Consider two objects with m1, m2 connected by a light string

[Ab17]

1. The problem statement, all variables and given/known

Consider two objects with M1 greater M2 connected by a light string that passes over a pulley having a moment of inertia I about its axis of rotation. The string does not slip on the pulley or stretch. The pulley turns with friction. The two objects are released from rest separated by a vertical distance 2h

(a) use the principal of conservation energy to find the translational speeds of the objects as they pass each other

(B) find angular speed of the pulley at this time

Homework Equations

m1gh = m2gh + 1/2mv^2 + 1/2m1v^2 + 1/2I(V^2/R^2)[/B]

V= sqrt(2(m1gh-m2gh)/m2 + m1 + I/R^2)

Is this the right answer because it considers when the m1 block moves 2h down not when it passes the other block. How is this solved then??

The Attempt at a Solution

 

[Doc Al]

Is this the right answer because it considers when the m1 block moves 2h down not when it passes the other block.

No it doesn't. Hint: How far has each block moved when they pass each other?

 

[Ab17]

2h? Thats the only height in the problrm

 

[Doc Al]

2h? Thats the only height in the problrm

Draw yourself a diagram. Hint: If one block goes up a distance x, the other goes down a distance x.

 

[Ab17]

So if one block goes a distance 2h down then the other block goes a distance 2h up since they are connected by the same string

 

[Doc Al]

So if one block goes a distance 2h down then the other block goes a distance 2h up since they are connected by the same string

That would be true, of course, but how far have they moved when they pass? If they start out at 2h apart, how far must each move to reach the other?

 

[Ab17]

H?

 

[Doc Al]

H?

Right. They meet after M1 moves down a distance h and M2 moves up a distance h. (If you're unsure of this, play it out with a piece of string.)

 

[haruspex]

The pulley turns with friction.

Should this say without?

 

[Ab17]

Yes mistake there

 

[Doc Al]

I assumed it was just a typo.