AP Physics 1 Quiz: Momentum

What this quiz covers

This quiz focuses on Momentum, giving you a quick way to practice the rules, question types, and explanations that matter most for AP Physics 1.

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. The ball (correct answer)
2. The cart
3. They have equal momentum magnitude
4. The cart, because it has greater mass

Explanation: This question assesses understanding of momentum magnitude comparison in AP Physics 1. Momentum is calculated as the product of mass and velocity, with magnitude being mass times speed. Direction is part of the vector but ignored for magnitude. Here, 0.5 kg times 8 m/s is 4 kg m/s, greater than 2 kg times 1 m/s which is 2 kg m/s. A common distractor is choice D, which prioritizes mass over the mass-speed product, overlooking the faster speed of the ball. For comparisons, always multiply mass by speed and compare the results numerically.

Question 2

1. Negative $x$ direction
2. Positive $x$ direction (correct answer)
3. Perpendicular to the velocity
4. Zero, because direction is undefined for momentum

Explanation: This question assesses understanding of momentum direction in AP Physics 1. Momentum is a vector quantity calculated as the product of mass and velocity, sharing the same direction as the velocity vector. For motion along the x-axis, a positive velocity indicates positive x-direction for momentum. The direction is inherent to the vector nature of momentum, not perpendicular or undefined. A common distractor is choice A, which might appeal if one mistakenly reverses the sign of the given positive velocity. When determining momentum direction, always align it with the velocity vector's direction for transferable problem-solving.

Question 3

1. It moves in the positive $x$ direction
2. It moves in the negative $x$ direction (correct answer)
3. It is at rest
4. Direction cannot be determined without mass

Explanation: This question assesses understanding of momentum direction from its sign in AP Physics 1. Momentum is the vector product of mass and velocity, so its sign indicates direction along an axis. A negative momentum value means motion in the negative x-direction. Mass is positive, so the sign comes solely from velocity's direction. A common distractor is choice D, which incorrectly claims direction needs mass, but mass doesn't affect direction. In one-dimensional problems, interpret the sign of p relative to your coordinate system for direction.

Question 4

1. $+12\,\text{kg}\cdot\text{m/s}$
2. $-12\,\text{kg}\cdot\text{m/s}$ (correct answer)
3. $+24\,\text{kg}\cdot\text{m/s}$
4. $-24\,\text{kg}\cdot\text{m/s}$

Explanation: This question assesses understanding of momentum as a signed quantity in AP Physics 1. Momentum is the product of mass and velocity, with sign indicating direction (e.g., east positive, west negative). Magnitude is the absolute value, but the full momentum includes the sign. For the second cart moving west with magnitude 12, it is -12 kg m/s. A common distractor is choice A, which omits the negative sign for west direction. Assign a consistent positive direction and apply signs accordingly for vector quantities like momentum.

Question 5

1. $6.0\,\text{kg}\cdot\text{m/s}$ west (correct answer)
2. $6.0\,\text{kg}\cdot\text{m/s}$ east
3. $3.0\,\text{J}$ west
4. $3.0\,\text{kg}\cdot\text{m/s}$ west

Explanation: This question assesses understanding of calculating momentum in AP Physics 1. Momentum is the product of mass and velocity, resulting in units of $\text{kg} \cdot \text{m/s}$. It is a vector, so direction like 'west' must be included in the description. The calculation is straightforward: $5 \, \text{kg}$ times $1.2 \, \text{m/s}$ equals $6 \, \text{kg} \cdot \text{m/s}$ west. A common distractor is choice C, which uses joules ($\text{J}$) instead of momentum units, likely from confusing with kinetic energy. Always verify units and include direction when reporting momentum for accurate problem-solving.

Question 6

1. Cart 1 has greater momentum magnitude because it is heavier
2. Cart 2 has greater momentum magnitude because it is faster
3. They have equal momentum magnitude (correct answer)
4. They have equal kinetic energy, so momentum magnitudes are equal

Explanation: This question assesses understanding of momentum magnitude with opposite directions in AP Physics 1. Momentum is the product of mass and velocity, a vector with direction matching velocity. Magnitude ignores direction, so it's mass times speed for comparison. Cart 1's 3m times v equals 3m v, same as cart 2's m times 3v. A common distractor is choice D, which confuses equal kinetic energies (both 1.5 m v²) with momentum, but they are distinct. To solve, calculate magnitudes separately and compare, regardless of direction.

Question 7

1. Object P
2. Object Q
3. They have equal momentum magnitude (correct answer)
4. Object Q, because its kinetic energy is larger

Explanation: This question assesses understanding of equal momentum magnitudes in AP Physics 1. Momentum is the vector product of mass and velocity, with magnitude mass times speed. Both objects move right, so directions are the same. P's m times 2v equals 2m v, matching Q's 4m times v/2. A common distractor is choice D, which mixes up momentum with kinetic energy (P has 2m v², Q has m v²). For such comparisons, focus solely on the m v product and verify calculations step-by-step.

