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Discussion Response Post to: Work-Energy Problem

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Soumen Goswami (2446)

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About potential energy ....

Lets take an example

Consider two masses kept at a distance from each other. Let one of the masses be fixed. The other mass experiences a gravitational attraction due to the fixed mass. If the free mass is not stopped, then it will accelerate towards the fixed mass and gain kinetic energy.

Now we will not let the free mass gain kinetic energy. Suppose an external agent applies a force equal and opposite to the gravitational force. Then the free mass is at equilibrium. Now suppose we move the free mass very slowly by an infinitesimal distance dx along the line joining the two particles, away from the fixed mass. The forces still approximately balance. (The gravitational force will change a little, but we may neglect it as the change is very small)

Now, the work done by the external force (against the gravitational force) during this small displacement does not increase the KE of the body, for the particle doesn't accelerate, So where does it go???

Now, work done always changes energy content. We define this work to correspond to the change in potential energy.
Hence
dW = F_ext dx = dU
As F_ext= F_gravdU = -F_grav dx

Or more generally,
dU =F_ext dx = -F_cons dx
That is change in PE is the amount of work done by an external force against a conservative force without changing the KE

All men dream but not equally. Those who dream by night in the dusty recesses of their minds wake in the day to find that it was vanity; but the dreamers of the day are dangerous men, for they may act their dream with open eyes to make it possible.

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