# Two Masses Hanging on a Massive Pulley

1. Dec 4, 2011

### Becca93

The problem statement, all variables and given/known data
A pulley with mass Mp and a radius Rp is attached to the ceiling, in a gravity field of 9.81 m/s2 and rotates with no friction about its pivot. Mass M2 is larger than mass m1. The quantities Tn and g are magnitudes.

(image attached)
Select T-True, F-False, G-Greater than, L-Less than, E-Equal to.
A) T1 is ..... m1g.
B) T2 is ..... T1.
C) The magnitude of the acceleration of m1 is ..... that of M2.
D) The center of mass of Mp+M1+M2 accelerates.
E) T1 + T2 is ..... T3.
F) m1g + M2g + Mpg is ..... T3.

The attempt at a solution

A) G - Because the m2 is greater than m1, the system is accelerating left, so tension in string one would be the weight plus ma.
B) L - System is accelerating left over a pulley, so would tension less?
C) E - The whole system is accelerating, so they should be equal.
D) T - I said true for this one because the distances of m2 and m1 from Mp are constantly changing.
E) L - T1+T2 is responsible for only m1 and m2. T3 is responsible for m1, m2, and Mp, so therefore T1+T2 should be less than T3
F) E - T3 is responsible for the weight of all three masses.
**I'm not sure about this one either. Would moment of inertia or any other rotational force factor in here to make T3 greater?

I've tried GLETLE AND GEETLE and both combinations are incorrect. There is a flaw in my reasoning and I am unable to see where it is.

Edit: My tries are as follows:
1 Incorrect. (Try 1) GLETLE
2 Incorrect. (Try 2) GEETLE
3 Incorrect. (Try 3) GEETLL
4 Incorrect. (Try 4) GLETLL

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Last edited: Dec 4, 2011
2. Dec 4, 2011

### grzz

I would think again re

B,D, E ... and I am still thinking re F!

3. Dec 4, 2011

### Becca93

But why? Am I missing a law or something?

4. Dec 4, 2011

### grzz

re B

The pulley needs a torque so that it can rotate. Hence T2 is .... than T1.

5. Dec 4, 2011

### grzz

I think your F is ok.

6. Dec 4, 2011

### Becca93

So T2 is greater than T1?

Okay. So, would
a-G
b-G
c-E
d-T
e-L
f-L

sound right?

7. Dec 4, 2011

### grzz

So T2 is greater than T1?....I think yes.

re D

If m2 goes down through distance x , what is the distance gone up by m1?

8. Dec 4, 2011

### Becca93

The following are my incorrect answers:
1 Incorrect. (Try 1) GLETLE
2 Incorrect. (Try 2) GEETLE
3 Incorrect. (Try 3) GEETLL
4 Incorrect. (Try 4) GLETLL
5 Incorrect. (Try 5) GGLFLL
6 Incorrect. (Try 6) GGEFLL

9. Dec 4, 2011

### grzz

If m2 goes down through distance x , what is the distance gone up by m1?

10. Dec 4, 2011

### grzz

re E

Is the pulley accelerating downwards or upwards?