains constant. In this scenario, as the bob falls from 1.5 m to the lowest point, its height changes from h=1.5 m to h=0 m, causing gravitational potential energy to decrease by $\Delta \text{PE} = mgh = (0.80 \, \text{kg})(10 \, \text{m/s}^2)(1.5 \, \text{m}) = 12 \, \text{J}$. By conservation of energy, this change would equal the increase in kinetic energy if no dissipation, but with small air resistance, some energy converts to thermal, so $\Delta \text{KE} < 12 \, \text{J}$. Choice A is correct because it accurately describes the energy transformation from gravitational potential energy mostly to kinetic energy with some to thermal. Choice D violates conservation of energy by suggesting total energy increases, when actually energy only transforms from one form to another or transfers between objects. When analyzing energy transfers: (1) identify all energy forms present initially and finally, (2) apply conservation of energy ($E_{\text{initial}} = E_{\text{final}}$), (3) account for all energy forms including those dissipated to thermal/sound if mechanical energy decreases, and (4) remember energy can transform and transfer but never disappear. Common mistake: assuming energy is lost when mechanical energy decreases—energy is never lost, only converted to less obvious forms like thermal energy (which spreads out and can't easily be recovered for mechanical work).

Question 12

1. Thermal energy transfers from the colder block to the hotter block until they reach the same temperature
2. Thermal energy transfers from the hotter block to the colder block until they reach the same temperature (correct answer)
3. No energy transfer occurs because both blocks are solids
4. Thermal energy is created in both blocks so their temperatures rise above $80^\circ\text{C}$

Explanation: This question tests understanding of energy transfer and energy transformations between objects in a system. Energy exists in multiple forms including kinetic energy (energy of motion, KE = ½mv²), gravitational potential energy (energy due to position, PE = mgh), elastic potential energy (stored in springs, PE = ½kx²), and thermal energy (internal energy related to temperature). In this scenario, thermal energy transfers from the hotter block (80°C) to the colder block (20°C) through conduction until they reach thermal equilibrium at an intermediate temperature, such as around 50°C (assuming same specific heats). No energy is created or destroyed; it's conserved as it transfers between the blocks. Choice B is correct because it accurately describes the direction of thermal energy transfer from hot to cold. Choice A reverses the direction of energy transfer, claiming thermal energy moves from colder to hotter, which violates the second law of thermodynamics. When analyzing energy transfers: (1) identify all energy forms present initially and finally, (2) apply conservation of energy (E_initial = E_final), (3) account for all energy forms including those dissipated to thermal/sound if mechanical energy decreases, and (4) remember energy can transform and transfer but never disappear.

Question 13

1. KE \u2192 PE_elastic (the cart\u2019s motion stores energy in the spring as it expands)
2. PE_g \u2192 KE (gravitational potential energy becomes kinetic energy on a level track)
3. PE_elastic \u2192 KE (elastic potential energy decreases and becomes kinetic energy of the cart) (correct answer)
4. PE_elastic is created as the spring releases, increasing total energy

Explanation: This question tests understanding of energy transfer and energy transformations between objects in a system. Energy transformations occur when energy changes from one form to another, such as gravitational potential energy converting to kinetic energy as an object falls, or kinetic energy converting to thermal energy due to friction. When the spring is compressed by 0.20 m, elastic potential energy PE_elastic = ½kx² = ½(200 N/m)(0.20 m)² = 4.0 J is stored. When released, this potential energy converts to kinetic energy of the attached mass: at maximum speed, KE = ½mv² = 4.0 J equals the initial elastic PE (assuming no energy loss to friction). Choice C is correct because it accurately describes the energy transformation from elastic potential energy to kinetic energy. Choice D violates conservation of energy by suggesting energy is created, when actually energy only transforms from one form to another or transfers between objects. When analyzing energy transfers: (1) identify all energy forms present initially and finally, (2) apply conservation of energy (E_initial = E_final), (3) account for all energy forms including those dissipated to thermal/sound if mechanical energy decreases, and (4) remember energy can transform and transfer but never disappear. Key energy transformations to recognize: falling objects convert PE → KE, rising objects convert KE → PE, friction converts KE → thermal, collisions redistribute KE and often convert some to thermal/sound, and springs alternate between elastic PE and KE.

Question 14

1. $PE_{g,i} = 80\,\text{J}$ and $KE_f = 80\,\text{J}$ (correct answer)
2. $PE_{g,i} = 8\,\text{J}$ and $KE_f = 8\,\text{J}$
3. $PE_{g,i} = 80\,\text{J}$ and $KE_f = 40\,\text{J}$ because half the energy is lost even without friction
4. $PE_{g,i} = 80\,\text{J}$ and $KE_f = 120\,\text{J}$ because speed increases on ramps

Explanation: This question tests understanding of energy transfer and energy transformations between objects in a system. The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another or transferred between objects, so the total energy in an isolated system remains constant. In this scenario, at the top, gravitational potential energy PE_initial = mgh = (2.0 kg)(10 m/s²)(4.0 m) = 80 J, with KE_initial = 0. At the bottom, PE_final = 0, so by conservation, KE_final = ½mv² = 80 J (since frictionless, no thermal loss). Choice A is correct because it properly applies conservation of energy showing E_initial = E_final = 80 J, with PE transforming to KE. Choice C fails to account for full energy conservation, incorrectly suggesting half the energy is lost without dissipation, violating that energy only transforms. When analyzing energy transfers: (1) identify all energy forms present initially and finally, (2) apply conservation of energy (E_initial = E_final), (3) account for all energy forms including those dissipated to thermal/sound if mechanical energy decreases, and (4) remember energy can transform and transfer but never disappear.

