Multiple Choice:

1. A ball is thrown horizontally from the top of a building. If air resistance is negligible, what is the shape of the ball's trajectory? (A) A straight line (B) A parabola (C) A circle (D) A hyperbola

2. A car accelerates uniformly from rest to a speed of 20 m/s in 5 seconds. What is the average acceleration of the car? (A) 2 m/s² (B) 4 m/s² (C) 5 m/s² (D) 10 m/s²

Free Response: A projectile is launched with an initial velocity of 30 m/s at an angle of 60 degrees above the horizontal. Neglect air resistance.

(a) Calculate the horizontal and vertical components of the initial velocity. (2 points) (b) Calculate the time it takes for the projectile to reach its maximum height. (2 points) (c) Calculate the maximum height reached by the projectile. (2 points) (d) Calculate the total time the projectile is in the air. (2 points) (e) Calculate the horizontal range of the projectile. (2 points)

Answer Key:

*Multiple Choice: 1. (B), 2. (B)

Free Response:

(a) $v_{ix} = 30 \cos(60) = 15 m/s$, $v_{iy} = 30 \sin(60) = 26 m/s$ (2 points) (b) $v_f = v_i + at$, $0 = 26 - 9.8t$, $t = 2.65 s$ (2 points) (c) $\Delta y = v_i t + \frac{1}{2}at^2$, $\Delta y = 26(2.65) - 4.9(2.65)^2 = 34.4 m$ (2 points) (d) Total time = 2 * time to max height = 2 * 2.65 = 5.3 s (2 points) (e) $x = v_x t = 15 * 5.3 = 79.5 m$ (2 points)

Multiple Choice:

1. A 10 kg block is pulled across a horizontal surface with a force of 50 N. If the coefficient of kinetic friction is 0.2, what is the net force acting on the block? (A) 10 N (B) 20 N (C) 30 N (D) 50 N

2. Two blocks, one with mass m and the other with mass 2m, are connected by a string and pulled across a frictionless surface with a force F. What is the tension in the string connecting the two blocks? (A) F/3 (B) F/2 (C) 2F/3 (D) F

Free Response: A 5 kg block is placed on a 30-degree incline. The coefficient of static friction is 0.4 and the coefficient of kinetic friction is 0.2. (a) Draw a free body diagram of all the forces acting on the block. (2 points) (b) Calculate the component of the gravitational force acting parallel to the incline. (2 points) (c) Calculate the component of the gravitational force acting perpendicular to the incline. (2 points) (d) Calculate the minimum static frictional force required to keep the block at rest. (2 points) (e) If the block starts to slide, calculate the acceleration of the block down the incline. (2 points)

Answer Key:

*Multiple Choice: 1. (C), 2. (A)

Free Response:

(a) Diagram should show weight (mg), normal force (N), and static friction (fs) (2 points) (b) $F_{g\parallel} = 5 * 9.8 * \sin(30) = 24.5 N$ (2 points) (c) $F_{g\perp} = 5 * 9.8 * \cos(30) = 42.4 N$ (2 points) (d) $F_{static} = F_{g\parallel} = 24.5 N$ (2 points) (e) $F_{net} = F_{g\parallel} - F_{kinetic}$, $F_{kinetic} = \mu_k * F_N = 0.2 * 42.4 = 8.48N$, $a = (24.5 - 8.48) / 5 = 3.2 m/s^2$ (2 points)

Multiple Choice:

1. A car travels around a circular track at a constant speed. What is the direction of the centripetal acceleration of the car? (A) Tangent to the circle (B) Toward the center of the circle (C) Away from the center of the circle (D) In the direction of motion

2. If the distance between two objects is doubled, how does the gravitational force between them change? (A) It is halved (B) It is doubled (C) It is quadrupled (D) It is quartered

Free Response: A satellite of mass m orbits a planet of mass M at a radius r.

(a) Derive an expression for the orbital speed of the satellite in terms of G, M, and r. (3 points) (b) Derive an expression for the period of the satellite in terms of G, M, and r. (3 points) (c) If the orbital radius is doubled, how does the orbital speed change? (2 points) (d) If the orbital radius is doubled, how does the period change? (2 points)

Answer Key:

*Multiple Choice: 1. (B), 2. (D)

Free Response:

(a) $G\frac{Mm}{r^2} = m\frac{v^2}{r}$, $v = \sqrt{\frac{GM}{r}}$ (3 points) (b) $v = \frac{2\pi r}{T}$, $T = \frac{2\pi r}{v} = \frac{2\pi r}{\sqrt{\frac{GM}{r}}} = 2\pi \sqrt{\frac{r^3}{GM}}$ (3 points) (c) If r is doubled, v becomes $v/\sqrt{2}$ (2 points) (d) If r is doubled, T becomes $T\sqrt{8}$ (2 points)

Multiple Choice:

1. A 2 kg ball is dropped from a height of 10 m. What is its kinetic energy just before it hits the ground? (Neglect air resistance). (A) 100 J (B) 196 J (C) 200 J (D) 392 J

2. A spring with a spring constant of 200 N/m is compressed by 0.2 m. What is the potential energy stored in the spring? (A) 4 J (B) 8 J (C) 16 J (D) 20 J

Free Response: A 0.5 kg block is released from rest at the top of a frictionless ramp that is 2 m high. At the bottom of the ramp, it slides along a horizontal surface and compresses a spring with a spring constant of 100 N/m.

