Atwood Machine Tensional Value Problem HELP!

1. Nov 29, 2010

naganalf

1. A pulley with mass Mp and a radius Rp is attached to the ceiling, in a gravity field of 9.81 m/s^2 and rotates with no friction about its pivot. Mass M2 is larger than mass m1. The quantities Tn and g are magnitudes.

A) T3 is ..... T1 + T2
B) T1 is ..... m1g.
C) The C.M. of Mp+m1+M2 does not accelerate.
D) T3 is ..... m1g + M2g + Mpg.
E) T2 is ..... T1
F) The magnitude of the acceleration of m1 is ..... that of M2.

I have not included a diagram, but this seems to be a standard Atwood machine. First of all, using Fnet = ma, for each mass, I found that:

T2 = M2g - M2a,
T1 = m1a + m1g
T3 (the tensional force holding the pulley to the ceiling) = M2g + m1g + Mpg

Using this knowledge, I determined that:

A) T3 > T1 + T2
B) T1 > m1g
C) True (because the pulley itself is not accelerating)
D) T3 = m1g + M2g + Mpg (I have a feeling this might be where I went wrong)
E) T2 > T1 (I wasn't sure about this one either, chose it because M2 is greater)
F) The magnitude of the acceleration of m1 is = that of M2

This is my last question of an assignment due in only two hours, and I'm completely stumped. Any help is greatly appreciated. Thanks!

EDIT*** figured it out - C is false and D is <
sorry

Last edited: Nov 29, 2010
2. Oct 10, 2015

SLesh

Why is D "<"? I also expected them to be equal.

3. Oct 11, 2015

haruspex

< is correct. This is a dynamic situation, so the tensions are lower than needed to retain stasis.