




Solution Define downward as negative. Here it's more convenient to draw a separate free body diagram. The dashed line box identifies the object in the free body diagram. Since 2 ropes protrude from the top of the dashed box, 2 tension forces are show on the free body diagram. Because ropes can only pull not push, the tension forces have to go upward. The pulley is modeled as massless and friction free, so the 2 tension forces have to be equal. To solve the problem, we must find the normal force. S F = ma Ft1 + Ft2 + Fw = ma since Ft1 = Ft2 2 Ft + Fw = ma 2 F_{t} = ma  Fw F_{t} = 1/2 (ma  Fw)
F_{t} = 1/2 [ ma  ( mg) ]
= 1/2 m(a + g)
= 640 n 

Conclusion and Significance Using the pulley and harness reduces the required tension force by 1/2. giving Bob a mechanical advantage of 2. The system, however, has a downside if Bob pulls the rope downward by 1 meter, he will go upward by only 1/2 a meter. In other words, there is no "free lunch". Bob will have to pay for the increase in total upward force by going upward half as fast. 
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