1. When a cannon sitting on a level frictionless surface fires a cannonball the cannon recoils because
   • (A) the kinetic energy of the cannonball/cannon system is conserved before and after the firing.
   • (B) the momentum of the cannonball/cannon system is conserved before and after the firing.
   • (C) the kinetic energy of the cannon must equal the kinetic energy of the cannonball.
   • (D) the momentum of the cannon is greater than the momentum of the cannonball.
   • (E) the momentum of the cannon is less than the momentum of the cannonball.

2. Consider an elastic, head-on collision between two objects of equal mass. Before the collision, Object 1 was moving to the right with speed v and Object 2 was at rest on a horizontal frictionless surface. Which of the following statements concerning the velocities after the collision is correct?
   • (A) Object 1 now moves to the left with speed v and Object 2 remains at rest.
   • (B) Object 1 is now at rest and Object 2 moves to the right with speed v.
   • (C) Both objects are now at rest.
   • (D) Both objects move to the right with speed v.
   • (E) Both objects move to the right with speed ½ v.

3. The wheel of a shopping cart is rolling without slipping. Consider a point on the wheel, A, that is halfway between the rim of the wheel and the axle. If v_A is the tangential speed of point A relative to the axle and v_cart is the translational speed of the wheel as it moves along the floor, then
   • (A) v_A = ¼ v_cart
   • (B) v_A = ½ v_cart
   • (C) v_A = v_cart
   • (D) v_A = 2 v_cart
   • (E) v_A = 4 v_cart

4. A uniform rod has a weight W and a length L. It is hinged to a wall by a pivot attached to one end and held in a horizontal position by a vertical massless string attached to the other end. What is the magnitude of the torque exerted by the string about a horizontal axis which passes through the hinge and is perpendicular to the rod?

   (A) ¼ W L (B) ½ W L (C) W L (D) 2 W L (E) 4 W L

5. Consider a mass m hanging freely from a cord attached to a cylindrical pulley of mass M and radius R. The pulley is mounted on a horizontal frictionless shaft and is initially held so that it does not rotate. If the pulley is now released, the acceleration of the mass m is:

   (A) g (B) 0 if M > m (C) < g (D) > g (E) < g, = g, > g depending on the relative sizes of m and M.

6. A student is spinning on a stool with her arms outstretched. When she brings her arms closer to her body which of the following is true? (Neglect any frictional effects on the stool's rotation.)
   • (A) Her angular momentum and angular velocity decrease;
   • (B) Her angular momentum decreases and her angular velocity remains constant;
   • (C) Her angular momentum remains constant and her angular velocity decreases;
   • (D) Her angular momentum remains constant and her angular velocity increases;
   • (E) Her angular momentum and angular velocity increase.

7. Consider a mass attached to an ideal spring. The mass is undergoing simple harmonic motion. Let x represent the displacement of the mass from equilibrium, v represent the velocity of the mass, and a represent the acceleration of the mass. Which of the following statements is correct?
   • (A) x and v reach maximum magnitude at the same time.
   • (B) v and a reach maximum magnitude at the same time.
   • (C) x and a reach maximum magnitude at the same time.
   • (D) a is constant throughout the motion of the mass.
   • (E) v is constant throughout the motion of the mass.

8. An object on a frictionless surface is attached to a horizontal ideal spring. The object is initially displaced a horizontal distance from the equilibrium position and then released. Which of the following statements is FALSE regarding the kinetic energy of the object when it passes through the equilibrium position?
   • (A) It depends on the spring constant.
   • (B) It depends on the magnitude of the initial displacement from equilibrium.
   • (C) It depends on the mass of the object.
   • (D) It is the same whether the initial displacement compresses or stretches the spring.
   • (E) It is positive when the mass is moving in the chosen negative direction.

9. When additional pressure is applied to the input piston of a hydraulic car lift,
   • (A) a lesser additional pressure acts on the output plunger.
   • (B) the same additional pressure acts on the output plunger.
   • (C) a greater additional pressure acts on the output plunger.
   • (D) the change in pressure on the output plunger cannot be determined since it depends on the ratio of the areas of the input piston and output plunger.
   • (E)the change in pressure on the output plunger cannot be determined since it depends on the height difference between the input piston and output plunger.

10. It is observed that a steel ball floats in liquid mercury and sinks in water. Which statement is correct regarding the buoyant force acting on the steel ball?
    • (A) It is greater when the ball is floating on the mercury;
    • (B) It is greater when the ball is totally submerged in water;
    • (C) It is the same in both cases (A) and (B);
    • (D) Either (A), (B), or (C) may be correct depending on the mass of the steel ball;
    • (E) Either (A), (B), or (C) may be correct depending on the volume of the steel ball.

ANSWERS:

1. (B) - Since the net external force on the cannonball/cannon system is 0, its momentum is conserved.
2. (B) - For an elastic collision, the kinetic energy as well as the momentum is conserved. Option (A) does not conserve the direction of the momentum, options (C) and (D) conserve neither momentum nor kinetic energy, and option (E) does not conserve kinetic energy.
3. (B) - Tangential speed is proportional to distance from the axis of rotation (the axle). Since the tangential speed of a point on the rim of the wheel equals the translational speed of the wheel along the floor, the tangential speed of a point halfway between the rim and the axle is ½ the translational speed.
4. (B) - The net torque on the rod is zero since it is in equilibrium. The torques about the pivot are those due to the rod's weight and the tension in the string. Since these torques must be equal and opposite, and the magnitude of the torque due to the weight of the rod is W (½ L), the magnitude of the torque due to the string is also W ½ L.
5. (C) - Tension in the cord provides the required torque to rotate the pulley. Therefore, the net force on the hanging mass is less than its weight and so its acceleration is less than g.
6. (D) - Ignoring friction, the net torque on the student/stool system is zero. Therefore angular momentum ( = Iw) is conserved (remains constant). Since I decreases when the arms are brought in, the angular velocity increases.
7. (C) - At maximum displacement, the mass is momentarily at rest (v = 0). However, since the magnitude of the spring force is proportional to displacement from equilibrium, maximum displacement corresponds to maximum acceleration.
8. (C) - The mechanical energy put into the system depends only on the spring constant and the initial displacement from equilibrium. Mechanical energy is conserved since no friction. When the mass passes through the equilibrium position, the kinetic energy equals the total energy (potential energy is 0 at equilibrium position), and since the total mechanical energy depends only on the spring constant and the initial displacement from equilibrium (not on the mass of the object), the kinetic energy does not depend on the mass of the object.
9. (B) - Pascal's Principle
10. (A) - Since the buoyant force in mercury is able to support the weight of the ball, and the buoyant force in water is not, the buoyant force in mercury is greater.

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