Physics Quiz: Design Momentum Conservation Experiments

What this quiz covers

This quiz focuses on Design Momentum Conservation Experiments, 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. Use absolute values of all velocities so momentum is always positive.
2. Compute $p_{\text{before}}$ and $p_{\text{after}}$ using signed velocities (with +/− directions) for both carts. (correct answer)
3. Compare $v_{1i}$ to $v_{1f}$; if they match, momentum is conserved.
4. Compute momentum for only the heavier cart, since it dominates the system momentum.

Explanation: This question tests understanding of experimental design for investigating momentum conservation in collisions. To verify that momentum is conserved (p_before = p_after), an experiment must measure the masses of both colliding objects using a balance, measure their velocities before the collision (v₁ᵢ, v₂ᵢ) and after the collision (v₁f, v₂f) using motion sensors or video analysis, then calculate total momentum before (p_before = m₁v₁ᵢ + m₂v₂ᵢ) and after (p_after = m₁v₁f + m₂v₂f) to verify they are equal within experimental uncertainty. For evidence/data analysis: Evidence that momentum is conserved comes from showing that p_before and p_after are approximately equal across multiple trials—for example, if p_before = 1.45 kg⋅m/s and p_after = 1.41 kg⋅m/s, the percent difference is |1.41-1.45|/1.45 × 100% = 2.8%, which is within typical experimental uncertainty and supports conservation. Graphing p_after versus p_before for multiple trials should produce a straight line with slope = 1 passing through the origin, further confirming that the momentum after equals the momentum before regardless of initial conditions. Choice B is correct because it properly describes using signed velocities to compute p_before and p_after, accounting for direction which is essential since momentum is a vector. Choice A is a tempting distractor but fails because it suggests using absolute values of velocities, ignoring direction in 1D collisions (rightward positive, leftward negative—this matters for momentum as a vector), which would lead to incorrect total momentum calculations. When designing momentum conservation experiments, remember this checklist: (1) measure masses with a balance—this is non-negotiable since p = mv requires knowing m, (2) measure velocities at two times (immediately before and immediately after collision) using motion sensors or video analysis, (3) calculate both p_before = m₁v₁ᵢ + m₂v₂ᵢ and p_after = m₁v₁f + m₂v₂f with careful attention to direction signs (positive/negative for 1D motion), (4) compare the two values—they should be equal within about 5% for a successful demonstration, and (5) conduct multiple trials to account for random errors. Common mistakes to avoid: (a) forgetting to measure masses (cannot calculate momentum without m), (b) measuring velocities at wrong times (need immediately before and after collision, not minutes later), (c) ignoring direction in 1D collisions (rightward velocity is positive, leftward is negative—this matters for momentum as a vector), (d) comparing individual object momenta instead of system totals (conservation applies to p₁ + p₂, not to p₁ alone), and (e) expecting perfect equality (experimental uncertainty means p_before and p_after will differ by small percentage, typically 2-5% is excellent agreement).

Question 2

1. Total momentum after the collision, $p_{\text{after}}$
2. Final shared velocity after sticking, $v_f$
3. Mass ratio $m_1/m_2$ (changed by adding masses) (correct answer)
4. Percent difference between $p_{\text{before}}$ and $p_{\text{after}}$

Explanation: This question tests understanding of experimental design for investigating momentum conservation in collisions. To verify that momentum is conserved (p_before = p_after), an experiment must measure the masses of both colliding objects using a balance, measure their velocities before the collision (v₁ᵢ, v₂ᵢ) and after the collision (v₁f, v₂f) using motion sensors or video analysis, then calculate total momentum before (p_before = m₁v₁ᵢ + m₂v₂ᵢ) and after (p_after = m₁v₁f + m₂v₂f) to verify they are equal within experimental uncertainty. The measured variables (dependent on experiment) are the velocities before and after collision, which are then used with the measured masses to calculate momentum. The controlled variables (kept constant) include the surface friction (use smooth track), the collision location (mark position on track), and the collision type (elastic with magnetic bumpers or inelastic with velcro)—controlling these ensures that any momentum change isn't due to external factors. The independent variable is often the initial velocity or mass ratio, which is deliberately varied to test if momentum conservation holds under different conditions. Choice C is correct because it correctly identifies the mass ratio m₁/m₂ as the independent variable—this is what students deliberately change by adding masses to cart 2 to test how momentum conservation holds under different mass ratio conditions. Choices A, B, and D all represent dependent variables (outcomes that are measured or calculated as a result of the collision) rather than the independent variable that is deliberately manipulated by the experimenter. When designing momentum conservation experiments, remember this checklist: (1) measure masses with a balance—this is non-negotiable since p = mv requires knowing m, (2) measure velocities at two times (immediately before and immediately after collision) using motion sensors or video analysis, (3) calculate both p_before = m₁v₁ᵢ + m₂v₂ᵢ and p_after = m₁v₁f + m₂v₂f with careful attention to direction signs (positive/negative for 1D motion), (4) compare the two values—they should be equal within about 5% for a successful demonstration, and (5) conduct multiple trials to account for random errors. Common mistakes to avoid: (a) forgetting to measure masses (cannot calculate momentum without m), (b) measuring velocities at wrong times (need immediately before and after collision, not minutes later), (c) ignoring direction in 1D collisions (rightward velocity is positive, leftward is negative—this matters for momentum as a vector), (d) comparing individual object momenta instead of system totals (conservation applies to p₁ + p₂, not to p₁ alone), and (e) expecting perfect equality (experimental uncertainty means p_before and p_after will differ by small percentage, typically 2-5% is excellent agreement).

Question 3

1. In one trial, $p_{\text{after}}$ is larger than $p_{\text{before}}$ by 20%, so the system gained momentum
2. Across multiple trials with different initial speeds, $p_{\text{before}} \approx p_{\text{after}}$ each time, with percent difference typically below 5% (correct answer)
3. The carts have equal masses, so momentum must be conserved without any measurements
4. The final velocities are equal ($v_{1f}=v_{2f}$), which proves momentum is conserved

