Acceleration and Tension in Multiple Pulleys

[Lanox]

Homework Statement

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.

Homework Equations

Sum(F) = ma

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

 

[Orodruin]

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

 

[Lanox]

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

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?

 

[Orodruin]

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?

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

 

[Lanox]

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

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?

 

[Orodruin]

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

 

[Mister T]

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?

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.

 

[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?