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My past year exam paper had a question about work done against the resistive force, where the answer key said it was resistive force * distance. As I understand it, work done is a measure of impact a force has on an object, but why is the resistive force, which is in the opposite direction of the direction of motion used?

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the resistive force is not "used", it comes on its own (these forces are found in nature as it is). they are generally unwanted but may be necessary sometimes. The best example is the force of friction. it opposes the objects motion and thus some work done by us to make a body move is dissipated as heat. However it is necessary as else without it we would not be able to move!!!!!. I hope I answered you

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  • $\begingroup$ other than friction i cant think of any other resistive force $\endgroup$ – ragvri Aug 29 '14 at 6:52
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The words by or on or against are important in deciding the sign of the work done and what is doing the work.

The applied force does work on the object, equal to the applied force times the distance moved in the direction of the applied force. The effect of this work is to increase the kinetic energy of the object.

At the same time the resistive force is also doing work on the object, in the opposite direction to the motion of the object. This work is the resistive force times the distance moved in the direction of this force. This work is -ve, indicating that the object has done work against the resistive force, ie it has taken energy from the object. It has decreased the kinetic energy of the object.

The work done by the applied force and the work done against the resistive force are not the same thing, and they are not necessarily equal :

Work done by the applied force = net increase in KE of object + work done against resistive force.

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