# Atwood with Sliding mass and real pulley

In summary, the conversation discussed a problem involving two blocks connected by a string and a pulley, with one block being released from rest and falling a certain distance. The goal was to calculate the speed of the second block and the angular speed of the pulley at a specific point. The solution involved using the equations for work and energy, and it was found that the accelerations of the blocks were the same due to being connected by the string on the pulley. The final answer was not correct and further clarification and information, such as a diagram and whether or not the pulley was frictionless, was needed for a more accurate solution. However, it was noted that the given information in the problem did not mention a frictionless pulley

## Homework Statement

Block 1 with mass m1=4.04 kg rests on a very low friction horizontal ledge. This block is attached to a string that passes over a pulley, and the other end of the string is attached to the hanging block 2 of mass m2=2.02 kg, as shown.

The pulley is a uniform disk of radius 11.85 cm and mass 1.980 kg. Calculate the speed of block 2 after it is released from rest and falls a distance of 1.84 m.

What is the angular speed of the pulley at the instant when block 2 has fallen a distance of 1.84 m ?

## Homework Equations

Wtot=change in Energy
KE=1/2 mv^2
W=integral of force*displacement
N2L for rotation and translation

## The Attempt at a Solution

The tension of 2 and 1 on the pulley should be different but the accelerations of the blocks would be the same?
a=m2*g/(mp/2 +m1+m2)
T2=m2(g-a)=13.27
T1=m1*a=13.0829
WEm2=integral from 0 to 1.84 (T2xdx) = 22.47 J
WT1m1=integral from 0 to 1.84 (T1xdx) = 22.1467 J
work energy theorem:
KE=W
1/2mv^2=WEm2+WT1m1
v=sqrt(2(WEm2+WT1m1)/mp)=3.33m/s

This is not the correct answer, I'm not sure what I am doing wrong would the energy side of the equation be only kinetic?

I think the diagram would be helpful. Is the pulley frictionless? Also why would the accelerations be same?

m1 and m2 are atached by a string on a pulley so wouldn't their accelerations be the same?

And all the information we were given is on the question so I'm assuming its not frictionless

m1 and m2 are atached by a string on a pulley so wouldn't their accelerations be the same?

Correct. I can't really understand what the equations for work you've written, up you can just use conservation of energy to do the problem.

## 1. What is an Atwood machine with sliding mass and real pulley?

The Atwood machine with sliding mass and real pulley is a physics apparatus that consists of a massless pulley, a string, and two masses. One mass is attached to the pulley, while the other is allowed to slide along the string. This setup allows for the study of the effects of friction and the real-world applications of pulleys.

## 2. How does the Atwood machine with sliding mass and real pulley work?

The Atwood machine works by utilizing the principles of Newton's laws of motion. The two masses experience an equal and opposite force due to the tension in the string. The sliding mass also experiences a frictional force due to its contact with the string. This setup allows for the measurement of acceleration and the effects of friction on the motion of the masses.

## 3. What are the factors that affect the motion of the Atwood machine with sliding mass and real pulley?

The motion of the Atwood machine is affected by several factors, including the masses of the objects, the tension in the string, and the coefficient of friction between the string and the sliding mass. Other external factors such as air resistance and the angle of the string can also affect the motion of the system.

## 4. What are the real-world applications of the Atwood machine with sliding mass and real pulley?

The Atwood machine with sliding mass and real pulley has several real-world applications, including elevators, cranes, and weightlifting machines. These systems utilize pulleys and friction to move objects with less force, making them more efficient and easier to operate.

## 5. How is the Atwood machine with sliding mass and real pulley different from other Atwood machines?

The Atwood machine with sliding mass and real pulley differs from other Atwood machines in that it takes into account the effects of friction and the real-world application of pulleys. Other Atwood machines often assume an idealized scenario with no friction and massless pulleys, which may not accurately reflect real-world situations.

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