Pulleys: One mass hanging between two other masses

[geralt]

Homework Statement

Explanation: There are three masses in this problem. Two masses are sitting on two opposite surfaces. These surfaces have a space in between them, where a third mass is hanging down. These masses are connected by a continuous pulley system.

μ = 0.

The question asks us to find the acceleration of the hanging block, and the tension in the string. We are given the following hint: You will need to find a relationship between a1 (acceleration), a2, and a3. If m1 moves distance d1, and m3 moves a distance d3, how far does m2 move?

I've already determined that the acceleration of the hanging block is the average of the acceleration of the other two blocks, but I don't know where to go from there. Any help would be greatly appreciated!

The Attempt at a Solution

The only force would be the hanging mass pulling down on the other two blocks via the pulley. So the force would be m2g, m2 being the hanging mass. The mass would be the total masses of the three blocks. Then using f=ma, I get the equation a=m2g/(total mass). I have no idea for tension...

Please help me if you can!

 

[tiny-tim]

oy geralt! welcome to pf!

The only force would be the hanging mass pulling down on the other two blocks via the pulley. So the force would be m2g, m2 being the hanging mass. The mass would be the total masses of the three blocks. Then using f=ma, I get the equation a=m2g/(total mass). I have no idea for tension...

call the tension "T" (the string is continuous, and the pulleys are presumably massless and frictionless, so it'll be the same all the way along)

you need to do F = ma three times, once for each mass

that should give you enough equations to eliminate T and find the accelerations!

show us what you get ​