Ropes and Pulleys

Pulleys

Pulleys only change the direction of the tension force not the magnitude

A. greater thanB. less thanC. equal to

All three 50 kg blocks are at rest. Is the tension in rope 2 greater than, less than or equal to the tension in rope 1?

A. greater thanB. less thanC. equal to

All three 50 kg blocks are at rest. Is the tension in rope 2 greater than, less than or equal to the tension in rope 1?

Newton’s first law for the block on the left proves that the tension equals the weight. Newton’s first law for either of the individual blocks on the right proves that the tension equals the weight for an individual.

A. greater thanB. less thanC. equal to

The block on the far right is moving up with constant speed. Is the tension in rope 2 greater than, less than or equal to the tension in rope 1?

A. greater thanB. less thanC. equal to

The block on the far right is moving up with constant speed. Is the tension in rope 2 greater than, less than or equal to the tension in rope 1?

This is still a Newton’s first law situation!

In the figure to the right is the tension in the string greater than, less than, or equal to the weight of block B?

A. Greater thanB. Less thanC. Equal to

In the figure to the right is the tension in the string greater than, less than, or equal to the weight of block B?

A. Greater thanB. Less thanC. Equal to

This is a Newton’s second law situation for each of the blocks. Block A will accelerate to the right and block B will accelerate down. The net force on B must be down by Newton’s second law. The tension force exerted by the rope on block B must be less than the weight force exerted by the earth on block B.

Determine the reading on the spring scale

• Complete 1-6

Acceleration constraints

• Complete 1-5

Ropes and Pulleys (3)Blocks A and B are connected by a massless string over a massless, frictionless pulley. The blocks have just this instant been released from rest.

a. Will the blocks accelerate? If so, in what direction and why?

Ropes and Pulleys (3)b. Draw a separate free-body diagram for each block. Be sure vector lengths indicate the relative size of the force.

c. Rank in order, from largest to smallest, all of the vertical forces. Explain.

Ropes and Pulleys (3)In case a, block A is accelerated across a frictionless table by a hanging 10 N weight. In case b, the same block is accelerated by a steady 10 N tension in the string.

Is block A’s acceleration in case b greater than, less than, or equal to its acceleration in case a? Explain.

Ropes and PulleysMathematical Approach

Example A 60 kg prisoner wishes to escape from a third story window by going down a rope made of bed sheets tied together. Unfortunately, the rope can only hold 500 N. How fast must the prisoner accelerate down the rope if it is not to break?

Example: The two masses (m1 = 5 kg, m2 = 10 kg) are tied to opposite ends of a massless rope and the rope is hung over a massless and frictionless pulley. Find the acceleration of the masses. Find the tension in the rope.

A mass, m1 = 3.00kg, is resting on a frictionless horizontal table is connected to a cable that passes over a pulley and then is fastened to a hanging mass, m2 = 11.0 kg as shown below. Find the acceleration of each mass and the tension in the cable.

Problem #1A mass, m1 = 3.00kg, is resting on a frictionless horizontal table is connected to a cable that passes over a pulley and then is fastened to a hanging mass, m2 = 11.0 kg as shown below. Find the acceleration of each mass and the tension in the cable.

amT

amTgm

maFNet

1

22

2

21

2

122

122

212

/7.714

)8.9)(11(

)(

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gma

mmagm

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