Wheel Rotated By Force on String.

[Zebulinn]

Homework Statement

A heavy wheel (radius = 0.3 meters, mass = 12 kg) has a rope spooled around it. A woman
pulls on the rope from below with a constant force. She is able to bring the wheel from
rest up to 1 radian per second in 10 seconds.
[Ignore friction in the hub of the wheel.]
a) When the wheel is at its final speed, at what linear speed v is the rope unspooling?
b) How much (average) force was exerted by the woman?
c) How much work was done on the wheel by the woman?

Homework Equations

The Attempt at a Solution

For a) I used (2*R*pi)/2*pi and got .3 m/s for the final linear speed of the rope.

For b) I started with .5*M*R(alpha)=RT with alpha=a/R to get .5*M*a=T with T being the force of tension which would be the force exerted by the woman? I must be using the wrong formula or something here.

would c) be the force times the length of string unspooled?

 

[Basic_Physics]

b) seems fine
c) rather use E_K = 1/2 ω² that is the work done by the torque is equal to the change in kinetic energy of the wheel.

 

[haruspex]

For b) I started with .5*M*R(alpha)=RT with alpha=a/R to get .5*M*a=T

.5*M*R²α=RT, but the next equation is right, so maybe that was an error in writing the post.

would c) be the force times the length of string unspooled?

Yes. You could use Basic_Physics' method (but it's E_K = 1/2 I ω² = 1/4 MR² ω²), but seems to me the question is leading you towards force x distance.

 

[Zebulinn]

Thanks. What does EK stand for? The kinetic energy?

 

[haruspex]

Thanks. What does EK stand for? The kinetic energy?

Yes, I assumed that's what BasicPhysics intended. I just copied that notation.