An object is suspended from the ceiling by a spring aligned along a vertical x a
ID: 1363301 • Letter: A
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.
What force(s) is exerted on the object during the round trip, and in what direction(s)?
The spring force, directed downward.
How much work is done on the object by the spring as the object travels away from x1 and back to x1?
The spring force, directed upward. Gravitational force, directed downward. Gravitational force, directed upward.The spring force, directed downward.
Explanation / Answer
The force acts on the object during the round trip are gravitational force and spring force. The spring force always acts towards the equilibrium position of the spring and the gravitational force acts always vertically downwards.
When the object is below the equilibrium position, the spring force is directed upwards. When the object is above the equilibrium position, the spring force is directed downwards.
From the work energy theorem, the work done on the object is equal to the sum of the change in spring potential and gravitational potential energy. As the object’s initial and final positions are same, the change in potential energy is zero. Thus, the work done on the object by the spring is zero.
This is also known as the work done by a conservative force in a round trip is zero.