Problem: In order to stop a moving object, the object must be caused to expend a total of 75 Joules of energy. This is caused by exerting a force on the moving object, which must then exert an equal and opposite opposing force and must hence do work. How much force must be exerted against the object if it is to be stopped within a distance of 5 meters?
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Solution: The work done in the 5meter distance must be equal to the 75 Joules of energy used up. Since work equals force times distance, 75 Joules is equal to 5 meters multiplied by the force. This could be written as an equation 75 J = ( 5 m)(force). It is clear that force = 75J/ 5m = 15 Newtons.
Generalized Response: Since work is the product of parallel force and distance, the work necessary to dissipate energy E over a distance `ds will be `dW = E = F `ds and F will be the quotient `dW / `ds, or equivalently E / `ds.
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Figure description: The figure below shows the relationships among force, displacement and work for the case of force parallel to displacement. The relationship F = `dW / `ds tells us, for example, that if we wish to do a lot of work `dW over a long distance `ds we must exert only a little force. The relationship `ds = `dW / F tells us, for example, that if we wish to do a lot of work `dW using a large force we need only exert that force through a short distance. The relationship `dW = F `ds tells us, for example, that the more force we exert and the greater the distance over which we exert it, the more work we do.