Question 8

1. Ball 2 has the same momentum because the masses are equal.
2. Ball 2 has twice the momentum, in the same direction. (correct answer)
3. Ball 2 has four times the momentum, in the same direction.
4. Ball 2 has half the momentum, in the same direction.

Explanation: This question evaluates the relationship between speed and momentum for identical masses in AP Physics 1. Momentum is the product of mass and velocity, so for equal masses, it scales directly with velocity magnitude and shares its direction. Ball 1 has momentum m v, while Ball 2 has m times 2v, doubling the momentum in the same direction. This demonstrates how momentum depends linearly on velocity when mass is constant. Choice C distracts by confusing momentum with kinetic energy, which scales with velocity squared. A transferable strategy is to compare momenta by computing p = m v for each object and noting proportionalities.

Question 9

1. Left (negative $x$ direction) (correct answer)
2. Right (positive $x$ direction)
3. Zero, because the puck is sliding on a track
4. Cannot be determined without the puck’s kinetic energy

Explanation: This question assesses the understanding of momentum direction in AP Physics 1. Momentum is calculated as the product of mass and velocity, making it a vector that points in the direction of the velocity. For the puck moving left at 3.0 m/s with right as positive, its velocity is negative, so momentum is also negative, directed left. This highlights that momentum inherits the directional component from velocity, not just speed. Choice C is a distractor that wrongly assumes zero momentum due to the track, ignoring the puck's motion. A transferable strategy is to assign signs based on a chosen positive direction and compute p = m v accordingly.

Question 10

1. Cart A has greater momentum magnitude because it moves faster.
2. The carts have equal momentum and both are in the $+x$ direction.
3. The carts have equal momentum magnitude but opposite directions. (correct answer)
4. Cart B has greater momentum magnitude because it has greater mass.

Explanation: This question tests the concept of comparing momenta of objects with different masses and velocities in AP Physics 1. Momentum is a vector quantity defined as the product of an object's mass and its velocity, where velocity includes both speed and direction. In one dimension, the direction is indicated by the sign, with positive typically representing rightward motion. Thus, for Cart A, momentum is m times 2v positive, and for Cart B, it is 2m times -v, resulting in equal magnitudes but opposite directions. A common distractor like choice A incorrectly prioritizes speed over the mass-velocity product. A transferable strategy is to always calculate momentum as p = m v, accounting for signs, before comparing magnitudes or directions.

Question 11

1. The second robot has half the momentum magnitude.
2. The second robot has twice the momentum magnitude.
3. The momentum magnitudes are equal. (correct answer)
4. The first robot has greater momentum magnitude because it is more massive.

Explanation: This question examines momentum magnitude comparison with halved mass and doubled speed in AP Physics 1. Momentum is the product of mass and velocity, scaling with both factors. The first robot has m v, the second has (1/2 m) times 2v = m v, equal magnitudes. This demonstrates compensatory effects in the p = m v formula. Choice D distracts by overemphasizing mass without velocity adjustment. A transferable strategy is to factor out constants in p = m v to see equivalences when parameters inversely vary.

Question 12

1. Its velocity is in the negative direction (correct answer)
2. Its speed is $5\,\text{m/s}$
3. Its kinetic energy is negative
4. Its mass must be $5\,\text{kg}$

Explanation: This question tests understanding of what negative momentum implies about an object's motion. Momentum p = mv is a vector quantity, and its sign indicates the direction of motion in one-dimensional problems. Since pG = -5 kg·m/s is negative, and mass is always positive, the velocity must be negative to produce a negative momentum. This means object G moves in the negative direction of the chosen coordinate system. Choice C incorrectly suggests kinetic energy can be negative, but KE = ½mv² is always positive since v² ≥ 0. When momentum is negative in 1D motion, it always means velocity is in the negative direction.

Question 13

1. Glider 1
2. Glider 2
3. They have equal momentum magnitude (correct answer)
4. Neither; momentum depends only on speed, not mass

Explanation: This problem requires calculating momentum magnitude for objects moving in opposite directions. Momentum is mass times velocity (p = mv), and we must include direction when calculating. For glider 1: p₁ = 3m × (+2v) = +6mv. For glider 2: p₂ = 2m × (-3v) = -6mv. The magnitudes are |p₁| = 6mv and |p₂| = 6mv, which are equal. Choice D incorrectly states momentum depends only on speed, ignoring that mass is equally important. To find momentum magnitude, calculate mass × speed for each object, then compare the products.

Question 14

1. $+12\,\text{kg}\cdot\text{m/s}$
2. $-12\,\text{kg}\cdot\text{m/s}$ (correct answer)
3. $+18\,\text{kg}\cdot\text{m/s}$
4. $-18\,\text{kg}\cdot\text{m/s}$

Explanation: This problem tests momentum calculation with specific numerical values and direction. Momentum equals mass times velocity (p = mv), where velocity includes both magnitude and direction. Given m = 4 kg and v = -3 m/s (negative because leftward), we calculate p = 4 kg × (-3 m/s) = -12 kg·m/s. The negative sign indicates leftward motion along the x-axis. Choice C incorrectly multiplies 4 × 3 and adds a positive sign, ignoring the velocity's direction. Always include the velocity's sign when calculating momentum to preserve directional information.