Question 15

1. Thermal \u2192 KE (air molecules speed up the ball as it rises)
2. PE_g \u2192 KE (gravitational potential energy becomes kinetic energy as it rises)
3. KE \u2192 PE_g (kinetic energy decreases while gravitational potential energy increases) (correct answer)
4. KE is destroyed as it rises because gravity removes energy from the system

Explanation: This question tests understanding of energy transfer and energy transformations between objects in a system. Energy transformations occur when energy changes from one form to another, such as gravitational potential energy converting to kinetic energy as an object falls, or kinetic energy converting to thermal energy due to friction. In this scenario, as the ball rises, its initial kinetic energy KE_initial = ½mv² = ½(1.0 kg)(10 m/s)² = 50 J converts to gravitational potential energy, reaching maximum PE = 50 J at the top (h = v²/(2g) = 5 m). By conservation of energy, at any point, KE + PE = 50 J (ignoring air resistance). Choice C is correct because it accurately describes the energy transformation from kinetic energy to gravitational potential energy. Choice D violates conservation of energy by suggesting energy is destroyed, when actually energy only transforms from one form to another or transfers between objects. When analyzing energy transfers: (1) identify all energy forms present initially and finally, (2) apply conservation of energy (E_initial = E_final), (3) account for all energy forms including those dissipated to thermal/sound if mechanical energy decreases, and (4) remember energy can transform and transfer but never disappear. Key energy transformations to recognize: falling objects convert PE → KE, rising objects convert KE → PE, friction converts KE → thermal, collisions redistribute KE and often convert some to thermal/sound, and springs alternate between elastic PE and KE.

Question 16

1. The cart's KE is maximum and the spring's PE_elastic is minimum (approximately zero). (correct answer)
2. The cart's KE is zero and the spring's PE_elastic is maximum.
3. Both the cart's KE and the spring's PE_elastic are maximum at the unstretched length.
4. The cart's PE_g is maximum at the unstretched length because it is moving fastest there.

Explanation: This question tests understanding of energy transfer and energy transformations between objects in a system. Energy transformations occur when energy changes from one form to another, such as gravitational potential energy converting to kinetic energy as an object falls, or kinetic energy converting to thermal energy due to friction. In this scenario, when the spring is stretched by 0.30 m, elastic potential energy PE_elastic = ½kx² = ½ × 100 N/m × (0.30 m)² = 4.5 J is stored; ignoring friction, at the unstretched position, all PE_elastic converts to KE, which is maximum while PE_elastic is minimum (zero). Choice A is correct because it correctly identifies the energy states at different positions or times, with KE maximum and PE_elastic minimum at the equilibrium point. Choice B is a tempting distractor that reverses the energy transformation, claiming KE is zero when actually at the unstretched point KE is maximum while PE is minimum. When analyzing energy transfers: (1) identify all energy forms present initially and finally, (2) apply conservation of energy (E_initial = E_final), (3) account for all energy forms including those dissipated to thermal/sound if mechanical energy decreases, and (4) remember energy can transform and transfer but never disappear. Key energy transformations to recognize: falling objects convert PE → KE, rising objects convert KE → PE, friction converts KE → thermal, collisions redistribute KE and often convert some to thermal/sound, and springs alternate between elastic PE and KE.

Question 17

1. All of the initial KE is transferred into KE of the combined carts because momentum is conserved.
2. Some of the initial KE is transformed into thermal energy and sound energy during the inelastic collision. (correct answer)
3. The missing KE is destroyed because the carts stick together.
4. The missing KE becomes PE_g even though the carts remain at the same height.

Explanation: This question tests understanding of energy transfer and energy transformations between objects in a system. Energy exists in multiple forms including kinetic energy (energy of motion, KE = ½mv²), gravitational potential energy (energy due to position, PE = mgh), elastic potential energy (stored in springs, PE = ½kx²), and thermal energy (internal energy related to temperature). Before the collision, the total kinetic energy is KE_initial = ½(1.0 kg)(6.0 m/s)² + ½(2.0 kg)(0)² = 18 J. After the inelastic collision, the kinetic energy is KE_final = ½(3.0 kg)(2.0 m/s)² = 6 J, which is less than KE_initial. The missing energy was not destroyed but rather converted to thermal energy (heating the objects), sound energy, and deformation energy—this is characteristic of inelastic collisions. Choice B is correct because it correctly identifies where the lost mechanical energy went. Choice C violates conservation of energy by suggesting energy is destroyed, when actually energy only transforms from one form to another or transfers between objects. When analyzing energy transfers: (1) identify all energy forms present initially and finally, (2) apply conservation of energy (E_initial = E_final), (3) account for all energy forms including those dissipated to thermal/sound if mechanical energy decreases, and (4) remember energy can transform and transfer but never disappear. To check if energy is conserved: sum all energy forms at the initial state, sum all energy forms at the final state (including thermal if friction or inelastic collision), and verify the totals are equal—if not, identify what energy form you missed in your accounting.

