Confusing ROTATIONAL RIGID BODY QUESTION problem conceptualizing

[avenkat0]

Homework Statement

A piece of cloth with irrelavent mass is wrapped around a 67.5 kg cylinder of radius 0.167 m. Joe holds the free end of the cloth. The cylinder is released from rest, and Joe pulls the tape upward at a speed that just prevents the center of mass of the cylinder from falling as the tape unwinds. Assume:
- the cylinder is always parallel to the floor
- the tape is always perpendicular to the radius of the cylinder
- the tape does not slip over the cylinder

a) Find the magnitude of the tension in the tape as the cylinder turns.

Homework Equations

The Attempt at a Solution

I have no idea where to start... I don't think i quite understand it conceptually... like i don't quite see the picture in my head

Thank you for your help

 

[Doc Al]

If the cloth isn't pulled up, it will just unwind as the cylinder falls. (Imagine a heavy log rolled up in a carpet and you let it unwind.)

To answer the question, apply Newton's 2nd law. What forces act on the cylinder?

 

[avenkat0]

is it kind of like the logs that are floating on the water while people run on it... thus in turn staying in the same place?...
so the cloth is giving the cylinder a torque to equal its fall? making the center of mass stay at the same place?

 

[Doc Al]

is it kind of like the logs that are floating on the water while people run on it... thus in turn staying in the same place?...

Something like that.

so the cloth is giving the cylinder a torque to equal its fall?

The cloth is certainly exerting a torque on the cylinder.

making the center of mass stay at the same place?

Yes, the cloth is being pulled up fast enough that the center of mass doesn't move.

 

[avenkat0]

should the tension in the cloth equal mg down since the tension keeps it from falling down?
I keep confusing linear qualities with rotational qualities!...

 

[Doc Al]

should the tension in the cloth equal mg down since the tension keeps it from falling down?

Sounds good to me.

 

[avenkat0]

Thank you so much... One more thing...
c) Find the length of the cloth that has been unwound when the cylinder reaches an angular speed of 28.3 rad/s

I found the work done was 376.92 J...
Now i set Delta Theta = 376.92/Tourque...
i.e 376.92/I(alpha)
but how would i go about finding alpha?

because if i find alpha can't i find Theta and then 2pi (Theta) should be the length the cloth unwinds right?

 

[Doc Al]

To find alpha, use Newton's 2nd law for rotation. Then you can use kinematics to find theta and then the length. (No, 2pi(theta) is not the length.)

But if you've already found the work done, there's no need to find alpha or theta.

 

[avenkat0]

hmmm work done is torque(distance)... But I don't have the tension either how would I go about findig the distance?

I tried using I(alpha)=torque and then omega final and omegia0 is 0 but I'm missing theta time and alpha so I wasn't able to find alpha using kibematics...

Have I overlooked something??

Again Thank you

 

[Doc Al]

hmmm work done is torque(distance)...

Careful. Work is force*distance (or torque*angle).

But I don't have the tension either how would I go about findig the distance?

Sure you have the tension. That was the first thing you solved for.

I tried using I(alpha)=torque and then omega final and omegia0 is 0 but I'm missing theta time and alpha so I wasn't able to find alpha using kibematics...

Look for a kinematic formula that relates speed and distance, not time.