Explanation: This question tests understanding of experimental design for investigating momentum conservation in collisions. To verify that momentum is conserved (p_before = p_after), an experiment must measure the masses of both colliding objects using a balance, measure their velocities before the collision (v₁ᵢ, v₂ᵢ) and after the collision (v₁f, v₂f) using motion sensors or video analysis, then calculate total momentum before (p_before = m₁v₁ᵢ + m₂v₂ᵢ) and after (p_after = m₁v₁f + m₂v₂f) to verify they are equal within experimental uncertainty. Evidence that momentum is conserved comes from showing that p_before and p_after are approximately equal across multiple trials—for example, if p_before = 1.45 kg⋅m/s and p_after = 1.41 kg⋅m/s, the percent difference is |1.41-1.45|/1.45 × 100% = 2.8%, which is within typical experimental uncertainty and supports conservation. Graphing p_after versus p_before for multiple trials should produce a straight line with slope = 1 passing through the origin, further confirming that the momentum after equals the momentum before regardless of initial conditions. Choice B is correct because it properly describes evidence as p_before ≈ p_after within uncertainty across multiple trials. Choice D claims momentum is conserved if the velocities before equal the velocities after, but conservation of momentum means p_before = p_after (total momentum), not that individual velocities stay the same—in most collisions, velocities change dramatically even though momentum is conserved. Common mistakes to avoid: (a) forgetting to measure masses (cannot calculate momentum without m), (b) measuring velocities at wrong times (need immediately before and after collision, not minutes later), (c) ignoring direction in 1D collisions (rightward velocity is positive, leftward is negative—this matters for momentum as a vector), (d) comparing individual object momenta instead of system totals (conservation applies to p₁ + p₂, not to p₁ alone), and (e) expecting perfect equality (experimental uncertainty means p_before and p_after will differ by small percentage, typically 2-5% is excellent agreement).

Question 4

1. Use a higher-precision method for velocity (motion sensors or higher-frame-rate video), level the track carefully, and repeat multiple trials to average results (correct answer)
2. Switch from measuring momentum to measuring only kinetic energy, since energy is easier to conserve
3. Increase collision speed as much as possible so external forces are negligible
4. Change cart colors between trials to make the collision easier to see

Explanation: This question tests understanding of experimental design for investigating momentum conservation in collisions. To verify that momentum is conserved (p_before = p_after), an experiment must measure the masses of both colliding objects using a balance, measure their velocities before the collision (v₁ᵢ, v₂ᵢ) and after the collision (v₁f, v₂f) using motion sensors or video analysis, then calculate total momentum before (p_before = m₁v₁ᵢ + m₂v₂ᵢ) and after (p_after = m₁v₁f + m₂v₂f) to verify they are equal within experimental uncertainty. The essential equipment includes (1) a balance or scale to measure the masses of both objects in kilograms, which cannot be determined by observation alone, and (2) motion sensors (ultrasonic or photogate) or a video camera to measure velocities before and after the collision—without both mass and velocity data, momentum (p = mv) cannot be calculated. Additionally, a low-friction track or air track minimizes external forces that would cause momentum to not be conserved, making the experimental test valid. Choice A is correct because it identifies both essential improvements: using higher-precision velocity measurement reduces measurement uncertainty, leveling the track eliminates systematic error from gravity, and multiple trials reduce random error—all directly addressing the 12% discrepancy. Choice B suggests switching from measuring momentum to measuring only kinetic energy, but this changes what is being tested rather than improving the momentum conservation measurement. When designing momentum conservation experiments, remember this checklist: (1) measure masses with a balance—this is non-negotiable since p = mv requires knowing m, (2) measure velocities at two times (immediately before and immediately after collision) using motion sensors or video analysis, (3) calculate both p_before = m₁v₁ᵢ + m₂v₂ᵢ and p_after = m₁v₁f + m₂v₂f with careful attention to direction signs (positive/negative for 1D motion), (4) compare the two values—they should be equal within about 5% for a successful demonstration, and (5) conduct multiple trials to account for random errors. To improve experimental quality: use a low-friction track or air track to minimize external forces that would violate conservation, ensure the track is level so gravity doesn't add a constant force, use precise velocity measurement tools (motion sensors better than stopwatch/meterstick), take multiple trials and average to reduce random error, and always include uncertainty analysis showing that p_before and p_after agree within the combined measurement uncertainties.

Question 5

1. Push cart 1 into cart 2; measure only $v_{2f}$; conclude momentum is conserved if cart 2 moves.
2. Measure $m_1$ and $m_2$; set initial conditions; measure $v_{1i}$ and $v_{2i}$ just before collision; measure $v_{1f}$ and $v_{2f}$ just after; calculate $p_{\text{before}}$ and $p_{\text{after}}$; compute percent difference over multiple trials. (correct answer)
3. Measure $m_1$ and $m_2$; measure the force during collision; conclude momentum is conserved if the peak force is the same each time.
4. Set the carts to collide; measure how long the collision lasts; conclude momentum is conserved if the collision time is short.

Explanation: This question tests understanding of experimental design for investigating momentum conservation in collisions. To verify that momentum is conserved (p_before = p_after), an experiment must measure the masses of both colliding objects using a balance, measure their velocities before the collision (v₁ᵢ, v₂ᵢ) and after the collision (v₁f, v₂f) using motion sensors or video analysis, then calculate total momentum before (p_before = m₁v₁ᵢ + m₂v₂ᵢ) and after (p_after = m₁v₁f + m₂v₂f) to verify they are equal within experimental uncertainty. The experimental procedure must include these key steps: (1) measure and record the masses m₁ and m₂ of both objects before the collision, (2) set up the collision scenario with one object moving and one at rest (or both moving), (3) measure and record the velocities v₁ᵢ and v₂ᵢ immediately before collision using motion sensors or video analysis, (4) allow the collision to occur, (5) measure and record velocities v₁f and v₂f immediately after collision, (6) calculate p_before = m₁v₁ᵢ + m₂v₂ᵢ and p_after = m₁v₁f + m₂v₂f, then (7) compare the two values using percent difference = |p_after - p_before|/p_before × 100%—if percent difference is small (typically <5%), momentum is conserved within experimental uncertainty. Choice B is correct because it describes a complete procedure including measuring masses, measuring velocities before and after, calculating both momenta, and comparing them over multiple trials. Choice C is a tempting distractor but fails because it focuses on measuring the force during collision or the time duration, when actually momentum conservation can be verified more simply by measuring masses and velocities before and after, without needing to analyze the collision itself. When designing momentum conservation experiments, remember this checklist: (1) measure masses with a balance—this is non-negotiable since p = mv requires knowing m, (2) measure velocities at two times (immediately before and immediately after collision) using motion sensors or video analysis, (3) calculate both p_before = m₁v₁ᵢ + m₂v₂ᵢ and p_after = m₁v₁f + m₂v₂f with careful attention to direction signs (positive/negative for 1D motion), (4) compare the two values—they should be equal within about 5% for a successful demonstration, and (5) conduct multiple trials to account for random errors. To improve experimental quality: use a low-friction track or air track to minimize external forces that would violate conservation, ensure the track is level so gravity doesn't add a constant force, use precise velocity measurement tools (motion sensors better than stopwatch/meterstick), take multiple trials and average to reduce random error, and always include uncertainty analysis showing that p_before and p_after agree within the combined measurement uncertainties.

