Question

An object is suspended from the ceiling by a spring aligned along a vertical x axis, with upward defined as the positive x direction. When the spring is at its relaxed length, the object is at the origin of the axis. The object is pulled down to position −x1, held at rest, and released. Consider its motion from the instant of release until the instant it returns to −x1. Ignore friction, air drag, and the inertia of the spring.

part a

What force(s) is exerted on the object during the round trip, and in what direction(s)?

Check all that apply.

a,	The spring force, directed downward.
b,	The spring force, directed upward.
c,	Gravitational force, directed downward.
d,	Gravitational force, directed upward.

part b

How much work is done on the object by the spring as the object travels away from −x1 and back to−x1?

Express your answer in terms of some or all of the variables x1, mass of the object m, and gravitational acceleration g.

Answer 1

Solution: Part (a) The gravitational force and the spring force acts on the object during the round trip. The spring force always acts towards the equilibrium position of the spring. The gravitational force always acts vertically downwards. The spring force directs upward if the object is below the equilibrium position and the spring force directs downward if the object is above the equilibrium position. Part (b) From the work energy theorem, if the initial and final positions are same, the change in potential energy is zero. Therefore, the work done by the spring on the object is zero. In a round trip, the work done by a conservative force is zero.