The spring is unstretched at the position x = 0. under the action of a force p, the cart moves from the initial position x1 = -8 in. to the final position x2 = 5 in. determine (a) the work done on the cart by the spring and (b) the work done on the cart by its weight.

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Solution:
(a) The work done by the spring is given by

where k is the elastic constant of the spring and  is the stretch between the initial and final position. Since x1=-8 in=-0.203 m and x2=5 in=0.127 m, we have


(b) The work done by the weight is the product of the component of the weight parallel to the inclined plane and the displacement of the cart:

where  the negative sign is given by the fact that  points in the opposite direction of the displacement of the cart, and where

therefore, the work done by the weight is

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