A simple machine: two pulleys arranged to help lift a heavy load. A rope runs ar

Question

A simple machine: two pulleys arranged to help lift a heavy load. A rope runs around two massless, frictionless pulleys and the object hangs from one pulley. You exert a force of magnitude F on the free end of the cord and the object rises at a constant speed. Be sure to draw a complete free-body if it is needed to answer any part of this problem.

a) If the pulley/object system is to move up a distance h, through what distance must the applied force move? Express your answer in terms of h.
b) How much work is done by the rope on the pulley/object system? Express your answer in terms of m and h.
c) How much work do you do? Express your answer in terms of m and h.

Explanation / Answer

a) Note well: the length of the string is fixed. It's too bad I can't draw the free-body diagram on here, but I'll do my best with prose. Since in this situation, you have two tension forces (one exerted by one part of the rope on each side of the pulley) pulling up the object, if the object moves up a height h, that means that a length of 2h of the rope must be displaced. What this means is that since each part of the string on each side of the pulley is pulling up the object h in order to raise the object h units, 2h of the rope has to go somewhere. That somewhere is where you're pulling. Therefore, the applied force has to move through 2h units for the object to be raised h units.

b) Since the NET acceleration of the pulley/object system is zero, the NET work is zero. On the pulley/object system, you have two tension forces provided by the rope, and you have the weight of the object. The NET force has to be zero, so the sum of the magnitudes of the two tension forces has to equal the weight of the box because the tension forces and the weight are acting in opposite directions. Since the object moves through a distance h and since the tension forces are constant (because the applied force is constant), the work done by the rope has to equal the opposite of the work done by the weight (otherwise the net force would not be zero). The work done by the rope therefore equals mgh.

c) Since the weight of the box equals twice the tension force, and since the applied force equals the tension force, the magnitude of the applied force equals weight/2. Since the applied force moves through distance 2h as shown in part a, the work done by you is (mg/2)(2h) = mgh, which is the same amount of work done by the rope on the pulley object system.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.