AP Physics 1: Algebra-Based Unit 2: Force and Translational Dynamics Practice Exam

1. [Skill: 1.B | Topic: 2.1] Two carts, A and B, of masses 1.0 kg and 3.0 kg are on a horizontal frictionless track. The carts interact only through a compressed spring between them. At the instant shown, the spring exerts a 12 N force on cart A to the left and a 12 N force on cart B to the right. If the system is defined as (cart A + cart B + spring), which statement best describes the horizontal acceleration of the system’s center of mass at that instant?

2. [Skill: 1.A | Topic: 2.1] A thin, uniform plate has the shape of an isosceles triangle (uniform surface mass density). A student wants to determine the location of the plate’s center of mass. Which statement must be true about the center of mass of the plate?

3. [Skill: 2.A | Topic: 2.1] Three point masses lie on the x-axis at the following positions: - $m_1=2.0\,\text{kg}$ at $x_1=0.0\,\text{m}$ - $m_2=1.0\,\text{kg}$ at $x_2=3.0\,\text{m}$ - $m_3=3.0\,\text{kg}$ at $x_3=5.0\,\text{m}$ What is the x-coordinate of the center of mass of the three-mass system?

4. [Skill: 6.B | Topic: 2.1] Two ice skaters, Skater 1 (60 kg) and Skater 2 (40 kg), glide together on frictionless ice in a straight line at 2.0 m/s east. They then push off each other and move apart. Neglecting air resistance, which statement best describes the velocity of the center of mass of the two-skater system after they push off?

5. **1. [Skill: 1.A | Topic: 2.2]** A box rests on a table. A student makes the following statements about the forces involved: I. “The weight of the box is the force exerted by Earth on the box.” II. “The normal force is the reaction force to the weight.” III. “The reaction force to the weight is the gravitational force exerted by the box on Earth.” Which statement(s) are correct?

6. **2. [Skill: 1.B | Topic: 2.2]** A block is pulled across a rough horizontal floor by a rope that makes an angle above the horizontal, as shown. The block moves to the right. Which free-body diagram (FBD) correctly shows the forces exerted *on the block* by its environment? (Assume the block is not accelerating vertically.)

7. **3. [Skill: 1.B | Topic: 2.2]** Two blocks, X and Y, are in contact on a horizontal surface. A person applies a horizontal force to the left side of block X, pushing both blocks to the right. The surface is frictionless. A student draws an FBD for block Y. Which set of forces should appear on the FBD for block Y?

8. **4. [Skill: 1.B | Topic: 2.2]** A student draws the free-body diagram shown for a crate being pulled straight upward by a rope. Which statement correctly interprets the diagram?

9. [Skill: 1.B | Topic: 2.3] Two ice skaters, A and B, are initially at rest on frictionless ice. Skater A (mass 50 kg) pushes directly on skater B (mass 70 kg) for a short time interval. During the time that the skaters are in contact, which statement correctly describes the forces between them?

10. [Skill: 6.A | Topic: 2.3] Two low-friction carts on a horizontal track interact only with each other. Cart 1 and Cart 2 start at rest with a compressed spring between them. The spring is released, pushing the carts apart. A student claims: “Because the carts exert forces on each other, the center of mass of the two-cart system must start moving.” Which response best refutes the student’s claim?

11. [Skill: 1.B | Topic: 2.3] A massless, inextensible string passes over a frictionless, massless pulley. Mass $m_1=2.0\ \text{kg}$ hangs on the left end of the string and mass $m_2=3.0\ \text{kg}$ hangs on the right end. After release, the system accelerates. Let $T_L$ be the tension in the string segment directly above $m_1$, and let $T_R$ be the tension in the string segment directly above $m_2$. Which statement is correct for an ideal string and ideal pulley?

12. [Skill: 6.A | Topic: 2.3] Two students participate in a tug-of-war using an ideal rope (massless and does not stretch). Student 1 pulls to the left on one end of the rope with a force of 150 N. Student 2 pulls to the right on the other end with a force of 150 N. The rope remains straight and the center of the rope does not accelerate. What is the tension in the rope?

