AP Physics 1: Algebra-Based Unit 4: Linear Momentum Practice Exam

1. [Skill: 3.A | Topic: 4.1] An object of mass 0.50 kg moves with velocity $\vec{v} = (3\hat{i} - 4\hat{j})\ \text{m/s}$ on a horizontal surface. Which of the following is the object’s linear momentum $\vec{p}$?

2. [Skill: 4.A | Topic: 4.1] A 6.0 kg bowling ball and a 0.060 kg tennis ball roll east with the same speed of 2.0 m/s. Which statement correctly compares the magnitudes of their linear momenta?

3. [Skill: 3.A | Topic: 4.1] Two skaters move along a straight line (the x-axis). Skater 1 has mass 60 kg and velocity $+2.0\ \text{m/s}$. Skater 2 has mass 40 kg and velocity $-3.0\ \text{m/s}$. What is the total momentum of the two-skater system?

4. [Skill: 5.B | Topic: 4.1] A student analyzes an interaction between two carts on a horizontal track. During the 0.050 s interaction, force sensors show that the contact forces between the carts reach about 50 N. The net external force on the two-cart system during the interaction (from track friction and air resistance combined) is about 0.20 N. Which statement best justifies modeling the interaction as a collision for momentum analysis?

5. [Skill: 3.A | Topic: 4.1] Two carts are initially at rest on a low-friction track. Cart A has mass 2.0 kg and cart B has mass 1.0 kg. A compressed spring between them is released, pushing them apart (an explosion model). After release, cart A moves left with speed 1.5 m/s. What is the velocity of cart B immediately after the spring releases?

6. **1. [Skill: 1.B | Topic: 4.2]** A force sensor records the net force on a cart in the +x direction during a brief interaction. > [Image Cue]: Force–time graph, "Net Force vs. Time", axes labeled $F_x$ (N) vs. $t$ (ms). The graph starts at (0 ms, 0 N), increases linearly to (2 ms, 600 N), then decreases linearly to (6 ms, 0 N), forming a single triangular pulse entirely above the time axis. Which of the following is the cart’s change in momentum $\Delta p_x$ during the interaction?

7. **2. [Skill: 4.B | Topic: 4.2]** A 3.0 kg cart moves to the east with speed 2.0 m/s. A constant net external force of 12 N to the east acts on the cart for 0.50 s. What is the cart’s speed immediately after the force stops acting?

8. **3. [Skill: 3.A | Topic: 4.2]** Two students push on identical carts (same mass, initially at rest on a low-friction track) using different time-dependent forces. - Student 1 applies a large force for a short time. - Student 2 applies a smaller force for a longer time. In both cases, the force is in the +x direction and the force–time graphs have the same area. Which statement best describes the carts’ changes in momentum?

9. **4. [Skill: 2.C | Topic: 4.2]** A 0.20 kg hockey puck is moving in the +x direction when it hits a rigid wall and experiences an average net force of 150 N in the −x direction for 0.020 s. Which of the following is the impulse delivered to the puck (and therefore its change in momentum) during the collision?

10. **5. [Skill: 1.B | Topic: 4.2]** The graph shows the x-component of momentum, $p_x$, of an object as a function of time. > [Image Cue]: Momentum–time graph, "Momentum vs. Time", axes labeled $p_x$ (kg·m/s) vs. $t$ (s). Piecewise linear: from (0 s, 2 kg·m/s) to (1 s, 2 kg·m/s) horizontal; then from (1 s, 2 kg·m/s) to (3 s, 8 kg·m/s) straight increasing line; then from (3 s, 8 kg·m/s) to (4 s, 8 kg·m/s) horizontal. What is the net external force $F_x$ on the object during the interval from $t=1\ \text{s}$ to $t=3\ \text{s}$?

11. [Skill: 4.A | Topic: 4.3] Two carts move on a nearly frictionless track and collide. Cart A has mass 0.50 kg and initial velocity +2.0 m/s (to the right). Cart B has mass 1.0 kg and initial velocity -1.0 m/s (to the left). During the collision, the carts exert forces on each other, but external horizontal forces on the two-cart system are negligible. Which of the following is the center-of-mass velocity of the two-cart system after the collision?

12. [Skill: 6.B | Topic: 4.3] A student stands on a low-friction skateboard holding a ball. Initially, both the student and ball are at rest relative to the ground. The student then throws the ball horizontally forward. Assume horizontal external forces on the student+ball system are negligible during the throw. For which selected system is the total linear momentum conserved during the throw?

13. [Skill: 4.A | Topic: 4.3] Two pucks move on frictionless ice and collide, sticking together. Puck 1 has mass 0.20 kg and moves east at 3.0 m/s. Puck 2 has mass 0.10 kg and moves north at 4.0 m/s. External horizontal forces on the two-puck system are negligible. What is the magnitude and direction of the velocity of the stuck-together pucks immediately after the collision?

14. [Skill: 2.A | Topic: 4.3] Two carts collide on a nearly frictionless track. During the collision, a force sensor on cart A records the force exerted on A by B, $F_{B\to A}$, as a function of time. A second sensor on cart B simultaneously records $F_{A\to B}$. Both sensors show force-time pulses over the same time interval with equal areas in magnitude but opposite signs (one is positive and the other is negative). Which statement is most consistent with the sensor data and the conservation of momentum for the two-cart system?

15. [Skill: 2.B | Topic: 4.4] Two low-friction carts, A and B, move along a straight track and collide. The table shows the measured velocities just before and just after the collision. - Cart A: mass 1.0 kg, initial velocity +2.0 m/s, final velocity 0.0 m/s - Cart B: mass 1.0 kg, initial velocity 0.0 m/s, final velocity +2.0 m/s Which description best classifies the interaction?

16. [Skill: 1.B | Topic: 4.4] A 0.50 kg puck slides to the right at 4.0 m/s on frictionless ice and collides with a 1.5 kg puck that is initially at rest. After the collision, the two pucks are observed to stick together and move as a single object. Which statement best describes the collision?

17. [Skill: 2.C | Topic: 4.4] A student studies a collision between two objects on a low-friction track and graphs the total kinetic energy of the two-object system as a function of time. The collision occurs over a very short time interval centered at t = 2.0 s. [Image Cue]: Graph, "Total Kinetic Energy vs. Time", x-axis: time t (s) from 0 to 4, y-axis: total kinetic energy K (J) from 0 to 10; K is constant at 8 J from t = 0 to 1.9 s, then drops quickly during the collision near t = 2.0 s, then is constant at 5 J from t = 2.1 s to 4.0 s. Based on the graph, which best describes the interaction?

18. [Skill: 2.B | Topic: 4.4] In a laboratory collision, two carts move toward each other and collide. After the collision, video analysis shows the carts move together as one object at a constant speed. The total kinetic energy of the two-cart system is 10 J just before the collision and 6 J just after the collision. Which classification is correct?