Question 6

1. Motion sensors and a meter stick
2. Video camera with analysis software and a meter stick
3. Balance/scale and motion sensors (correct answer)
4. Balance/scale and a meter stick

Explanation: This question tests understanding of experimental design for investigating momentum conservation in collisions by selecting essential equipment. To verify that momentum is conserved (p_before = p_after), an experiment must measure the masses of both colliding objects using a balance, measure their velocities before the collision (v₁ᵢ, v₂ᵢ) and after the collision (v₁f, v₂f) using motion sensors or video analysis, then calculate total momentum before (p_before = m₁v₁ᵢ + m₂v₂ᵢ) and after (p_after = m₁v₁f + m₂v₂f) to verify they are equal within experimental uncertainty. For essential equipment: The essential equipment includes (1) a balance or scale to measure the masses of both objects in kilograms, which cannot be determined by observation alone, and (2) motion sensors (ultrasonic or photogate) or a video camera to measure velocities before and after the collision—without both mass and velocity data, momentum (p = mv) cannot be calculated; additionally, a low-friction track or air track minimizes external forces that would cause momentum to not be conserved, making the experimental test valid. Choice C is correct because it identifies both essential equipment: balance for mass and motion sensors for velocity, which are necessary to calculate p = mv with the least ambiguity. Choice D is a tempting distractor but fails because it lists equipment for measuring mass but omits precise velocity tools like motion sensors—using only a meter stick would require less accurate methods like stopwatch timing, increasing uncertainty in verifying conservation. When designing momentum conservation experiments, remember this checklist: (1) measure masses with a balance—this is non-negotiable since p = mv requires knowing m, (2) measure velocities at two times (immediately before and immediately after collision) using motion sensors or video analysis, (3) calculate both p_before = m₁v₁ᵢ + m₂v₂ᵢ and p_after = m₁v₁f + m₂v₂f with careful attention to direction signs (positive/negative for 1D motion), (4) compare the two values—they should be equal within about 5% for a successful demonstration, and (5) conduct multiple trials to account for random errors. To improve experimental quality: use a low-friction track or air track to minimize external forces that would violate conservation, ensure the track is level so gravity doesn't add a constant force, use precise velocity measurement tools (motion sensors better than stopwatch/meterstick), take multiple trials and average to reduce random error, and always include uncertainty analysis showing that p_before and p_after agree within the combined measurement uncertainties.

Question 7

1. Balance/scale and motion sensors (to measure $m_1, m_2$ and velocities before/after the collision). (correct answer)
2. Meter stick and stopwatch (to estimate average speeds over a long distance).
3. Motion sensors only (mass is not needed because the sensors measure momentum directly).
4. Balance/scale only (if masses are known, momentum conservation can be checked without velocities).

Explanation: This question tests understanding of experimental design for investigating momentum conservation in collisions. To verify that momentum is conserved (p_before = p_after), an experiment must measure the masses of both colliding objects using a balance, measure their velocities before the collision (v₁ᵢ, v₂ᵢ) and after the collision (v₁f, v₂f) using motion sensors or video analysis, then calculate total momentum before (p_before = m₁v₁ᵢ + m₂v₂ᵢ) and after (p_after = m₁v₁f + m₂v₂f) to verify they are equal within experimental uncertainty. The essential equipment includes (1) a balance or scale to measure the masses of both objects in kilograms, which cannot be determined by observation alone, and (2) motion sensors (ultrasonic or photogate) or a video camera to measure velocities before and after the collision—without both mass and velocity data, momentum (p = mv) cannot be calculated. Additionally, a low-friction track or air track minimizes external forces that would cause momentum to not be conserved, making the experimental test valid. Choice A is correct because it identifies both essential equipment: balance for mass and motion sensors for velocity, which are necessary to calculate p = mv. Choice C lists equipment for measuring velocity but omits a balance for measuring mass—without knowing the masses, momentum p = mv cannot be calculated, making it impossible to verify conservation. When designing momentum conservation experiments, remember this checklist: (1) measure masses with a balance—this is non-negotiable since p = mv requires knowing m, (2) measure velocities at two times (immediately before and immediately after collision) using motion sensors or video analysis, (3) calculate both p_before = m₁v₁ᵢ + m₂v₂ᵢ and p_after = m₁v₁f + m₂v₂f with careful attention to direction signs (positive/negative for 1D motion), (4) compare the two values—they should be equal within about 5% for a successful demonstration, and (5) conduct multiple trials to account for random errors. To improve experimental quality: use a low-friction track or air track to minimize external forces that would violate conservation, ensure the track is level so gravity doesn't add a constant force, use precise velocity measurement tools (motion sensors better than stopwatch/meterstick), take multiple trials and average to reduce random error, and always include uncertainty analysis showing that p_before and p_after agree within the combined measurement uncertainties.

Question 8

1. Momentum is conserved only if kinetic energy is also conserved
2. Momentum is conserved if each cart’s individual momentum stays the same through the collision
3. Momentum is conserved if the system total satisfies $p_{\text{before}} \approx p_{\text{after}}$ within experimental uncertainty (e.g., percent difference $<5\%$) over multiple trials (correct answer)
4. Momentum is conserved if the carts exchange velocities exactly in every collision

Explanation: This question tests understanding of experimental design for investigating momentum conservation in collisions. To verify that momentum is conserved (p_before = p_after), an experiment must measure the masses of both colliding objects using a balance, measure their velocities before the collision (v₁ᵢ, v₂ᵢ) and after the collision (v₁f, v₂f) using motion sensors or video analysis, then calculate total momentum before (p_before = m₁v₁ᵢ + m₂v₂ᵢ) and after (p_after = m₁v₁f + m₂v₂f) to verify they are equal within experimental uncertainty. Evidence that momentum is conserved comes from showing that p_before and p_after are approximately equal across multiple trials—for example, if p_before = 1.45 kg⋅m/s and p_after = 1.41 kg⋅m/s, the percent difference is |1.41-1.45|/1.45 × 100% = 2.8%, which is within typical experimental uncertainty and supports conservation. Choice C is correct because it properly describes evidence as p_before ≈ p_after within uncertainty (e.g., percent difference <5%) across multiple trials, which is the correct criterion for momentum conservation regardless of whether the collision is elastic or inelastic. Choice A claims momentum is conserved only if kinetic energy is also conserved, but conservation of momentum applies to all collisions while kinetic energy is only conserved in elastic collisions—momentum conservation is more fundamental. When designing momentum conservation experiments, remember this checklist: (1) measure masses with a balance—this is non-negotiable since p = mv requires knowing m, (2) measure velocities at two times (immediately before and immediately after collision) using motion sensors or video analysis, (3) calculate both p_before = m₁v₁ᵢ + m₂v₂ᵢ and p_after = m₁v₁f + m₂v₂f with careful attention to direction signs (positive/negative for 1D motion), (4) compare the two values—they should be equal within about 5% for a successful demonstration, and (5) conduct multiple trials to account for random errors. Common mistakes to avoid: (a) forgetting to measure masses (cannot calculate momentum without m), (b) measuring velocities at wrong times (need immediately before and after collision, not minutes later), (c) ignoring direction in 1D collisions (rightward velocity is positive, leftward is negative—this matters for momentum as a vector), (d) comparing individual object momenta instead of system totals (conservation applies to p₁ + p₂, not to p₁ alone), and (e) expecting perfect equality (experimental uncertainty means p_before and p_after will differ by small percentage, typically 2-5% is excellent agreement).

