John (mass 80) rests on top of a light cube (mass = 0). A light rope passes horizontally from him over the front edge, and vertically down to Brian (mass 60kg) who hangs in contact with the front face as shown. The cube is on a horizontal surface and there is no friction anywhere. Joe (mas 70kg) has his back to a wall and applies a horizontal push perpendicular to the rear face. Calculate the value of the force, which will prevent both John and Brian from sliding over the surface of the cube.
Here is the diagram which i redrew from the book.
The Attempt at a Solution
I first found how fast the people would accelerate on top of the cube.
For the 80kg person: Ft=80a
For the 60kg person: -Ft+60(9.8)=60a
Add the two equations to solve for acceleration: 588=140a
So the acceleration for both of the is 4.2m/s^2
I think that means that John will have to accelerate the cube in a way such that it cancels out the acceleration of the people on top.
The combined weight of the people on the cube is 140kg, and they are accelerating at 4.2m/s^2.
Fa(by john to the cube)=140(4.2)
So therefor, John must apply a force of 588N to prevent them from falling off.
I don't know if i got it right, or if i made the right assumptions. Does my answer look correct to you guys? Any hints if i got it wrong?