We now consider how we can find a conservative force if we are given the associated potential energy function. According to equation, an infinitesimal change in potential energy dU is related to the work done by the conservative force Fc in an infinitesimal displacement ds as follows
dU = -
In one dimension, the above equation reduces to dU = -Fxdx
Thus, Fx =
Let us see how equation can be used for the common known cases:
For gravitational potential energy,
Ug = mgy Fy = -
For spring potential energy,
US = kx2 Fx = = -kx
A conservative force can be derived from a scalar potential energy function
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