Question 9

1. Do multiple trials for each setup and average the calculated $p_{\text{before}}$ and $p_{\text{after}}$ (correct answer)
2. Use different colored carts so they are easier to see
3. Increase the collision speed as much as possible so the carts make a louder sound
4. Measure only one cart’s velocity (the other cart’s velocity can be assumed to be zero)

Explanation: This question tests understanding of experimental design for investigating momentum conservation in collisions. To verify that momentum is conserved (p_before = p_after), an experiment must measure the masses of both colliding objects using a balance, measure their velocities before the collision (v₁ᵢ, v₂ᵢ) and after the collision (v₁f, v₂f) using motion sensors or video analysis, then calculate total momentum before (p_before = m₁v₁ᵢ + m₂v₂ᵢ) and after (p_after = m₁v₁f + m₂v₂f) to verify they are equal within experimental uncertainty. Evidence that momentum is conserved comes from showing that p_before and p_after are approximately equal across multiple trials—for example, if p_before = 1.45 kg⋅m/s and p_after = 1.41 kg⋅m/s, the percent difference is |1.41-1.45|/1.45 × 100% = 2.8%, which is within typical experimental uncertainty and supports conservation. Choice A is correct because it describes conducting multiple trials and averaging to reduce random error, which directly improves the reliability and precision of the momentum comparison by reducing the uncertainty in the calculated values. Choice D suggests measuring only one cart's velocity (the other cart's velocity can be assumed to be zero), but this would introduce systematic error since both carts typically move after collision—momentum conservation requires comparing the total momentum of the system (both objects together) before and after collision. When designing momentum conservation experiments, remember this checklist: (1) measure masses with a balance—this is non-negotiable since p = mv requires knowing m, (2) measure velocities at two times (immediately before and immediately after collision) using motion sensors or video analysis, (3) calculate both p_before = m₁v₁ᵢ + m₂v₂ᵢ and p_after = m₁v₁f + m₂v₂f with careful attention to direction signs (positive/negative for 1D motion), (4) compare the two values—they should be equal within about 5% for a successful demonstration, and (5) conduct multiple trials to account for random errors. To improve experimental quality: use a low-friction track or air track to minimize external forces that would violate conservation, ensure the track is level so gravity doesn't add a constant force, use precise velocity measurement tools (motion sensors better than stopwatch/meterstick), take multiple trials and average to reduce random error, and always include uncertainty analysis showing that p_before and p_after agree within the combined measurement uncertainties.

Question 10

1. In one trial, $p_{\text{before}}$ equals $p_{\text{after}}$ exactly, but other trials differ by 15–20%
2. Across all trials, $p_{\text{after}}$ is consistently within about 5% of $p_{\text{before}}$ using the same sign convention (correct answer)
3. The carts have the same speed after the collision, so momentum must be conserved
4. Kinetic energy before and after is the same in every trial, so momentum must be conserved

Explanation: This question tests understanding of experimental design for investigating momentum conservation in collisions. To verify that momentum is conserved (p_before = p_after), an experiment must measure the masses of both colliding objects using a balance, measure their velocities before the collision (v₁ᵢ, v₂ᵢ) and after the collision (v₁f, v₂f) using motion sensors or video analysis, then calculate total momentum before (p_before = m₁v₁ᵢ + m₂v₂ᵢ) and after (p_after = m₁v₁f + m₂v₂f) to verify they are equal within experimental uncertainty. Evidence that momentum is conserved comes from showing that p_before and p_after are approximately equal across multiple trials—for example, if p_before = 1.45 kg⋅m/s and p_after = 1.41 kg⋅m/s, the percent difference is |1.41-1.45|/1.45 × 100% = 2.8%, which is within typical experimental uncertainty and supports conservation. Graphing p_after versus p_before for multiple trials should produce a straight line with slope = 1 passing through the origin, further confirming that the momentum after equals the momentum before regardless of initial conditions. Choice B is correct because it properly describes evidence as p_before ≈ p_after within uncertainty across multiple trials—consistency across all trials with small percent differences (about 5%) provides strong evidence for conservation. Choice A describes inconsistent results where only one trial shows conservation while others differ by 15-20%, which actually suggests experimental problems rather than momentum conservation. When designing momentum conservation experiments, remember this checklist: (1) measure masses with a balance—this is non-negotiable since p = mv requires knowing m, (2) measure velocities at two times (immediately before and immediately after collision) using motion sensors or video analysis, (3) calculate both p_before = m₁v₁ᵢ + m₂v₂ᵢ and p_after = m₁v₁f + m₂v₂f with careful attention to direction signs (positive/negative for 1D motion), (4) compare the two values—they should be equal within about 5% for a successful demonstration, and (5) conduct multiple trials to account for random errors. Common mistakes to avoid: (a) forgetting to measure masses (cannot calculate momentum without m), (b) measuring velocities at wrong times (need immediately before and after collision, not minutes later), (c) ignoring direction in 1D collisions (rightward velocity is positive, leftward is negative—this matters for momentum as a vector), (d) comparing individual object momenta instead of system totals (conservation applies to p₁ + p₂, not to p₁ alone), and (e) expecting perfect equality (experimental uncertainty means p_before and p_after will differ by small percentage, typically 2-5% is excellent agreement).

Question 11

1. Use a consistent sign convention so leftward velocities are negative and rightward velocities are positive in both $p_{before}$ and $p_{after}$. (correct answer)
2. Use absolute values of all velocities so momentum is always positive.
3. Ignore the velocity of cart 2 because only the moving cart contributes to system momentum.
4. Convert masses to grams so the momentum units match m/s.

