An arrangement of two pulleys, as shown in the figure, is used t o lift a 47.9-

Question

An arrangement of two pulleys, as shown in the figure, is used t o lift a 47.9- kg mass a distance of 3.70 m above the starting point, Assume the pulleys and rope are Ideal and that all rope sections are essentially vertical. What is the mechanical advantage of this system? (In other words, by what factor is the force you exert to lift the weight multiplied by the pulley system?) What is the change in the potential energy of the weight when it is lifted a distance of 3.70 m? How much work must be done to lift the 47.9-kg mass a distance of 3.70 m? What length of rope must be pulled by the person lifted the weight 3.70 m higher in the air?

Explanation / Answer

now the tension in the strimgs = T= F. the weight is balanced by a force equivalent to 2F ==> mg = 2F. hence , the mechanical advantage is = 2. change in PE= mgh = 47.9 X 9.8 X 3.70 = 1736.85 J. work done = 1/2 of PE = 868.42 J. twice the length of the rope must be pulled. ==> L= 7.4 mts.

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