Applying force vs applying weight to an atwood machine

waycoo

I have two problems which appear equivalent, but apparently they are not.

The first one is this:
M, a solid cylinder (M=1.75 kg, R=0.131 m) pivots on a thin, fixed, frictionless bearing. A string wrapped around the cylinder pulls downward with a force F which equals the weight of a 0.750 kg mass, i.e., F = 7.357 N. Calculate the angular acceleration of the cylinder.

The second one is this:
If instead of the force F an actual mass m = 0.750 kg is hung from the string, find the angular acceleration of the cylinder.

I know how to solve for the second one, but I don't know how to solve for the first because I see no difference between the two problems.

Could anyone explain?

ehild

In the first case the torque of the applied force accelerates rotation of the cylinder.
In the second case, the gravitational force acting on the hanging mass accelerates both this mass and the rotation of the cylinder. Strictly speaking, you have the force of gravity and the tension of the cord acting on the mass, and the torque of the tension acting on the cylinder.

ehild

Doc Al

They appear equivalent, but they are not. You probably think that the tension in the string is the same in both cases, but not so. Think about it: If in the second one the tension equaled the weight of the hanging mass, the mass would be in equilibrium and wouldn't accelerate. In the second problem you must solve for the tension; in the first, it's given.