(a) Calculate the potential energy of the block at the top of the ramp. (2 points) (b) Calculate the kinetic energy of the block at the bottom of the ramp. (2 points) (c) Calculate the speed of the block at the bottom of the ramp. (2 points) (d) Calculate the maximum compression of the spring. (2 points) (e) If friction is present on the horizontal surface, how would the maximum compression of the spring change? Explain. (2 points)

Answer Key:

*Multiple Choice: 1. (B), 2. (A)

Free Response:

(a) $PE = mgh = 0.5 * 9.8 * 2 = 9.8 J$ (2 points) (b) $KE = PE = 9.8 J$ (2 points) (c) $KE = \frac{1}{2}mv^2$, $9.8 = \frac{1}{2} * 0.5 * v^2$, $v = 6.26 m/s$ (2 points) (d) $PE_{spring} = \frac{1}{2}kx^2$, $9.8 = \frac{1}{2} * 100 * x^2$, $x = 0.44 m$ (2 points) (e) The maximum compression would be less because some energy would be lost due to friction as thermal energy. (2 points)

Multiple Choice:

1. A 2 kg ball moving at 5 m/s collides head-on with a 1 kg ball at rest. If the collision is perfectly inelastic, what is the final velocity of the combined mass? (A) 2.5 m/s (B) 3.33 m/s (C) 5 m/s (D) 10 m/s

2. A force of 10 N acts on an object for 2 seconds. What is the impulse exerted on the object? (A) 5 Ns (B) 10 Ns (C) 20 Ns (D) 40 Ns

Free Response: A 0.5 kg cart is moving to the right at 2 m/s and collides with a 1 kg cart that is initially at rest. After the collision, the 0.5 kg cart moves to the left at 1 m/s.

(a) Calculate the initial momentum of the system. (2 points) (b) Calculate the final momentum of the 0.5 kg cart. (2 points) (c) Calculate the final velocity of the 1 kg cart. (2 points) (d) Is this collision elastic or inelastic? Justify your answer. (2 points) (e) Calculate the change in kinetic energy of the system. (2 points)

Answer Key:

*Multiple Choice: 1. (B), 2. (C)

Free Response:

(a) $p_i = (0.5 * 2) + (1 * 0) = 1 kg m/s$ (2 points) (b) $p_{1f} = 0.5 * -1 = -0.5 kg m/s$ (2 points) (c) $p_i = p_f$, $1 = -0.5 + 1 * v_{2f}$, $v_{2f} = 1.5 m/s$ (2 points) (d) Inelastic. $KE_i = 0.5 * 2^2 / 2 = 1J$, $KE_f = (0.5 * (-1)^2 / 2) + (1 * 1.5^2 / 2) = 1.375J$ Kinetic energy is not conserved. (2 points) (e) $\Delta KE = 1.375 - 1 = 0.375J$ (2 points)

Multiple Choice:

1. A mass-spring system oscillates with a period T. If the mass is doubled, what is the new period of oscillation? (A) T/2 (B) T/\sqrt{2} (C) T\sqrt{2} (D) 2T

2. A simple pendulum has a length L and a period T. If the length of the pendulum is quadrupled, what is the new period of oscillation? (A) T/2 (B) T (C) 2T (D) 4T

Free Response: A 0.2 kg mass is attached to a spring with a spring constant of 50 N/m. The mass is pulled 0.1 m from its equilibrium position and released.

(a) Calculate the period of oscillation of the mass-spring system. (2 points) (b) Calculate the maximum speed of the mass during its oscillation. (2 points) (c) Calculate the total energy of the system. (2 points) (d) If the amplitude of oscillation is doubled, how does the maximum speed change? (2 points) (e) If the amplitude of oscillation is doubled, how does the period change? (2 points)

Answer Key:

*Multiple Choice: 1. (C), 2. (C)

Free Response:

(a) $T = 2\pi\sqrt{\frac{m}{k}} = 2\pi\sqrt{\frac{0.2}{50}} = 0.4 s$ (2 points) (b) $v_{max} = A\sqrt{\frac{k}{m}} = 0.1\sqrt{\frac{50}{0.2}} = 1.58 m/s$ (2 points) (c) $E = \frac{1}{2}kA^2 = \frac{1}{2} * 50 * 0.1^2 = 0.25 J$ (2 points) (d) Maximum speed doubles (2 points) (e) Period does not change (2 points)

Multiple Choice:

1. A force is applied to a door handle. At which location will the force create the most torque? (A) Near the hinge (B) In the middle of the door (C) At the edge of the door, farthest from the hinge (D) At any point, torque is the same

2. A solid cylinder and a hollow cylinder with the same mass and radius are released from the top of an incline. Which cylinder will reach the bottom first? (A) The solid cylinder (B) The hollow cylinder (C) They will reach the bottom at the same time (D) It depends on the incline angle

Free Response: A 2 kg solid disk with a radius of 0.5 m is rotating at 10 rad/s. A frictional force is applied at the edge of the disk, bringing it to rest in 5 seconds.

(a) Calculate the initial rotational kinetic energy of the disk. (2 points) (b) Calculate the angular acceleration of the disk. (2 points) (c) Calculate the torque applied by the frictional force. (2 points) (d) Calculate the work done by the frictional force to stop the disk. (2 points) (e) If the radius of the disk is doubled, how does the rotational inertia change? (2 points)

Answer Key:

*Multiple Choice: 1. (C), 2. (A)

Free Response:

(a) $I = \frac{1}{2}mr^2 = \frac{1}{2} * 2 * 0.5^2 = 0.25 kgm^2$, $KE_{rot} = \frac{1}{2}I\omega^2 = \frac{1}{2} * 0.25 * 10^2 = 12.5 J$ (2 points) (b) $\alpha = \frac{\Delta \omega}{\Delta t} = \frac{0 - 10}{5} = -2 rad/s^2$ (2 points) (c) $\tau = I\alpha = 0.25 * -2 = -0.5 Nm$ (2 points) (d) $W = \Delta KE_{rot} = 0 - 12.5 = -12.5 J$ (2 points) (e) Rotational inertia is quadrupled (2 points)