# How Do You Solve a Physics Problem Involving Two Masses and a Pulley?

• joemama69
In summary: SUB] - .5m1/SUB]g + .25m2/SUB])/(g/2) = (.25m2/SUB] + .5m1/SUB])/gIn summary, we are given a system where an unknown mass m1 hangs from a massless string and descends with an acceleration g/2, while the other end is attached to a mass m2 sliding on a frictionless horizontal table. The string goes over a uniform cylinder of mass m2/2 and radius R, rotating without friction about a horizontal axis. To find the tension in the horizontal and vertical sections of the string, we use free-body diagrams and equations involving the masses, acceleration, and
joemama69

## Homework Statement

An unknown mass, m1, hangs from a massless string and descends with an acceleration g/2. The other end is attached to a mass m2 which slides on a frictionless horizontal table. The string goes over a uniform cylinder of mass m2/2 and radius R. The cylinder rotates about a horizontal axis without friction and the string does not slip on the cylinder. Express your answers in parts b, c, and d in terms of g, m2 and R.

a) Draw free-body diagrams for the cylinder and the two masses.

b) What is the tension in the horizontal section of the string?

c) What is the tension in the vertical section of the string?

d) What is the value of the unknown mass m1?

## The Attempt at a Solution

part b)

T1/SUB] = m2/SUB]a
T2/SUB] -m1/SUB]g = -m1/SUB]a
T2/SUB]R - T1/SUB]R = MR2/SUP]$$\alpha$$...T2/SUB] - T1/SUB] = Ma

T1/SUB] = T2/SUB] - Ma = m1/SUB]g - .5m1/SUB]g - .25m2/SUB]g = g(.5m1/SUB] - .25m2/SUB])

part c)

T2/SUB] = T1/SUB] + Ma = .5m2/SUB]g + .25m2/SUB]g = .75m2/SUB]g

part d) it keeps canceling out,, is something wrong above

#### Attachments

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?m1/SUB] = (T2/SUB] - T1/SUB])/(g/2) = (.75m2/SUB] - (g(.5m1/SUB] - .25m2/SUB]))/(g/2)

?

I would first commend the student for their attempt at solving the problem and using the appropriate equations. However, it seems that there may be some errors in their calculations. I would suggest going back and carefully checking each step to ensure accuracy. Additionally, it may be helpful to draw a free-body diagram for each mass and the cylinder to better visualize the forces at play. Once the equations are correctly set up, solving for the unknown mass m1 should be possible.

## 1. What is a pulley and how does it work?

A pulley is a simple machine that is used to change the direction of a force. It consists of a wheel with a groove around its circumference, and a rope or chain that runs through the groove. When a force is applied to one end of the rope, the other end moves in the opposite direction. This allows for the transfer of force from one point to another without changing the magnitude of the force.

## 2. How does a pulley affect the movement of two masses?

A pulley can be used to distribute the weight of two masses so that they are easier to move. By connecting the two masses with a rope or chain and running it through the pulley, the force needed to lift both masses is reduced. This is because the weight of each mass is distributed between the two sides of the pulley, making it easier to lift.

## 3. What is the difference between a fixed pulley and a movable pulley?

A fixed pulley is attached to a stationary object, while a movable pulley is attached to the object being lifted. In a fixed pulley, the direction of the force remains the same, but the force required to lift the object is reduced. In a movable pulley, the direction of the force changes, but the force required to lift the object is also reduced.

## 4. Can a pulley system be used to lift objects that are heavier than the input force?

Yes, a pulley system can be used to lift objects that are heavier than the input force. This is possible because the force required to lift an object is reduced when using a pulley. However, the trade-off is that the distance the input force must travel is increased.

## 5. How does friction affect the movement of two masses connected by a pulley?

Friction can have a significant impact on the movement of two masses connected by a pulley. If there is a lot of friction between the pulley and the rope or chain, it can reduce the efficiency of the system and make it more difficult to lift the masses. To minimize the effects of friction, it is important to use a well-lubricated pulley and a strong, high-quality rope or chain.

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