A block of mass

Two blocks of mass

Hint and answer

Two blocks of mass

Two blocks of mass

Hint and answer

Two blocks of mass

Two blocks of mass

Hint and answer

A block of mass

Hint and answer

A block of mass

Hint and answer

A block of mass

Hint and answer

The hints and answers for these pulley problems will be given next.

Hint and answer for Problem # 2

This is called the Atwood machine and is commonly used for demonstration in physics classes.

Apply Newton's second law to the block on the left. We have

Answer:

Hint and answer for Problem # 4

For the maximum mass

For the minimum mass

Answer: Minimum

Hint and answer for Problem # 6

This is a challenging problem! It took me a while to figure this one out!

At some angle

It is known that

If

Apply the equilibrium equation to block

There is no need to consider block

For no sliding

This is the same as case 1, by symmetry. Hence, the final inequality for this case is:

The blocks will slide together in one direction or the other. To determine the direction we must first calculate the net force pulling down on each block along their respective inclines, as a result of gravity. We do this as follows:

For block

For block

We now have three sub-cases to consider. The final inequalities for this case will be given within these three sub-cases, as follows.

If

If

Hence, for no sliding:

If

Hence, for no sliding:

We are done!

Hint and answer for Problem # 7

Apply the condition of static equilibrium to the block. We have 2

Answer:

Hint and answer for Problem # 8

Apply the condition of static equilibrium to the block. We have 2

Answer:

Hint and answer for Problem # 9

Upon close inspection we see that the bottom two pulleys are held up by four segments of rope. The tension in the rope is assumed equal throughout its length (a good assumption for ropes in general since they weigh little). Three of the four rope segments are vertical while the remaining rope segment is at a small angle with the vertical. But for ease of calculation we can treat it as being exactly vertical. Since we are ignoring the mass of the pulleys, the tension in the four rope segments must equal the weight of the mass, in order to satisfy the condition of static equilibrium. Hence, 4

Answer:

A conveyor belt carrying aggregate is illustrated in the figure below. A motor turns the top roller at a constant speed, and the remaining rollers are allowed to spin freely. The belt is inclined at an angle

Find the point of maximum tension in the belt. You don’t have to calculate it, just find the location and give a reason for it.

You can get the solution for this in PDF format. It's available through this link

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