How Do Mechanical Advantages Affect Accelerations in a Pulley System?

[windwitch]

Homework Statement

The original question is: What are the accelerations of the two masses?

Given:
M=8kg
m=3kg
g=10m/s^2
Fapp=120N

Assume all pulleys and strings are massless and frictionless

My problem is whether there is a mechanical advantage in the question so I should divide the acceleration of the smaller mass by 2, and the acceleration of the larger mass by 4.

Homework Equations

F=ma

The Attempt at a Solution

Since the two masses are independent of each other, I thought that the accelerations of both masses were separate.

So, for the first mass,

F = 2T - mg
ma = 2T - mg

I thought that tension force was equal to the applied force so,

a = [2(120) - (3)(10)]/3
a = 70m/s^2


For the second mass,

F = 2T - Mg
Ma = 2T - Mg
a = [2(120) - (8)(10)]/8
a = 20m/s^2

The reason I believe that there is a mechanical advantage is because if you pull the string by 1m, then the small mass will only move up by 0.5m, and the large mass, 0.25m

 

[jtebb]

I don't understand the question itself. If you hold the string end still, the large mass will fall and pull the small mass up. What are they actually asking you?

I just read what you wrote for givens again. Are you asking what a is for each mass if 120N of tension?

If so, simply apply F=ma on each one and one string has one tension T=120N, so for small mass: 2T-3g=3a and for large: 8g-2T=8a, sub in T and solve for a for each (they will be different a values for large and small masses).