A uniform rod of length L and weight W is placed on a fulcrum a distance of 0.2L from the left end.On the left end is placed a mass of weight 3W and on the right end a vertical force F is applied to keep the system in balance.What are the magnitude and direction of the force F?

A) W,up
B) W,up
C) W,down
D) W,down
E) 0.6W,down

Question

A uniform rod of length L and weight W is placed on a fulcrum a distance of 0.2L from the left end.On the left end is placed a mass of weight 3W and on the right end a vertical force F is applied to keep the system in balance.What are the magnitude and direction of the force F?
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A) W,up 
B) W,up 
C) W,down 
D) W,down 
E) 0.6W,down

Quizplus · Accepted Answer

The first step is to find the distance between the right end and the fulcrum. Since the fulcrum is 0.2L from the left end, the distance between the right end and the fulcrum is 0.8L. We can then use the principle of moments to solve for F. The clockwise moment (due to the weight of the rod) is W(0.5L), and the counterclockwise moments are 3W(L) and F(0.8L). For the system to be in balance, the moments must be equal, so we have:
W(0.5L) = 3W(L) + F(0.8L)
Simplifying and solving for F, we get:
F = (0.5W/0.8L)(L) = 0.625W
Since the weight is pulling down, the force F must pull up to balance the system, so the answer is 0.625W, up. Choice C is the only one that matches this answer.

A Uniform Rod of Length L and Weight W Is