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Cam Mechanisms

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 sliding wedge duplicates the function of a rotating eccentric disk on a camshaft of your car. Assume there is no friction between the wedge and the base, between the pushrod and the wedge, or between the rod and the guide through which it slides. When the wedge is pushed to the left by the force , 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 theta =15.0 degrees. 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. What force must be applied to the wedge? Take m=0.250 kg and M=0.500 kg.

Solution Preview

For free body diagram, please see the attached figure.

Because, for rod:
s = u*t + (1/2)*a*t^2
s = displacement = 1.00 mm = 1*10^(-3) m
u = 0 (at rest)
t = 8 ms = 8*10^(-3) s
a = a2 (in m/s^2) ...

Solution Summary

Step by step computation, after mentioning the formulas used in computation.