Conceptual Questions

  1. If a particle’s speed increases by a factor of 3, by what factor does its kinetic energy change?

  2. Particle A has half the mass and eight times the kinetic energy of particle B. What is the speed ratio vA/vB?

  3. An elevator held by a single cable is ascending but slowing down. Is the work done by tension positive, negative, or zero? What about the work done by gravity? Explain.

  4. The rope in FIGURE Q9.4 pulls the box to the left across a rough surface. Is the work done by tension positive, negative, or zero? Explain.

    FIGURE Q9.4

    The figure shows a rope pulling a box to the left across a rough surface. A force vector arrow from the free end of the rope points to the left.

  5. A 0.2 kg plastic cart and a 20 kg lead cart both roll without friction on a horizontal surface. Equal forces are used to push both carts forward a distance of 1 m, starting from rest. After traveling 1 m, is the kinetic energy of the plastic cart greater than, less than, or equal to the kinetic energy of the lead cart? Explain.

  6. A particle moving to the left is slowed by a force pushing to the right. Is the work done on the particle positive or negative? Or is there not enough information to tell? Explain.

  7. A particle moves in a vertical plane along the closed path seen in FIGURE Q9.7, starting at A and eventually returning to its starting point. Is the work done by gravity positive, negative, or zero? Explain.

    FIGURE Q9.7

    The figure illustrates a closed path of a particle, starting and ending at point "A". An arrow labeled Up at the center of the path points upward.

  8. You need to raise a heavy block by pulling it with a massless rope. You can either (a) pull the block straight up height h, or (b) pull it up a long, frictionless plane inclined at a 15° angle until its height has increased by h. Assume you will move the block at constant speed either way. Will you do more work in case a or case b? Or is the work the same in both cases? Explain.

  9. A ball on a string travels once around a circle with a circumference of 2.0 m. The tension in the string is 5.0 N. How much work is done by tension?

  10. A sprinter accelerates from rest. Is the work done on the sprinter positive, negative, or zero? Explain.

  11. A spring has an unstretched length of 10 cm. It exerts a restoring force F when stretched to a length of 11 cm.

    1. For what length of the spring is its restoring force 3F?

    2. At what compressed length is the restoring force 2F?

  12. The left end of a spring is attached to a wall. When Bob pulls on the right end with a 200 N force, he stretches the spring by 20 cm. The same spring is then used for a tug-of-war between Bob and Carlos. Each pulls on his end of the spring with a 200 N force. How far does the spring stretch? Explain.

  13. The driver of a car traveling at 60 mph slams on the brakes, and the car skids to a halt. What happened to the kinetic energy the car had just before stopping?

  14. The motor of a crane uses power P to lift a steel beam. By what factor must the motor’s power increase to lift the beam twice as high in half the time?