What are the accelerations of the blocks?

[Vitani11]

Homework Statement

Two blocks of mass m1 = 0.500kg and m2 = 0.510kg are connected by a string that passes over a pulley with frictionless bearings. The pulley is a uniform 0.050kg disk with a radius of 0.04m. Assume that the string is massless and inextensible and that it does not slip on the pulley.

a. What are the accelerations of the blocks?

b. What is the tension in the string between block 1 and the pulley? Block 2 and the pulley? By how much do these tensions differ?

c. If the pulley were massless, what would your answers for a) and b) be?

Homework Equations

T1 = tension in string attached to mass 1
T2 = tension in string attached to mass 2
m1 = 0.500kg mass of mass 1
m2 = 0.510kg mass of mass 2
m3 = 0.050kg mass of pulley
r = 0.04m radius of pulley
I = 1/2MR^2 moment of inertia for pulley
alpha = angular acceleration of pulley

The Attempt at a Solution

I set up three equations using force diagrams. For mass 1 I have T1 = m1a. For mass two I have T2 = m2a. For the pulley I used Torque = (1/2)MR^2 * alpha = rF where there are two cases of F being T1 or being T2.

I'm not sure what to do about finding the acceleration. I would like help with the a) but if you can help with b) that would be greatly appreciated.

My solution for a) is a=2T1/m3 for mass one which is obviously wrong. I got the same for mass two.

 

[Simon Bridge]

Your diagram shows both blocks on a horizontal surface, with the pulley between them.
So how would anything be in motion at all?

Could it be that one or both blocks should be acted on by gravity?
ie. neither are sitting on a surface?

Your approach to free body diagrams needs to be revised: for instance, make sure you pice a direction to count as positive. Newton's law is $\sum \vec F = m\vec a$ Not $\sum F = T-ma = 0$. (ma is the result of an unbalanced force, not a force itself).

 

[Vitani11]

Your diagram shows both blocks on a horizontal surface, with the pulley between them.
So how would anything be in motion at all?

Could it be that one or both blocks should be acted on by gravity?
ie. neither are sitting on a surface?

Your approach to free body diagrams needs to be revised: for instance, make sure you pice a direction to count as positive. Newton's law is $\sum \vec F = m\vec a$ Not $\sum F = T-ma = 0$. (ma is the result of an unbalanced force, not a force itself).

They're literally both as the diagram says unless you can interpret the problem statement differently. I also didn't understand how they could be moving but I figured this is what had to be going on since they're accelerating

 

[Vitani11]

They're literally both as the diagram says unless you can interpret the problem statement differently. I also didn't understand how they could be moving but I figured this is what had to be going on since they're accelerating

In fact now that I think of it you're likely correct in saying gravity would come into play because that's all general physics one was about. My professor is not so explicit - sorry for the ambiguity.

 

[Vitani11]

Okay so it is a typical Atwood machine just with a mass and so torque for the pulley... still sort of stuck

 

[Simon Bridge]

Okay so it is a typical Atwood machine just with a mass and so torque for the pulley... still sort of stuck

That's what I thought ... generally when things are supposed to be sitting on a surface, the problem statement will say that in pretty much those words. When they hang by a string that passes over a pulley, it's usually an Atwood machine.

You go through the free body diagrams as usual - remember to pick a direction for positive, be careful to consistently link the equations.
ie. if m1 is on the left and m2 on the right of the pulley, then the pulley will rotate which way?

I'll start you off:
For the 1st mass, the forces are $m_1g$ down and $T_1$ up, pick "up=positive" and write $T_1-m_1g = m_1a$ call it eq(1).
(Since the string does not stretch, both masses have the same magnitude acceleration.)
You will need a similar equation for the other mass and the pulley.
You can save some work by thoughtful selection of which way to call "positive".