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Object attached to spring is at rest.

A force is then exerted in the positive x-direction that at each position is equal and opposite to the force exerted by the spring - in other words, a force is exerted such that the object on the spring moves with constant velocity in the positive x-direction.

Net work on object is equal to 0. So then where does the "extra" potential energy in the object come from, when it is displaced by that force in the positive x-direction? If I pull an object in this way 5m to the right and keep it at 5m, its potential energy has increased but kinetic energy hasn't.

Please explain as simply as possible. Thanks very much in advance!

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The external force is doing work on the system. The work it does increases the energy of the system. If the spring weren't there, it would increase the kinetic energy of the mass. Because the spring is there, it is increasing the potential energy of the spring.

Looking at the work done only on the mass is not sufficient to account for all the work done on the system.

When we lift a mass into the air at constant speed, the same situation is happening. There is no net work done on the mass (speed is constant), but work is done on the mass/earth system to increase the energy of that system.

Don't think of the potential energy being stored in an object. Instead think of it as the property of your system (be it spring, gravitational, or whatever).


Equivalently you can look at the work being done by the forces. Although the net work done on the mass is zero, the external force is doing positive work and the spring force is doing negative work.

The spring force doing negative work on the mass means that the mass is doing positive work on the spring. This positive work on the spring is increasing the potential energy stored in the spring.

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