Question 18

1. It is converted mainly to thermal energy (and a small amount of sound) in the carts and track (correct answer)
2. It is converted into gravitational potential energy because the carts are on a track
3. It disappears; energy is not conserved in inelastic collisions
4. It becomes additional kinetic energy of the carts, so total kinetic energy must stay the same

Explanation: This question tests understanding of energy transfer and energy transformations between objects in a system. Energy exists in multiple forms including kinetic energy (energy of motion, KE = ½mv²), gravitational potential energy (energy due to position, PE = mgh), elastic potential energy (stored in springs, PE = ½kx²), and thermal energy (internal energy related to temperature). Before the collision, the total kinetic energy is KE_initial = ½(1.5 kg)(6.0 m/s)² + ½(1.5 kg)(0)² = 27 J. After the inelastic collision, the pair moves at v_final = (1.5*6.0)/(3.0) = 3.0 m/s, so KE_final = ½(3.0 kg)(3.0 m/s)² = 13.5 J, which is less than KE_initial. The missing energy was not destroyed but rather converted to thermal energy (heating the objects), sound energy, and deformation energy—this is characteristic of inelastic collisions. Choice A is correct because it properly applies conservation of energy showing E_initial = E_final and correctly identifies where the lost mechanical energy went. Choice C violates conservation of energy by suggesting energy disappears, when actually energy only transforms from one form to another or transfers between objects. When analyzing energy transfers: (1) identify all energy forms present initially and finally, (2) apply conservation of energy (E_initial = E_final), (3) account for all energy forms including those dissipated to thermal/sound if mechanical energy decreases, and (4) remember energy can transform and transfer but never disappear.

Question 19

1. $mgh = \tfrac{1}{2}mv$
2. $mgh = \tfrac{1}{2}mv^2$ (correct answer)
3. $mgh + \tfrac{1}{2}mv^2 = 0$
4. $\tfrac{1}{2}mv^2 = mgh + 100\,\text{J}$

Explanation: This question tests understanding of energy transfer and energy transformations between objects in a system. The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another or transferred between objects, so the total energy in an isolated system remains constant. In this scenario, as the ball falls from height 5.0 m to ground level (h = 0), its gravitational potential energy decreases by ΔPE = mgh = (2.0 kg)(10 m/s²)(5.0 m) = 100 J. By conservation of energy, this decrease in PE must equal the increase in kinetic energy: the ball starts at rest (KE₁ = 0) and gains KE₂ = 100 J at the bottom, so mgh = ½mv², which is exactly what choice B states. Choice B is correct because it properly applies conservation of energy, showing that all the initial gravitational potential energy (mgh) transforms into kinetic energy (½mv²) when the ball reaches the ground. Choice A incorrectly omits the squared term on velocity in the kinetic energy formula, using ½mv instead of ½mv², which would give incorrect units (kg·m/s instead of Joules). When analyzing energy transfers: (1) identify all energy forms present initially and finally, (2) apply conservation of energy (E_initial = E_final), (3) account for all energy forms including those dissipated to thermal/sound if mechanical energy decreases, and (4) remember energy can transform and transfer but never disappear.

Question 20

1. Some of Puck A\u2019s KE is transferred to Puck B as KE, and a small amount may be converted to thermal and sound energy during the impact (correct answer)
2. Puck B gains PE_g because it starts moving on level ice
3. Energy is created during the collision, so the total kinetic energy after must be greater than before
4. All of Puck A\u2019s KE must be transferred to Puck B, so Puck A must stop completely in every collision

Explanation: This question tests understanding of energy transfer and energy transformations between objects in a system. Energy transformations occur when energy changes from one form to another, such as gravitational potential energy converting to kinetic energy as an object falls, or kinetic energy converting to thermal energy due to friction. Before the collision, Puck A's kinetic energy is KE_initial = ½(0.60 kg)(8.0 m/s)² = 19.2 J, with Puck B at 0 J. After the collision, KE is redistributed: in a nearly elastic collision on ice, most KE transfers from A to B, but some converts to thermal and sound during impact. Choice A is correct because it accurately describes the energy transfer of KE between pucks with possible small dissipation to thermal and sound. Choice C violates conservation of energy by suggesting energy is created, when actually energy only transforms from one form to another or transfers between objects. When analyzing energy transfers: (1) identify all energy forms present initially and finally, (2) apply conservation of energy (E_initial = E_final), (3) account for all energy forms including those dissipated to thermal/sound if mechanical energy decreases, and (4) remember energy can transform and transfer but never disappear. Common mistake: assuming energy is lost when mechanical energy decreases—energy is never lost, only converted to less obvious forms like thermal energy (which spreads out and can't easily be recovered for mechanical work).