# Tension & Pulley system

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1. Jul 11, 2017

1. The problem statement, all variables and given/known data
M = M
There is another mass "m" attached to mass "M" with a rope
There is an acceleration (clockwise)
Does Tension2 smaller,bigger or equal to Tension1?

2. Relevant equations
F = ma

3. The attempt at a solution
So this is what I understand just by the logic:
In any case - T1 > T2 ,

I tried to put it into equations:
T2 = mg - ma
T1 = T2 +Mg - Ma

→→ T1 = mg - ma + Mg - Ma = m⋅(g-a) + M⋅(g-a)

"(g-a)" is constant value. Hence no matter what is the mass correlation between M & m , T2 will always be smaller than T1

Am I right?

Thanks a lot.

2. Jul 11, 2017

### TSny

I think you essentially have it, except for maybe one loose end. As you said, (g-a) is a constant. What must be true about this constant in order for your argument to hold?

3. Jul 11, 2017

mm..
If g=a we get 0 . which means there is no tension in the ropes?

4. Jul 11, 2017

### TSny

Yes, but could a = g?

Maybe I'm being too picky. But is seems to me that your argument requires that (g-a) be a positive constant.
Your equation T1 = T2 + Mg - Ma can be written as

T1 = T2 +M(g-a).

So, T1 is greater than T2 as long as (g-a) is positive. It's not hard to find a reason why (g-a) is positive.

5. Jul 11, 2017

If "m" is big enough to create 9.8 m/s2 acceleration. so a=g . Logically,I think, it could be the case.
Actually I can't find a reason why "(g-a)" must be positive when "a" is bigger than g... maybe that's the direction of the accelaration? if it minus this term will be always positive. but we already defined the direction of the acceleration within the equation.
so I dont know

6. Jul 11, 2017

### TSny

Tension in a string cannot be negative. So, your equation T2 = mg - ma implies g - a cannot be negative. So, you just need to rule out a = g which would imply T2 = 0.

If T2 = 0, then the free body diagrams for the two blocks of mass M would be identical. Yet you know that one block must accelerate upward while the other accelerates downward.

[EDIT: Another approach is to treat the system as a whole. Taking clockwise motion around the pulley as positive, the net external force acting on the system is Fnet = mg + Mg - Mg = mg. Thus the acceleration is Fnet divided by the total mass of the system. You can easily check that this is less than g.]

Last edited: Jul 11, 2017