Acceleration and Tension in Multiple Pulleys

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1. Oct 10, 2015

Lanox

1. The problem statement, all variables and given/known data
Block "m1" sits on a horizontal frictionless surface. Block "m2" is hanging below the pulleys as shown. All of the pulleys are massless and frictionless. Given [m1, m2]. Determine:

a. The tension in each rope.
b. The acceleration of each block.

2. Relevant equations
Sum(F) = ma

3. The attempt at a solution
block m1:
F = m1a
Tension = m1a

block m2:
m2g - T - T = m2a
m2g - 2T = m2a
2T = m2g - m2a

*insert tension found through working block m1

2(m1a) = m2g - m2a
2m1a + m2a = m2g
a(2m1 + m2) = m2g
a = m2g/(2m1 + m2)

a. T = m1a
b. Acceleration = m2g/(2m1 + m2)

I've been been looking around the internet and asking my peers about this problem and we all seem to have varying answers. Could someone verify as to whether or not i'm doing this properly?

Thanks

2. Oct 10, 2015

Orodruin

Staff Emeritus
You have assumed both masses have the same acceleration. Do they?

3. Oct 10, 2015

Lanox

Hm, might it be that block m1 has a greater acceleration due to the rope pulling directly on it? If so how would the acceleration differ?

4. Oct 11, 2015

Orodruin

Staff Emeritus
If mass 1 moves 1 cm, how far does mass 2 move? Hint: The rope is likely assumed to have a fixed length.

5. Oct 11, 2015

Lanox

I believe that mass 2 would also move one centimeter, or would the existence of the rope connected to the hook create a different outcome?

6. Oct 11, 2015

Orodruin

Staff Emeritus
I suggest you write the length of the rope as a function of the positions of the masses.

7. Oct 11, 2015

Mister T

I recommend a pulley. Connect one to a string and use it to lift something. If you don't have a pulley make one out of a key ring. Just loop the string (or a shoe lace) through the ring and use it to lift the keys, just as you would to lift m2.

8. Oct 11, 2015

ehild

Supposing mass m2 moves down by 1 cm. How much longer became both vertical pieces of the rope?
The length of the whole rope is constant. How much shorter becomes the horizontal piece?