Aim: How do we apply conservation of energy to solving problems?

Conservative Forces We have only spoken about two forms of potential energy; gravitational potential energy and elastic potential energy. However, we know that there must exist other forms of potential energy. What is the link between the force and its associated potential energy function?

F=-dU/dx Since the work done by a conservative force is equal to negative the change in potential energy and the work done by a conservative force is equal to the integral of the force with respect to position, we can derive that WC=-ΔU and W=∫Fdx F=-dU/dx

Derive an equation for the force function of the following potential energy function 1) U(x) = 4x3 -7x dU/dx=12x2-7 F=-12x2 + 7 2) U(x) = -10x2 + 4 dU/dx=-20x F=20x 3) U(x) = 10/x5 +8/x4 dU/dx=-50x-6 -32x-5 F=50x-6 +32x-5 4) U(r) = -5r7 dU/dr= -35r6 F=35r6 5) U(r) = 2/r3 – 11/r dU/dr = -2r-4 + 22r-2 F=2r-4 -22r-2