Analyzing Acceleration and Forces in a Pulley System

[Corky]

A motor raises a mass (m = 1100kg), it produces a tension of 1.46 *10^-4 in the cable on the right side of the pulley. the pulley has a moment of inertia of 73.8Kg*m^2 and a radius of 0.712m. The cable rides over the pulley without slipping. Determine the acceleration of mass m.

The question come with diagram with a motor beside the mass on the group, a rope goes up from the motor - around a pulley - and then back down to attach to the mass.

 

[Doc Al]

Well, give it a shot. Show your work and you'll get some help.

 

[Corky]

Oh right forgot about that detail. Well I caculated weight = mass * gravity for the tension on the leftn side of the pully to be (1100kg) * (9.81) and from there I am not really sure. I would expect to have to subtract the given motion of inertia from the tention on the right, and then subtract the tension on the left side from that number to get the upward force on the mass. Is that right?

 

[Doc Al]

Let's do it step by step. The picture I have is a pulley with a rope hanging over it. The mass (m) is attached to the left end of the rope; a motor is attached to the right. Correct?

What you know: The tension in the right-side rope: T_right.

You also should realize: the acceleration is the same at all points along the rope. So how does the angular acceleration of the pulley relate to the acceleration of the rope? Figure that out first.

Now consider the forces on the mass: its weight pulls down, the tension in the left side rope (T_left) pulls up. Apply F=ma to this body.

Do something similar for the pulley. There are two forces on it: the tensions of the two sides of rope. (Note: those tensions are not equal--if they were, the pulley (and rope) would not accelerate!) Now figure out what torques those tensions give to the pulley. Then apply the torque equation to this body: Torque_net = Ix(angular acceleration).

 

[Corky]

All right, at this point I have subtract tention left (w = 10791N) from tention right (14600N)and got a net force of 3809N. I used the equation [I(moment of intertia)= 0.5mr^2] to calculate the mass of the disk to be 291.2kg. Then I used the net force, 3809, with the equation F=ma to find the acceleration of the system to be 13.08m/s^2. Is this the correct procedure?

 

[Doc Al]

Don't skip steps. I asked you to do three things. Start with the first thing. Then we'll go from there.

1) First answer my question about how the angular acceleration of the pulley relates to the linear acceleration of the mass.

2) Then analyze the forces on the mass.

3) Then the pulley.