What is the acceleration of the block in this system?

[ooohlala]

Homework Statement

In the system shown all pulleys are light and smooth and all strings are light and inextensible. A block of mass m = 20 kg is attached to the movable pulley. A constant force, F, applied at the free end of the string, makes the point of application of force move down with a constant acceleration of 4 m/s^2. The applied for F is (g = 10 m/s^2)

a) 40 N
b) 80 N
c) 120 N
d) 160 N

Homework Equations

F = ma

For the block,

mg - 2T = ma
20*10 - 2T = 20a
200 - 2T = 20a

For the free end of the string,

F - T = ma

But there is no mass. Hence

F - T = 0
F = T

The Attempt at a Solution

Is what I have done so far correct? I know that the free end of the string and the block have different accelerations, but how do I relate them? The figure for this is here:

http://img299.imageshack.us/img299/166/47373170.png

 

[PhanthomJay]

You are correct so far. Now all you have to do is determine the acceleartion of the mass. You're given that the acceleration of the point force is 4m/s^2. Now you have to do a little imagination to realize that if the Force, F, moves down say 2 feet, the 2nd pulley and mass must move up by___ ft. (The acceleration of the mass will be less than 4). Watch your signage in your first equation for the mass acceleration.