Net torque on a system with a pulley and hanging mass

[sunniexdayzz]

Homework Statement

Part A:
A 5.73 kg mass is attached to a light cord, which is wound around a pulley. The pulley is a uniform solid cylinder of radius 9.14 cm and mass 1.26 kg. The acceleration of gravity is 9.8 m/s2 . What is the resultant net torque on the system about the center of the wheel? Answer in units of kg m2/s2.
Part B:
When the falling mass has a speed of 5.92m/s, the pulley has an angular velocity of v/r. Determine the total angular momentum of the system about the center of the wheel. Answer in units of kgm2/s.
Part C:
Using the fact that τ = dL/dt and your result from the previous part, calculate the acceleration of the falling mass. Answer in units of m/s2.
(L is the angular momentum)

Please show me the steps and explain everything!
Thank you!

Homework Equations

I=1/2mr^2
a=\alpha*r
\sum\tau=I\alpha

The Attempt at a Solution

I found the sum of the forces for each body (the pulley and the hanging mass) and then i found the torque to be the radius x tension in cord. then i tried to solve for \tau but my answer is wrong .. the final equation i got is
torque = .5m(pulley)*r(m(hanging)*g/(.5m(pulley)+m(box))

i don't even know where to start with the other two because i don't have the first part

PLEASE HELP!

 

[Doc Al]

Please show me the steps and explain everything!

It's your job to do the work. We're just here to help.

The Attempt at a Solution

I found the sum of the forces for each body (the pulley and the hanging mass) and then i found the torque to be the radius x tension in cord.

The radius*tension would be the torque on the pulley, but they asked for the net torque on the system.

 

[sunniexdayzz]

Sorry, I didn't mean to ask that. =]

Okay, I thought there would be no torque on the hanging mass because it's not rotating? I'm assuming now that that is faulty. So how would I go about figuring out the torque on the mass? If that's even what I should be trying to do

 

[Doc Al]

Okay, I thought there would be no torque on the hanging mass because it's not rotating? I'm assuming now that that is faulty.

Yes, that's faulty because we want torques about the center of the pulley (not the center of the hanging mass).

So how would I go about figuring out the torque on the mass? If that's even what I should be trying to do

Don't think in terms of torque "on the mass". Think in terms of forces acting on the system and what torque they exert about the center of the pulley. What forces act on the system? (Do internal forces contribute to the net torque?)

 

[sunniexdayzz]

wouldn't the weight of the mass exert a force? so that would have something to do with the tension?

 

[Doc Al]

wouldn't the weight of the mass exert a force?

Sure, gravity exerts a force on the mass (and on the pulley).

so that would have something to do with the tension?

Why do you care about the tension?

 

[sunniexdayzz]

Why do you care about the tension?
Because the tension is pulling the pulley and making it rotate (at least i think so)

 

[Doc Al]

Why do you care about the tension?
Because the tension is pulling the pulley and making it rotate (at least i think so)

That's true, but it's also pulling on the mass. Does it contribute to the net torque on the system? (Consider the parenthetical question I asked at the end of post #4.)

 

[sunniexdayzz]

I don't know the difference between internal or external forces and which ones would contribute to the torque of the system. I don't really know what else to say?.. =[

 

[Doc Al]

I don't know the difference between internal or external forces and which ones would contribute to the torque of the system.

Don't worry about it. Do this: Identify every force acting on the system. Then figure out the torque each force exerts about the center of the pulley. Add those torques (paying attention to signs) to find the net torque.

 

[sunniexdayzz]

Okay .. so on the system there is gravity on the pulley, the tension pulling down on the pulley, the normal force pulling up on the pulley, the tension pulling up on the mass, and the gravity pulling down on the mass. How do i find the torque on the forces on the mass if I don't know how how far the mass is from the pulley?

I think in the end I will have that the normal force and gravity of the pulley have no torque because the point of rotation is equal the point of action, and the Tension forces will cancel each other out because they are equal and opposite so I will only be left with the gravity of the mass as acting on the system?

so would the net torque on the system be
torque=m(hanging)*gravity*radius(pulley)*sin(90)?

 

[Doc Al]

Okay .. so on the system there is gravity on the pulley, the tension pulling down on the pulley, the normal force pulling up on the pulley, the tension pulling up on the mass, and the gravity pulling down on the mass.

Good.

How do i find the torque on the forces on the mass if I don't know how how far the mass is from the pulley?

All you need to know is the radius of the pulley. (Express everything symbolically before plugging in numbers.)

I think in the end I will have that the normal force and gravity of the pulley have no torque because the point of rotation is equal the point of action, and the Tension forces will cancel each other out because they are equal and opposite so I will only be left with the gravity of the mass as acting on the system?

Yes!

so would the net torque on the system be
torque=m(hanging)*gravity*radius(pulley)*sin(90)?

Yes.

 

[sunniexdayzz]

Finally lol I feel so dumb sometimes when it comes to physics!

Can I check my answer? I got 5.1324756 kg m^2 / s^2

 

[Doc Al]

Can I check my answer? I got 5.1324756 kg m^2 / s^2

Looks good. But please round off to a reasonable number of significant figures.

 

[sunniexdayzz]

For our homework, we have to go to like 5 or 6 decimal places because it's online. Thank you sooooooo much! I will work on the other two parts and hopefully I won't need your help! Thanks again!