Chapter 23.1, Problem 3aTH

We begin by considering the forces exerted on a ring that is connected to a spring and that is free to slide along a rod. (See the top view diagram at right.)

Assume that the ring is massless and that the rod is frictionless.

1. What is the n, force on the ring? (Hint: Consider what happens to the net force on an object as its mass approaches zero.) Explain.

Does the net force on a massless ring depend on the acceleration of the ring? Explain

What is the magnitude of the gravitational force exerted on the ring? (Recall that the ring is massless.)

Does the foe exe on the ring by the md have a component that is parallel to the rod? Explain. (Hint: Recall the assumptions made above.)

In the space at right, draw and label a free−body diagram for the ring at the instant when it is farthest from its equilibrium position. (Hint: Which objects are in contact with the ring?)

Check that your free-body diagram is consistent with your answers to pans i and ii.

For the instant shown in your free-body diagram, does the force exerted on the ring by the spring have a component that is parallel to the rod? Explain.

Would your answer above differ if you considered an instant when the free end was not at its farthest point from its equilibrium position? Explain.

What do your results in part iv suggest about the shape of the spring very near the ring? In particular, which of the diagrams at right best represents the “slope” of the spring at the point where the spring is connected to the ring?