Question 15

1. Object A, because it has greater mass
2. Object B, because it has greater speed
3. They have equal momentum magnitude (correct answer)
4. Object A, because momentum depends on $m^2v$

Explanation: This problem tests momentum calculation for objects with different mass-velocity combinations. Momentum equals mass times velocity (p = mv), calculated separately for each object. For object A: p_A = 2m × v = 2mv. For object B: p_B = m × 2v = 2mv. Both momenta equal 2mv in the +x direction, so their magnitudes are equal. Choice D incorrectly suggests momentum depends on m²v, but the correct formula is simply mv. When mass and velocity vary inversely (one doubles while the other halves), momentum remains constant.

Question 16

1. $p_X > p_Y$ because X moves faster
2. $p_Y > p_X$ because Y is more massive
3. $p_X = p_Y$ (correct answer)
4. $p_X = 3p_Y$ because speed is tripled

Explanation: This problem tests understanding of the momentum formula p = mv. Momentum is the product of mass and velocity, where both factors contribute equally to the result. For object X: p_X = m × 3v = 3mv. For object Y: p_Y = 3m × v = 3mv. Since both products equal 3mv and both move in the +x direction, their momenta are equal. Choice D incorrectly assumes momentum depends only on speed, ignoring the role of mass. When comparing momenta, always calculate the full product of mass times velocity for each object.

Question 17

1. $p$
2. $-p$ (correct answer)
3. $0$
4. $2p$

Explanation: This problem tests how momentum changes when velocity reverses direction. Momentum is the product of mass and velocity (p = mv), and is a vector quantity that depends on direction. Initially, with velocity +v, momentum is p = m(+v) = +p. When velocity becomes -v (same speed, opposite direction), the new momentum is p' = m(-v) = -p. The magnitude remains the same, but the sign changes to indicate opposite direction. Choice C incorrectly suggests momentum becomes zero when only direction changes. Remember that reversing velocity direction reverses momentum direction while preserving magnitude.

Question 18

1. The $2m$ cart, because it is heavier
2. The $m$ cart, because its speed is larger
3. They have equal momentum magnitude (correct answer)
4. The $2m$ cart, because it has greater kinetic energy

Explanation: This question tests understanding of momentum magnitude calculation. Momentum is the product of mass and velocity (p = mv), and since it's a vector quantity, it has both magnitude and direction. For the 2m cart moving east at speed v, the momentum magnitude is |p₁| = (2m)(v) = 2mv. For the m cart moving west at speed 2v, the momentum magnitude is |p₂| = (m)(2v) = 2mv. Choice A incorrectly assumes heavier objects always have more momentum, ignoring velocity's role. Since both carts have momentum magnitude 2mv, they are equal. When calculating momentum magnitude, multiply mass by speed (ignoring direction) and compare the products.

Question 19

1. Momentum stays the same because the speed is unchanged
2. Momentum reverses direction but keeps the same magnitude (correct answer)
3. Momentum doubles in magnitude because the velocity changes sign
4. Momentum becomes zero because the velocities cancel

Explanation: This question tests understanding how momentum changes with velocity reversal. Momentum is p = mv, so initially p₁ = (1.0 kg)(-2.0 m/s) = -2.0 kg·m/s, and later p₂ = (1.0 kg)(+2.0 m/s) = +2.0 kg·m/s. The magnitude remains |p| = 2.0 kg·m/s in both cases, but the direction reverses from negative to positive. Choice A incorrectly ignores that velocity includes direction, not just speed. When velocity reverses direction but maintains the same speed, momentum reverses direction while keeping the same magnitude. Remember that changing velocity direction changes momentum direction, even if speed stays constant.

Question 20

1. $|p_E|>|p_F|$ because $E$ is heavier
2. $|p_E|<|p_F|$ because $F$ is faster
3. $|p_E|=|p_F|$ because $4mv = m(4v)$ (correct answer)
4. $|p_E|=|p_F|$ because they have the same kinetic energy

Explanation: This question examines momentum magnitude comparison when mass and velocity vary inversely. Momentum magnitude is calculated as |p| = m × v, taking the absolute value of the product. Object E has momentum magnitude |pE| = 4m × v = 4mv, while Object F has momentum magnitude |pF| = m × 4v = 4mv. Since both products equal 4mv, the momentum magnitudes are equal despite different mass-velocity combinations. Choice D incorrectly relates momentum to kinetic energy; while they may have equal kinetic energies (½mv²), this is coincidental and not the reason for equal momentum magnitudes. When comparing momenta, calculate the full m × v product—different combinations can yield the same result.