Explanation: This question tests understanding of experimental design for investigating momentum conservation in collisions, particularly data-handling rules to avoid systematic errors in calculations. To verify that momentum is conserved (p_before = p_after), an experiment must measure the masses of both colliding objects using a balance, measure their velocities before the collision (v₁ᵢ, v₂ᵢ) and after the collision (v₁f, v₂f) using motion sensors or video analysis, then calculate total momentum before (p_before = m₁v₁ᵢ + m₂v₂ᵢ) and after (p_after = m₁v₁f + m₂v₂f) to verify they are equal within experimental uncertainty. For data analysis in a head-on collision where directions oppose, the procedure must include assigning consistent signs (e.g., rightward positive, leftward negative) to all velocities, ensuring the vector nature of momentum is respected; controlled variables like track friction should be minimized, and multiple trials help confirm consistency. Choice A is correct because it emphasizes using a consistent sign convention for directions in both p_before and p_after calculations, which is crucial to avoid systematic errors in vector summation for 1D momentum. Choice B is a tempting distractor but fails because using absolute values ignores the vector nature of momentum—momentum can cancel (e.g., in head-on collisions), and treating all as positive would incorrectly suggest non-conservation or inflate values. When designing momentum conservation experiments, remember this checklist: (1) measure masses with a balance—this is non-negotiable since p = mv requires knowing m, (2) measure velocities at two times (immediately before and immediately after collision) using motion sensors or video analysis, (3) calculate both p_before = m₁v₁ᵢ + m₂v₂ᵢ and p_after = m₁v₁f + m₂v₂f with careful attention to direction signs (positive/negative for 1D motion), (4) compare the two values—they should be equal within about 5% for a successful demonstration, and (5) conduct multiple trials to account for random errors. Common mistakes to avoid: (a) forgetting to measure masses (cannot calculate momentum without m), (b) measuring velocities at wrong times (need immediately before and after collision, not minutes later), (c) ignoring direction in 1D collisions (rightward velocity is positive, leftward is negative—this matters for momentum as a vector), (d) comparing individual object momenta instead of system totals (conservation applies to p₁ + p₂, not to p₁ alone), and (e) expecting perfect equality (experimental uncertainty means p_before and p_after will differ by small percentage, typically 2-5% is excellent agreement).

Question 12

1. Run one collision, record only $v_{1f}$ and $v_{2f}$, and conclude momentum is conserved if the carts move slower afterward.
2. Measure $m_1$ and $m_2$ with a balance, measure $v_{1i}, v_{2i}$ just before collision and $v_{1f}, v_{2f}$ just after collision, compute $p_{before}$ and $p_{after}$, then repeat multiple trials and compare using percent difference. (correct answer)
3. Measure $m_1$ and $m_2$, then calculate theoretical velocities from formulas without measuring any velocities, and compare the theory to itself.
4. Measure the time the carts are in contact during collision and use that time to prove momentum is conserved.

Explanation: This question tests understanding of experimental design for investigating momentum conservation in collisions, emphasizing the procedure sequence for reliable verification. To verify that momentum is conserved (p_before = p_after), an experiment must measure the masses of both colliding objects using a balance, measure their velocities before the collision (v₁ᵢ, v₂ᵢ) and after the collision (v₁f, v₂f) using motion sensors or video analysis, then calculate total momentum before (p_before = m₁v₁ᵢ + m₂v₂ᵢ) and after (p_after = m₁v₁f + m₂v₂f) to verify they are equal within experimental uncertainty. The experimental procedure must include these key steps: (1) measure and record the masses m₁ and m₂ of both objects before the collision, (2) set up the collision scenario with one object moving and one at rest (or both moving), (3) measure and record the velocities v₁ᵢ and v₂ᵢ immediately before collision using motion sensors or video analysis, (4) allow the collision to occur, (5) measure and record velocities v₁f and v₂f immediately after collision, (6) calculate p_before = m₁v₁ᵢ + m₂v₂ᵢ and p_after = m₁v₁f + m₂v₂f, then (7) compare the two values using percent difference = |p_after - p_before|/p_before × 100%—if percent difference is small (typically <5%), momentum is conserved within experimental uncertainty. Choice B is correct because it describes a complete procedure including measuring masses, measuring velocities before and after, calculating both momenta, and comparing them across multiple trials to account for uncertainty. Choice A is a tempting distractor but fails because it describes a procedure that measures velocities only after the collision and relies on qualitative observation (slower motion)—momentum conservation requires quantitative comparison of p_before to p_after, and a single trial without full data cannot verify it reliably. When designing momentum conservation experiments, remember this checklist: (1) measure masses with a balance—this is non-negotiable since p = mv requires knowing m, (2) measure velocities at two times (immediately before and immediately after collision) using motion sensors or video analysis, (3) calculate both p_before = m₁v₁ᵢ + m₂v₂ᵢ and p_after = m₁v₁f + m₂v₂f with careful attention to direction signs (positive/negative for 1D motion), (4) compare the two values—they should be equal within about 5% for a successful demonstration, and (5) conduct multiple trials to account for random errors. To improve experimental quality: use a low-friction track or air track to minimize external forces that would violate conservation, ensure the track is level so gravity doesn't add a constant force, use precise velocity measurement tools (motion sensors better than stopwatch/meterstick), take multiple trials and average to reduce random error, and always include uncertainty analysis showing that p_before and p_after agree within the combined measurement uncertainties.

Question 13

1. Measure $m_1$ and $m_2$ with a balance and measure $v_{1i}, v_{2i}, v_{1f}, v_{2f}$ with motion sensors (or video analysis). (correct answer)
2. Measure only $v_{1f}$ and $v_{2f}$ after the collision; initial velocities are not needed if the track is low friction.
3. Measure only $m_1$ and $m_2$; if masses are known, momentum conservation can be assumed without velocity data.
4. Measure the collision sound level and the cart colors to distinguish elastic from inelastic collisions.

Explanation: This question tests understanding of experimental design for investigating momentum conservation in collisions, specifically the essential measurements needed for different collision types. To verify that momentum is conserved (p_before = p_after), an experiment must measure the masses of both colliding objects using a balance, measure their velocities before the collision (v₁ᵢ, v₂ᵢ) and after the collision (v₁f, v₂f) using motion sensors or video analysis, then calculate total momentum before (p_before = m₁v₁ᵢ + m₂v₂ᵢ) and after (p_after = m₁v₁f + m₂v₂f) to verify they are equal within experimental uncertainty. For essential measurements in comparing elastic and inelastic collisions, the procedure requires determining masses m₁ and m₂ with a balance (as they cannot be assumed) and velocities before and after with precise tools like motion sensors or video to enable momentum calculations for both types, while controlling factors like track friction to ensure validity. Choice A is correct because it identifies both essential measurements: masses with a balance and velocities with motion sensors or video analysis, which are necessary to calculate p = mv for the system before and after. Choice B is a tempting distractor but fails because it omits initial velocities—momentum conservation requires comparing p_before (which needs v₁ᵢ and v₂ᵢ) to p_after, so both sets are essential, and low friction alone does not eliminate the need for initial data. When designing momentum conservation experiments, remember this checklist: (1) measure masses with a balance—this is non-negotiable since p = mv requires knowing m, (2) measure velocities at two times (immediately before and immediately after collision) using motion sensors or video analysis, (3) calculate both p_before = m₁v₁ᵢ + m₂v₂ᵢ and p_after = m₁v₁f + m₂v₂f with careful attention to direction signs (positive/negative for 1D motion), (4) compare the two values—they should be equal within about 5% for a successful demonstration, and (5) conduct multiple trials to account for random errors. To improve experimental quality: use a low-friction track or air track to minimize external forces that would violate conservation, ensure the track is level so gravity doesn't add a constant force, use precise velocity measurement tools (motion sensors better than stopwatch/meterstick), take multiple trials and average to reduce random error, and always include uncertainty analysis showing that p_before and p_after agree within the combined measurement uncertainties.

