Question

A spring is laid horizontally on a frictionless table and attached at one end to a rigid wall. A mass is attached to the other end of the spring, and the spring is either stretched or compressed away from its equilibrium position by pulling the mass along the frictionless table. The mass is then released. Characterize the work done by the spring on the mass as the mass is pulled/pushed from the extended/compressed position back towards the spring's equilibrium position. Select the correct answer

O The work done by the spring on the mass is always negative throughout the return to the equilibrium position.
O The work done by the spring on the mass is always positive throughout the return to the equilibrium position.
O During the return to the equilibrium position, the work done by the spring on the mass is negative half of the time, and positive the other half of the time
O During the return to the equilibrium position, the work done by the spring on the mass is negative if it was stretched and positive if it was compressed
O During the return to the equilibrium position, the work done by the spring on the mass is positive if it was stretched and negative if it was compressed

Answer 1

The work done by the spring on the mass as it returns to its equilibrium position is always positive because the force exerted by the spring and the displacement of the mass is in the same direction, and as the spring moves towards equilibrium, its potential energy is converted to the kinetic energy of the mass.

Step-by-step explanation:

Characterizing the Work Done by a Spring on a Mass

When characterizing the work done by a spring on a mass as it moves from an extended or compressed position back toward the spring's equilibrium position, it is important to understand the forces at play.

According to Hooke's Law, the force exerted by a spring is Fx = -kx, meaning it is always opposite to the displacement (positive x for stretch, negative x for compression). Thus, as the spring returns to its equilibrium position (x = 0), the work done by the spring on the mass is positive because the force exerted by the spring and the displacement of the mass is in the same direction.

Therefore, the correct statement is: The work done by the spring on the mass is always positive throughout the return to the equilibrium position.

This can be further understood by considering that the potential energy stored in the spring is given by PEs = 1/2kx². As the spring approaches the equilibrium position, the potential energy decreases indicating that work is done by the spring on the mass, increasing the kinetic energy of the mass until it reaches the equilibrium position.