Rotational Mechanics (Pulley and Mass)

[Californiarol]

Homework Statement

I am studying for a final exam and I do not know how to solve this problem:

A 10 kg mass hangs by a rope of negligible mass. The upper end of the rope is attached to and is wound around the other edge of a solid uniform wheel which is free to rotate on a horizontal frictionless axle. (So its basically a pulley (a wheel with a single mass hanging down one side)). The 10kg mass is released from rest and accelerates 4.9m/s^2

a) What are all the forces acting on this system?

b) What is the tension of the rope as the 10kg mass falls?

c) Calculate the mass of the wheel.


2. The attempt at a solution

a) For this part, I put the obvious ones, ie: weight, and tension. Are there any others, especially with regard to the wheel?

b) For the y-component, we have T-W = -4.9m/s^2 and solving for T gives 49N. However, this seems kind of trivial and the question is worth 5 points so I'm not certain this is right.

c) I have no idea about this part. I know angular acceleration = 4.9/R and that's about as far as I got on this part.

Any help would be appreciated!

 

[AEM]

Homework Statement

I am studying for a final exam and I do not know how to solve this problem:

A 10 kg mass hangs by a rope of negligible mass. The upper end of the rope is attached to and is wound around the other edge of a solid uniform wheel which is free to rotate on a horizontal frictionless axle. (So its basically a pulley (a wheel with a single mass hanging down one side)). The 10kg mass is released from rest and accelerates 4.9m/s^2

a) What are all the forces acting on this system?

b) What is the tension of the rope as the 10kg mass falls?

c) Calculate the mass of the wheel.


2. The attempt at a solution

a) For this part, I put the obvious ones, ie: weight, and tension. Are there any others, especially with regard to the wheel?

b) For the y-component, we have T-W = -4.9m/s^2 and solving for T gives 49N. However, this seems kind of trivial and the question is worth 5 points so I'm not certain this is right.

c) I have no idea about this part. I know angular acceleration = 4.9/R and that's about as far as I got on this part.

Any help would be appreciated!

For part (b), shouldn't you be writing T - W = ma, which is T - W = m(4.9) ? Just a small thing, but small things lead to errors.

Now about part (c), recall that $$\tau = I \alpha$$
where tau is the torque, I is the moment of inertia, and alpha is the angular acceleration. That will allow you to calculate the mass of the wheel.

 

[Californiarol]

Thanks. I have gotten the answer, your hint really helped =)