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Cam mechanisms are used in many machines. For example, cams open and close the valves in your car engine to admit

gasoline vapor to each cylinder and to allow the escape of exhaust. The principle is illustrated in following figure, showing a follower rod (also called a pushrod) of mass m resting on a wedge of mass M. The sliding wedge duplicates the function of a rotating eccentric disk on a camshaft in your car. Assume that there is no friction between the rod and the guide through which it slides, but the coeficients of kinetic friction between the wedge and the base and between the pushrod and the wedge are 0.2. When the wedge is pushed to the left by the force F, the rod moves upward and does something, such as opening a valve. By varying the shape of the wedge, the motion of the follower rod could be made quite complex, but assume that the wedge makes a constant angle of  =15.0°. Suppose you want the wedge and the rod to start from rest and move with constant acceleration, with the rod moving upward 1.00 mm in 8.00 ms. Take m = 0.250 kg and M = 0.500 kg. What force F must be applied to the wedge?

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