Unwinding Spool vs. Standard Block

[ssturb]

Pulling an Unwinding Spool vs. Standard Block

Homework Statement

This problem is done on a frictionless surface
There is a block pulled by a string with tension T.
Next to it, there is a spool with a string wrapped around it and may unwind. It is pulled with the same tension as System A. The spool is standing on its base, so it slides, and doesn't roll.
The question is whether the block or spool will cross the finish line first, which force does more work, and whether the total kinetic energy (trans. + rot.) are equal.

Homework Equations

conceptual

The Attempt at a Solution

They should cross the line at the same time because it shouldn't matter where the force is applied, the object will still accelerate at the same speed. However, the spool should have more total KE because it is spinning and moving when it crosses the finish line, which also means more work is done on it. What I'm confused about is where the extra work comes from. Does the force on the spool do more work because the string is also unwinding, so the force acts over a greater distance than the force acting on the block?

 

[Doc Al]

They should cross the line at the same time because it shouldn't matter where the force is applied, the object will still accelerate at the same speed.

Right! The same force produces the same acceleration of the center of mass.

However, the spool should have more total KE because it is spinning and moving when it crosses the finish line, which also means more work is done on it.

Right again.

What I'm confused about is where the extra work comes from. Does the force on the spool do more work because the string is also unwinding, so the force acts over a greater distance than the force acting on the block?

Absolutely right!

Someone pulling the string must do a lot more pulling as the spool unwinds, thus they do more actual work on the spool. That extra work goes into rotational KE.

 

[bocobuff]

Does that mean the translational kinetic energy of the block and spool will be the same?

 

[Doc Al]

Does that mean the translational kinetic energy of the block and spool will be the same?

That's right.