Question 14

1. Level the track carefully, use the same collision point each time, and perform multiple trials then average the calculated $p_{before}$ and $p_{after}$ values. (correct answer)
2. Replace the balance with a meter stick because distance measurements are more important than mass.
3. Increase the collision speed as much as possible so friction becomes irrelevant.
4. Switch from measuring velocities to measuring only the carts’ kinetic energies to avoid sign errors.

Explanation: This question tests understanding of experimental design for investigating momentum conservation in collisions, focusing on reducing uncertainty in percent difference calculations. To verify that momentum is conserved (p_before = p_after), an experiment must measure the masses of both colliding objects using a balance, measure their velocities before the collision (v₁ᵢ, v₂ᵢ) and after the collision (v₁f, v₂f) using motion sensors or video analysis, then calculate total momentum before (p_before = m₁v₁ᵢ + m₂v₂ᵢ) and after (p_after = m₁v₁f + m₂v₂f) to verify they are equal within experimental uncertainty. For improving the design when percent differences are high (12–15%), key steps include controlling variables like track levelness to minimize gravity effects, using consistent collision points to reduce positional errors, and averaging multiple trials to mitigate random uncertainties in velocity measurements, all while maintaining low friction for validity. Choice A is correct because it addresses sources of systematic and random error by leveling the track (controls gravity), using the same collision point (consistency), and averaging multiple trials, directly reducing uncertainty without altering the core physics. Choice C is a tempting distractor but fails because increasing collision speed might amplify friction effects or sensor inaccuracies rather than reduce them—higher speeds do not inherently make friction irrelevant, and could introduce more uncertainty from air resistance or imprecise timing. When designing momentum conservation experiments, remember this checklist: (1) measure masses with a balance—this is non-negotiable since p = mv requires knowing m, (2) measure velocities at two times (immediately before and immediately after collision) using motion sensors or video analysis, (3) calculate both p_before = m₁v₁ᵢ + m₂v₂ᵢ and p_after = m₁v₁f + m₂v₂f with careful attention to direction signs (positive/negative for 1D motion), (4) compare the two values—they should be equal within about 5% for a successful demonstration, and (5) conduct multiple trials to account for random errors. Common mistakes to avoid: (a) forgetting to measure masses (cannot calculate momentum without m), (b) measuring velocities at wrong times (need immediately before and after collision, not minutes later), (c) ignoring direction in 1D collisions (rightward velocity is positive, leftward is negative—this matters for momentum as a vector), (d) comparing individual object momenta instead of system totals (conservation applies to p₁ + p₂, not to p₁ alone), and (e) expecting perfect equality (experimental uncertainty means p_before and p_after will differ by small percentage, typically 2-5% is excellent agreement).

Question 15

1. It is sufficient because force is the same as momentum, so velocity data are unnecessary.
2. It is insufficient because without measuring velocities (before and after), you cannot directly compute $p_{\text{before}}$ and $p_{\text{after}}$ from $p=mv$. (correct answer)
3. It is sufficient because the collision force is always zero on a low-friction track.
4. It is insufficient because masses do not matter in momentum calculations.

Explanation: This question tests understanding of experimental design for investigating momentum conservation in collisions by evaluating a proposal to use only force sensors. To verify that momentum is conserved (p_before = p_after), an experiment must measure the masses of both colliding objects using a balance, measure their velocities before the collision (v₁ᵢ, v₂ᵢ) and after the collision (v₁f, v₂f) using motion sensors or video analysis, then calculate total momentum before (p_before = m₁v₁ᵢ + m₂v₂ᵢ) and after (p_after = m₁v₁f + m₂v₂f) to verify they are equal within experimental uncertainty. For essential equipment and procedure: The essential equipment includes (1) a balance or scale to measure the masses of both objects in kilograms, which cannot be determined by observation alone, and (2) motion sensors (ultrasonic or photogate) or a video camera to measure velocities before and after the collision—without both mass and velocity data, momentum (p = mv) cannot be calculated; additionally, a low-friction track or air track minimizes external forces that would cause momentum to not be conserved, making the experimental test valid, but force sensors measure impulse (∫F dt = Δp), which can indirectly check change in momentum but not directly compare total p_before and p_after without velocity data. Choice B is correct because it explains that the proposal is insufficient without velocity measurements to directly compute p_before and p_after using p = mv, as required for the lab goal. Choice A is a tempting distractor but fails because it claims force is the same as momentum, when actually momentum conservation can be verified more simply by measuring masses and velocities before and after, without needing to analyze the collision itself via forces. When designing momentum conservation experiments, remember this checklist: (1) measure masses with a balance—this is non-negotiable since p = mv requires knowing m, (2) measure velocities at two times (immediately before and immediately after collision) using motion sensors or video analysis, (3) calculate both p_before = m₁v₁ᵢ + m₂v₂ᵢ and p_after = m₁v₁f + m₂v₂f with careful attention to direction signs (positive/negative for 1D motion), (4) compare the two values—they should be equal within about 5% for a successful demonstration, and (5) conduct multiple trials to account for random errors. Common mistakes to avoid: (a) forgetting to measure masses (cannot calculate momentum without m), (b) measuring velocities at wrong times (need immediately before and after collision, not minutes later), (c) ignoring direction in 1D collisions (rightward velocity is positive, leftward is negative—this matters for momentum as a vector), (d) comparing individual object momenta instead of system totals (conservation applies to p₁ + p₂, not to p₁ alone), and (e) expecting perfect equality (experimental uncertainty means p_before and p_after will differ by small percentage, typically 2-5% is excellent agreement).

Question 16

1. Measure $m_1$ and $m_2$ only; momentum conservation can be checked without measuring velocities.
2. Measure $v_{1i}$ and $v_{2i}$ only; if the carts start on a low-friction track, then $p_{\text{after}}$ must equal $p_{\text{before}}$.
3. Measure $m_1$, $m_2$, $v_{1i}$, $v_{2i}$, $v_{1f}$, and $v_{2f}$ for each trial, then compare $p_{\text{before}}$ to $p_{\text{after}}$. (correct answer)
4. Measure $v_{1f}$ and $v_{2f}$ only; if the carts stick (inelastic), momentum conservation is confirmed automatically.

