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Multiple pulley problem

by jumptheair
Tags: multiple, pulley, solved
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Oct12-07, 02:31 PM
P: 16
1. The problem statement, all variables and given/known data

**Image of apparatus

When a patient's injured neck is healing, it is often desirable to prevent the weight of the head from pushing down on the neck. This can be accomplished with the system of pulleys shown in the figure. The pulleys are small and light and have no appreciable friction. The rope about pulleys 1 and 3 make an angle of θ1 = θ2 = 26.0; pulleys 1 and 3 are constrained to move only in the vertical direction. Typically, a person's head makes up 7.00 % of the body weight. If the head of a 65.0 kg person is to be supported completely by the apparatus shown, what should the mass M of the weight W be?

2. Relevant equations


3. The attempt at a solution

I started with the head component and determined that pulley 1 and 3 are each responsible for maintaining half of the weight of the head of 44.59N. From then on, I do not know how to draw the FBD of neither pulley 1 or 3 as a system. I would appreciate any help that can hint me on figuring out the answer. Thanks.
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Oct12-07, 08:17 PM
Astronuc's Avatar
P: 21,870
The weight W puts a tension in the line, and in a static situation T = W =Mg. With frictionless pulleys, the tension in the line must be the same along the length of the line.

Then either pulley 1 or 3 support half the head weight.

For either pulley, the tension pulls upward - one side vertically, and the other side at angle 26.0 from vertical.

Determine the tension T, necessary to support half the head, then M = T/g.
Oct12-07, 08:33 PM
P: 16
Got it. Thanks!

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