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. 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 2

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 3

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 4

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 5

1. Cart A, because it moves faster
2. Cart B, because it has greater mass
3. They have equal momentum magnitude (correct answer)
4. Cannot be determined without knowing the forces

Explanation: This problem tests understanding of momentum calculation and magnitude. Momentum is the product of mass and velocity, calculated as p = mv, and is a vector quantity with both magnitude and direction. For cart A: p_A = m × v = mv (rightward). For cart B: p_B = 2m × (v/2) = mv (leftward). Since we're comparing magnitudes, we ignore direction and find |p_A| = mv and |p_B| = mv, so they are equal. Choice A incorrectly focuses only on speed without considering mass. When calculating momentum magnitude, always multiply mass times speed, then compare the products.

Question 6

1. Cart $A$, because it has the greater speed
2. Cart $B$, because it has the greater mass
3. They have equal momentum magnitude
4. Cart $A$, because $|p_A|=3mv$ and $|p_B|=2mv$ (correct answer)

Explanation: This question tests understanding of momentum magnitude in one-dimensional motion. Momentum is the product of mass and velocity, calculated as p = mv, where direction matters for the full vector but magnitude is the absolute value. Cart A has momentum pA = m × 3v = 3mv eastward (positive), while Cart B has momentum pB = 2m × (-v) = -2mv (westward, negative). The magnitude of Cart A's momentum is |pA| = 3mv, and the magnitude of Cart B's momentum is |pB| = 2mv. Choice B incorrectly focuses only on mass without considering velocity. When comparing momentum magnitudes, always calculate the full product m × v before taking absolute values.

Question 7

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 8

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 9

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 10

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 11

1. $+0.60\ \text{kg·m/s}$
2. $-0.60\ \text{kg·m/s}$ (correct answer)
3. $-1.8\ \text{kg·m/s}$
4. $+0.90\ \text{J}$

Explanation: This question tests calculating momentum with negative velocity. Momentum equals mass times velocity: p = mv. With m = 0.20 kg and v = -3.0 m/s (negative for -x direction), the momentum is p = (0.20 kg)(-3.0 m/s) = -0.60 kg·m/s. The negative sign indicates motion in the -x direction. Choice D incorrectly gives units of energy (Joules), confusing momentum with kinetic energy. Momentum must have units of kg·m/s, and the sign indicates direction. When velocity is in the negative direction, include the negative sign in your calculation to get the correct momentum vector.

Question 12

1. Object X (correct answer)
2. Object Y
3. They are equal
4. Object Y, because momentum is proportional to $v^2$

Explanation: This question tests comparing momentum magnitudes with different mass-velocity combinations. Momentum magnitude is |p| = |mv|. Object X has momentum magnitude |p_X| = |(4m)(v)| = 4mv. Object Y has momentum magnitude |p_Y| = |(m)(3v)| = 3mv. Since 4mv > 3mv, Object X has greater momentum magnitude. Choice D incorrectly suggests momentum depends on v², confusing it with kinetic energy (which does depend on v²). Momentum is linear in velocity, not quadratic. To compare momentum magnitudes, calculate mass × speed for each object and compare the products directly.

Question 13

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 14

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 15

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 16

1. It must be in the $+x$ direction.
2. It must be in the $-x$ direction.
3. It could be in either the $+x$ or $-x$ direction. (correct answer)
4. It must be zero because the magnitudes are equal.

Explanation: This question probes the possible directions of momentum given equal magnitudes in AP Physics 1. Momentum is the vector product of mass and velocity, allowing equal magnitudes in either direction depending on velocity sign. The first cart's momentum is 3 kg times 2 m/s positive, magnitude 6 kg m/s; the second could match this positively or negatively. This shows direction is not fixed by magnitude alone. Choice D incorrectly assumes equal magnitudes imply zero momentum, misunderstanding vector nature. A transferable strategy is to solve for possible velocities that yield the required momentum magnitude, considering both directions.

Question 17

1. Same magnitude, opposite direction. (correct answer)
2. Same direction, half the magnitude.
3. Twice the magnitude, opposite direction.
4. Zero at $t_2$ because the speeds are equal.

Explanation: This question analyzes momentum change with velocity reversal in AP Physics 1. Momentum is mass times velocity, so direction flips with velocity sign while magnitude persists if speed is constant. At t1, p = m (+v) = +m v; at t2, p = m (-v) = -m v, same magnitude oppositely directed. This underscores momentum's vector sensitivity to direction. Choice D wrongly suggests zero momentum from equal speeds, ignoring directional change. A transferable strategy is to evaluate p = m v at specific times, comparing components separately.

Question 18

1. Object A
2. Object B
3. Object C (correct answer)
4. All three have equal momentum magnitude.

Explanation: This question identifies the object with greatest momentum magnitude among several in AP Physics 1. Momentum magnitude is |m v|, the absolute product of mass and speed, independent of direction. Object A: |m * 3v| = 3 m v; B: |3m * v| = 3 m v; C: |2m * 2v| (left) = 4 m v, the largest. This compares how different m and v combinations yield varying magnitudes. Choice D distracts by assuming equality without calculation. A transferable strategy is to compute |p| = m * speed for each, ranking them regardless of direction.

Question 19

1. Cart A
2. Cart B
3. They have equal momentum magnitude (correct answer)
4. Cannot be determined without kinetic energy

Explanation: This question assesses understanding of momentum magnitude in AP Physics 1. Momentum is a vector quantity defined as the product of an object's mass and its velocity. The magnitude of momentum is the absolute value of this product, disregarding direction. Since direction is included in the vector form, opposite directions result in momenta with the same magnitude but opposite signs. A common distractor is choice D, which incorrectly suggests that kinetic energy is needed to determine momentum magnitude, but momentum depends only on mass and velocity. To compare momentum magnitudes generally, calculate |m v| for each object and ignore directional signs.

Question 20

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.