Mastering Physics Solutions: Mechanical Advantage

Mastering Physics Solutions: Mechanical Advantage

On September 28, 2013, in Chapter 04: Force and Motion, by Mastering Physics Solutions

Mechanical Advantage

Part A = 254.8 N
Part B = 509.6 N
Part C = 509.6 N

Solution Below:

The pulley system shown in the figure is used to lift a 52-kg crate. Note that one chain connects the upper pulley to the ceiling and a second chain connects the lower pulley to the crate. Assume the masses of the chains, pulleys, and ropes are negligible.

Part A

Determine the force F required to lift the crate with constant speed.

Since this is a pulley system, we have to count the number of “ropes” involved. There are two halves of rope on the pulley holding up the block, so the amount of force required for each is one half the total. The total force is just mass times gravity:

2T = mg
2T = 52 * 9.8
T = 254.8 N

254.8 N

Part B

Determine the tension in the upper chain.

The chains are not part of the pulley system. Each chain is subject to the same magnitude of force as the gravitational force on the block:

T = mg
T = 509.6 N

509.6 N

Part C

Determine the tension in the lower chain.

This is the same as in Part B (509.6 N)

509.6 N

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