13. [Skill: 2.A | Topic: 2.4] A student analyzes a puck sliding on a horizontal air table (friction is negligible). The system is the puck. At an instant during the motion, the student records the external forces acting on the puck as shown: - Tension from string 1: 5.0 N to the right - Tension from string 2: 5.0 N to the left - Weight: 2.0 N downward - Normal force from the table: 2.0 N upward Which of the following is most consistent with the puck’s motion immediately after that instant (as viewed from an inertial reference frame)?

14. [Skill: 1.B | Topic: 2.4] A cart moves along a straight horizontal track. The cart’s velocity as a function of time is shown. [Image Cue]: Graph, "Velocity vs. Time for a Cart", axes labeled t (s) on horizontal and v (m/s) on vertical. The graph shows: from t = 0 to 2 s, v is constant at +3 m/s (horizontal line). From t = 2 to 5 s, v increases linearly from +3 m/s to +9 m/s (straight line with positive slope). From t = 5 to 6 s, v is constant at +9 m/s (horizontal line). During which time interval(s) is the net external force on the cart equal to zero, as viewed in an inertial reference frame?

15. [Skill: 4.A | Topic: 2.4] A hockey puck glides on perfectly frictionless ice. Two observers analyze the puck. - Observer P stands on the ground next to the rink. - Observer Q rides on a cart that moves along the rink and is speeding up (its speed is increasing in a straight line). At some instant, the puck is not in contact with any object and has no horizontal forces exerted on it. Which statement correctly identifies an inertial reference frame and its implication for the puck’s motion?

16. [Skill: 2.B | Topic: 2.5] A hockey puck moves on a frictionless, horizontal surface. The net external force on the puck in the direction of motion is measured as a function of time. [Image Cue]: Graph, "Net Force vs. Time for a Puck", x-axis: time t (s) from 0 to 10, y-axis: net force F_net (N). Piecewise-constant values: F_net = 0 N from 0–2 s; F_net = +4 N from 2–5 s; F_net = 0 N from 5–7 s; F_net = −2 N from 7–9 s; F_net = 0 N from 9–10 s. During which time interval(s), if any, is the puck’s velocity guaranteed to remain constant (constant speed and constant direction)?

17. [Skill: 3.A | Topic: 2.5] Two spacecraft, A and B, are far from other objects in deep space, so external forces other than the thrust can be neglected. Each spacecraft’s engine provides the same constant net external force of magnitude 2000 N in the +x direction. Spacecraft A has mass 500 kg. Spacecraft B has mass 1000 kg. Which statement correctly compares the accelerations of A and B while the engines fire?

18. [Skill: 1.A | Topic: 2.5] A 3.0 kg block is on a frictionless horizontal surface. Two horizontal forces act on the block at the same time: one force of 10 N to the right and one force of 6 N to the left. [Image Cue]: Diagram, "Block with Opposing Horizontal Forces", a block on a horizontal line with two labeled force arrows: 10 N to the right, 6 N to the left. No friction force shown. Which statement correctly describes the motion of the block’s center of mass while the forces act?

19. **1. [Skill: 5.A | Topic: 2.6]** A student investigates the gravitational interaction between two small spheres by measuring the magnitude of the force on one sphere due to the other for several center-to-center separations. The measured data are shown. | Separation $r$ (m) | Force magnitude $F$ (arb. units) | |---:|---:| | 2 | 16 | | 4 | 4 | | 8 | 1 | Which of the following relationships between $F$ and $r$ is most consistent with the data?

20. **2. [Skill: 1.A | Topic: 2.6]** A 1.0 kg object is moved from Earth’s surface to a higher altitude. Earth’s radius is approximately $R_E = 6.4 \times 10^6\ \text{m}$. In which situation is it most appropriate to model the gravitational force on the object as constant (i.e., use $mg$ with the same $g$ throughout the motion)?

21. **3. [Skill: 2.B | Topic: 2.6]** Two blocks, $m_1 = 2.0\ \text{kg}$ and $m_2 = 5.0\ \text{kg}$, rest on separate scales on the floor of an elevator. The elevator accelerates upward with acceleration magnitude $a = 2.0\ \text{m/s}^2$. Take $g = 9.8\ \text{m/s}^2$. Which statement correctly compares the apparent weights (scale readings) of the two blocks while the elevator accelerates upward?

