Atwood with Sliding mass and real pulley

AI Thread Summary
The discussion revolves around calculating the speed of a hanging block and the angular speed of a pulley in a system involving two blocks and a pulley. The user attempts to apply the work-energy theorem and Newton's second law for both translation and rotation but struggles with the calculations and understanding of forces. There is confusion regarding the tension in the string and whether the pulley is frictionless, as well as the relationship between the accelerations of the two blocks. A suggestion is made to simplify the problem using conservation of energy instead of the work equations presented. The conversation emphasizes the importance of correctly applying fundamental physics principles to solve the problem.
SadDan
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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?
 
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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?
Screen Shot 2017-04-03 at 12.21.06 AM.png
 
And all the information we were given is on the question so I'm assuming its not frictionless
 
SadDan said:
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.
 
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