Explanation: This question tests understanding of experimental design for investigating momentum conservation in collisions by identifying the minimum essential measurements needed. To verify that momentum is conserved (p_before = p_after), an experiment must measure the masses of both colliding objects using a balance, measure their velocities before the collision (v₁ᵢ, v₂ᵢ) and after the collision (v₁f, v₂f) using motion sensors or video analysis, then calculate total momentum before (p_before = m₁v₁ᵢ + m₂v₂ᵢ) and after (p_after = m₁v₁f + m₂v₂f) to verify they are equal within experimental uncertainty. For essential measurements in this elastic vs inelastic comparison: The minimum set includes measuring m₁, m₂, v₁ᵢ, v₂ᵢ, v₁f, and v₂f for each trial and collision type, as these allow direct calculation of p_before and p_after without assuming outcomes based on collision type—equipment like motion sensors or video analysis ensures accurate velocity data, while a balance provides masses. Choice C is correct because it identifies the complete set of essential measurements (masses and all velocities) necessary to calculate and compare p_before to p_after for both elastic and inelastic collisions. Choice A is a tempting distractor but fails because it suggests measuring only masses without velocities, which prevents calculating momentum since p = mv requires both m and v. When designing momentum conservation experiments, remember this checklist: (1) measure masses with a balance—this is non-negotiable since p = mv requires knowing m, (2) measure velocities at two times (immediately before and immediately after collision) using motion sensors or video analysis, (3) calculate both p_before = m₁v₁ᵢ + m₂v₂ᵢ and p_after = m₁v₁f + m₂v₂f with careful attention to direction signs (positive/negative for 1D motion), (4) compare the two values—they should be equal within about 5% for a successful demonstration, and (5) conduct multiple trials to account for random errors. Common mistakes to avoid: (a) forgetting to measure masses (cannot calculate momentum without m), (b) measuring velocities at wrong times (need immediately before and after collision, not minutes later), (c) ignoring direction in 1D collisions (rightward velocity is positive, leftward is negative—this matters for momentum as a vector), (d) comparing individual object momenta instead of system totals (conservation applies to p₁ + p₂, not to p₁ alone), and (e) expecting perfect equality (experimental uncertainty means p_before and p_after will differ by small percentage, typically 2-5% is excellent agreement).

Question 17

1. $p_{\text{after}} = m_1v_{1f} + m_2v_{2f}$ (using the chosen sign convention for $v_{1f}$ and $v_{2f}$) (correct answer)
2. $p_{\text{after}} = (m_1+m_2)(v_{1f}+v_{2f})$
3. $p_{\text{after}} = m_1 + m_2 + v_{1f} + v_{2f}$
4. $p_{\text{after}} = \frac{m_1}{v_{1f}} + \frac{m_2}{v_{2f}}$

Explanation: This question tests understanding of experimental design for investigating momentum conservation in collisions by selecting the correct calculation for total momentum after collision. To verify that momentum is conserved (p_before = p_after), an experiment must measure the masses of both colliding objects using a balance, measure their velocities before the collision (v₁ᵢ, v₂ᵢ) and after the collision (v₁f, v₂f) using motion sensors or video analysis, then calculate total momentum before (p_before = m₁v₁ᵢ + m₂v₂ᵢ) and after (p_after = m₁v₁f + m₂v₂f) to verify they are equal within experimental uncertainty. For data analysis: Evidence that momentum is conserved comes from showing that p_before and p_after are approximately equal across multiple trials—for example, if p_before = 1.45 kg⋅m/s and p_after = 1.41 kg⋅m/s, the percent difference is |1.41-1.45|/1.45 × 100% = 2.8%, which is within typical experimental uncertainty and supports conservation; graphing p_after versus p_before for multiple trials should produce a straight line with slope = 1 passing through the origin, further confirming that the momentum after equals the momentum before regardless of initial conditions. Choice A is correct because it properly calculates p_after as the sum of individual momenta m₁v₁f + m₂v₂f, using signs for direction, which is essential for verifying conservation in 1D collisions. Choice B is a tempting distractor but fails because it incorrectly multiplies the total mass by the sum of velocities, which would only apply if velocities were the same (as in perfectly inelastic collisions where they stick), but not generally for all collision types. When designing momentum conservation experiments, remember this checklist: (1) measure masses with a balance—this is non-negotiable since p = mv requires knowing m, (2) measure velocities at two times (immediately before and immediately after collision) using motion sensors or video analysis, (3) calculate both p_before = m₁v₁ᵢ + m₂v₂ᵢ and p_after = m₁v₁f + m₂v₂f with careful attention to direction signs (positive/negative for 1D motion), (4) compare the two values—they should be equal within about 5% for a successful demonstration, and (5) conduct multiple trials to account for random errors. Common mistakes to avoid: (a) forgetting to measure masses (cannot calculate momentum without m), (b) measuring velocities at wrong times (need immediately before and after collision, not minutes later), (c) ignoring direction in 1D collisions (rightward velocity is positive, leftward is negative—this matters for momentum as a vector), (d) comparing individual object momenta instead of system totals (conservation applies to p₁ + p₂, not to p₁ alone), and (e) expecting perfect equality (experimental uncertainty means p_before and p_after will differ by small percentage, typically 2-5% is excellent agreement).

Question 18

1. Final velocities $v_{1f}$ and $v_{2f}$
2. Mass ratio $m_1/m_2$ (set by adding masses to one cart) (correct answer)
3. Total momentum $p_{\text{after}}$
4. Track friction (because it changes during the trial)

Explanation: This question tests understanding of experimental design for investigating momentum conservation in collisions by identifying the independent variable in a mass ratio study. To verify that momentum is conserved (p_before = p_after), an experiment must measure the masses of both colliding objects using a balance, measure their velocities before the collision (v₁ᵢ, v₂ᵢ) and after the collision (v₁f, v₂f) using motion sensors or video analysis, then calculate total momentum before (p_before = m₁v₁ᵢ + m₂v₂ᵢ) and after (p_after = m₁v₁f + m₂v₂f) to verify they are equal within experimental uncertainty. For variables: The measured variables (dependent on experiment) are the velocities before and after collision, which are then used with the measured masses to calculate momentum; the controlled variables (kept constant) include the surface friction (use smooth track), the collision location (mark position on track), and the collision type (elastic with magnetic bumpers or inelastic with velcro)—controlling these ensures that any momentum change isn't due to external factors; the independent variable is often the initial velocity or mass ratio, which is deliberately varied to test if momentum conservation holds under different conditions. Choice B is correct because it correctly identifies the mass ratio m₁/m₂ as the independent variable, which is deliberately varied by adding masses to test its effect on final velocities while verifying conservation. Choice A is a tempting distractor but fails because it confuses measured variables with controlled variables, suggesting that final velocities should be the independent variable when actually final velocities are dependent variables that result from the collision and are measured to calculate p_after. When designing momentum conservation experiments, remember this checklist: (1) measure masses with a balance—this is non-negotiable since p = mv requires knowing m, (2) measure velocities at two times (immediately before and immediately after collision) using motion sensors or video analysis, (3) calculate both p_before = m₁v₁ᵢ + m₂v₂ᵢ and p_after = m₁v₁f + m₂v₂f with careful attention to direction signs (positive/negative for 1D motion), (4) compare the two values—they should be equal within about 5% for a successful demonstration, and (5) conduct multiple trials to account for random errors. Common mistakes to avoid: (a) forgetting to measure masses (cannot calculate momentum without m), (b) measuring velocities at wrong times (need immediately before and after collision, not minutes later), (c) ignoring direction in 1D collisions (rightward velocity is positive, leftward is negative—this matters for momentum as a vector), (d) comparing individual object momenta instead of system totals (conservation applies to p₁ + p₂, not to p₁ alone), and (e) expecting perfect equality (experimental uncertainty means p_before and p_after will differ by small percentage, typically 2-5% is excellent agreement).