22. 1. [Skill: 2A | Topic: 2.7] A student places a 5.0 kg box on a horizontal floor and pulls it with a horizontal force measured by a force sensor. The force increases smoothly until the box starts moving, then the student adjusts the force so the box moves at constant speed. [Image Cue]: Graph, "Applied Force vs. Time", x-axis: time (s), y-axis: applied force (N). Key features: (i) From t = 0 to t = 3.0 s, force increases linearly from 0 N to 20 N while the box remains at rest. (ii) At t = 3.0 s the box begins to move. (iii) For t > 3.0 s, the applied force is constant at 14 N and the box moves at constant speed. What is the coefficient of kinetic friction between the box and the floor? (Use g = 9.8 m/s^2.)

23. 2. [Skill: 1B | Topic: 2.7] A 2.0 kg block is at rest on a rough incline that makes an angle of 20° with the horizontal. The coefficient of static friction between the block and the incline is mu_s = 0.50, and the coefficient of kinetic friction is mu_k = 0.30. Which of the following correctly describes the block’s motion and the friction force acting on the block? (Use g = 9.8 m/s^2.)

24. 3. [Skill: 1A | Topic: 2.7] A 10 kg box rests on a horizontal floor. A student pulls horizontally on the box with a spring scale. The student observes that the box just begins to move when the scale reads 60 N. After the box is moving, the student adjusts the pull so the box moves at constant speed; the scale then reads 45 N. Which of the following pairs of coefficients (mu_s, mu_k) is most consistent with the observations? (Use g = 9.8 m/s^2.)

25. [Skill: 2.B | Topic: 2.8] A student investigates an ideal spring by attaching it to a cart on a horizontal track. The cart’s displacement $x$ is measured from the cart’s equilibrium position, with positive $x$ to the right. A force sensor measures the force exerted by the spring on the cart, $F_s$, where positive force is to the right. The data are shown in the graph. Which of the following best describes the spring force on the cart when the cart is at $x=+0.20\ \text{m}$?

26. [Skill: 4.A | Topic: 2.8] An ideal spring with spring constant $k=150\ \text{N/m}$ has a relaxed length of $0.30\ \text{m}$. One end is attached to a wall and the other end is attached to a block on a frictionless horizontal surface. The spring’s length is measured to be $0.38\ \text{m}$. Which of the following gives the magnitude and direction of the force exerted by the spring on the block?

27. [Skill: 5.B | Topic: 2.8] A cart is attached to an ideal spring on a horizontal track. The cart’s position $x$ is measured from a fixed origin along the track. A force probe measures the spring force on the cart, and the sign convention is positive force to the right. The measured values are: - At $x=0.20\ \text{m}$, $F_s=+3\ \text{N}$ - At $x=0.30\ \text{m}$, $F_s=0\ \text{N}$ - At $x=0.40\ \text{m}$, $F_s=-3\ \text{N}$ Which equation best models the spring force as a function of position $x$ (in meters), consistent with Hooke’s law?

28. [Skill: 5.A | Topic: 2.9] A small cart moves on a horizontal circular track of radius 2.0 m. A motion sensor measures the cart’s tangential speed as a function of time, shown in the graph. At time t = 1.0 s, which of the following best describes the direction of the cart’s acceleration vector? Assume the cart is moving counterclockwise and the center of the circle is to the cart’s left at that instant.

29. [Skill: 2.A | Topic: 2.9] A 1000 kg car travels at a constant speed of 20 m/s around a flat (unbanked) circular curve of radius 50 m. The only horizontal force on the car is static friction from the road. What minimum coefficient of static friction, $\mu_s$, is required to keep the car from sliding? Use g = 9.8$\ \text{m/s}^2$.

30. [Skill: 2.A | Topic: 2.9] Two satellites, A and B, move in circular orbits around the same planet. Satellite A orbits with radius R and period T. Satellite B orbits with radius 4R. Assuming the planet’s mass is much larger than either satellite’s mass and the orbits are circular, what is the period of satellite B in terms of T?