Question 19

1. Plot $p_{\text{after}}$ vs $p_{\text{before}}$ for all trials; momentum conservation is supported if points lie near a 1:1 line (slope $\approx 1$). (correct answer)
2. Plot $v_{1f}$ vs $v_{1i}$; momentum conservation is supported if the slope is 1.
3. Plot kinetic energy after vs kinetic energy before; momentum conservation is supported if the slope is 1.
4. Plot mass $m_1$ vs mass $m_2$; momentum conservation is supported if the masses are equal.

Explanation: This question tests understanding of experimental design for investigating momentum conservation in collisions by choosing the best data analysis method. To verify that momentum is conserved ($p_{\text{before}} = p_{\text{after}}$), an experiment must measure the masses of both colliding objects using a balance, measure their velocities before the collision ($v_{1i}$, $v_{2i}$) and after the collision ($v_{1f}$, $v_{2f}$) using motion sensors or video analysis, then calculate total momentum before ($p_{\text{before}} = m_1 v_{1i} + m_2 v_{2i}$) and after ($p_{\text{after}} = m_1 v_{1f} + m_2 v_{2f}$) to verify they are equal within experimental uncertainty. For evidence/data analysis: Evidence that momentum is conserved comes from showing that $p_{\text{before}}$ and $p_{\text{after}}$ are approximately equal across multiple trials—for example, if $p_{\text{before}} = 1.45 \ \text{kg} \cdot \text{m/s}$ and $p_{\text{after}} = 1.41 \ \text{kg} \cdot \text{m/s}$, the percent difference is $|1.41-1.45|/1.45 \times 100\% = 2.8\%$, which is within typical experimental uncertainty and supports conservation; graphing $p_{\text{after}}$ versus $p_{\text{before}}$ for multiple trials should produce a straight line with slope = 1 passing through the origin, further confirming that the momentum after equals the momentum before regardless of initial conditions. Choice A is correct because it describes plotting $p_{\text{after}}$ vs $p_{\text{before}}$ and checking for a 1:1 line, which directly tests if momentum is conserved across trials and collision types. Choice C is a tempting distractor but fails because it confuses momentum conservation with kinetic energy conservation (momentum is conserved in all collisions, KE only in elastic). When designing momentum conservation experiments, remember this checklist: (1) measure masses with a balance—this is non-negotiable since $p = mv$ requires knowing m, (2) measure velocities at two times (immediately before and immediately after collision) using motion sensors or video analysis, (3) calculate both $p_{\text{before}} = m_1 v_{1i} + m_2 v_{2i}$ and $p_{\text{after}} = m_1 v_{1f} + m_2 v_{2f}$ with careful attention to direction signs (positive/negative for 1D motion), (4) compare the two values—they should be equal within about 5% for a successful demonstration, and (5) conduct multiple trials to account for random errors. To improve experimental quality: use a low-friction track or air track to minimize external forces that would violate conservation, ensure the track is level so gravity doesn't add a constant force, use precise velocity measurement tools (motion sensors better than stopwatch/meterstick), take multiple trials and average to reduce random error, and always include uncertainty analysis showing that $p_{\text{before}}$ and $p_{\text{after}}$ agree within the combined measurement uncertainties.

Question 20

1. Only $v_{1i}$, $v_{1f}$, and $m_1$ (cart 2 is not needed)
2. $m_1$, $m_2$, $v_{1i}$, $v_{2i}$, $v_{1f}$, and $v_{2f}$ (correct answer)
3. Only $m_1$ and $m_2$ (velocities cancel in a collision)
4. Only kinetic energies before and after (momentum can be inferred from energy)

Explanation: This question tests understanding of experimental design for investigating momentum conservation in collisions. To verify that momentum is conserved (p_before = p_after), an experiment must measure the masses of both colliding objects using a balance, measure their velocities before the collision (v₁ᵢ, v₂ᵢ) and after the collision (v₁f, v₂f) using motion sensors or video analysis, then calculate total momentum before (p_before = m₁v₁ᵢ + m₂v₂ᵢ) and after (p_after = m₁v₁f + m₂v₂f) to verify they are equal within experimental uncertainty. The essential equipment includes (1) a balance or scale to measure the masses of both objects in kilograms, which cannot be determined by observation alone, and (2) motion sensors (ultrasonic or photogate) or a video camera to measure velocities before and after the collision—without both mass and velocity data, momentum (p = mv) cannot be calculated. Choice B is correct because it identifies all necessary quantities: both masses (m₁ and m₂) and all four velocities (v₁ᵢ, v₂ᵢ, v₁f, v₂f), which are required to calculate p_before = m₁v₁ᵢ + m₂v₂ᵢ and p_after = m₁v₁f + m₂v₂f for the complete system. Choice A suggests measuring only one object's momentum, when conservation requires comparing the total momentum of the system (both objects together) before and after collision. When designing momentum conservation experiments, remember this checklist: (1) measure masses with a balance—this is non-negotiable since p = mv requires knowing m, (2) measure velocities at two times (immediately before and immediately after collision) using motion sensors or video analysis, (3) calculate both p_before = m₁v₁ᵢ + m₂v₂ᵢ and p_after = m₁v₁f + m₂v₂f with careful attention to direction signs (positive/negative for 1D motion), (4) compare the two values—they should be equal within about 5% for a successful demonstration, and (5) conduct multiple trials to account for random errors. Common mistakes to avoid: (a) forgetting to measure masses (cannot calculate momentum without m), (b) measuring velocities at wrong times (need immediately before and after collision, not minutes later), (c) ignoring direction in 1D collisions (rightward velocity is positive, leftward is negative—this matters for momentum as a vector), (d) comparing individual object momenta instead of system totals (conservation applies to p₁ + p₂, not to p₁ alone), and (e) expecting perfect equality (experimental uncertainty means p_before and p_after will differ by small percentage, typically 2-5% is excellent agreement).