Solving Block & Spool: Finishing Line & Work-Energy

[Zach_Sch]

Homework Statement

A block and a spool are each pulled across a level, frictionless surface by a string.
The string wrapped around the spool will unwind as it is pulled.
Both the block and the spool have the same mass and are pulled with the same constant tension.

Which will cross the finish line (distance: d) first?
Which mass had more work done on it?
Which mass has a larger total kinetic energy and which has a larger translational kinetic energy?

Homework Equations

Newton's second law: Fnet = ma
Work-Energy Theorem: W = KEf - KEi

The Attempt at a Solution

I get that the blocks will cross the finish line at the same time, they are pulled by the same force and their masses are equal, therefor both the spool and the block have the same accelerations. (NII law)

For the work and kinetic energy questions I am a bit confused:
The equation for work is: Work = Force*Distance*cos(theta)

--- Both of the mass were pulled by the same force over the same distance so wouldn't the work done on each be identical?
But then, using the work energy theorem: Work = KEf - KEi
I get something different. The spool should have more kinetic energy at the instant it crosses the finish line due to their equivalent translational kinetic energies (velocities are also the same), but the the spool also has rotational kinetic energy, making its total kinetic energy greater than that of the block.---?

 

[BvU]

Hello Zach,

Both of the mass were pulled by the same force over the same distance

You sure about that ? Hint: look at this from the viewpoint of the pulling force at the other end of the string that is being pulled...

 

[Zach_Sch]

Hello Zach,
You sure about that ? Hint: look at this from the viewpoint of the pulling force at the other end of the string that is being pulled...

So the spool's string will unwind and the hand pulling on it will move farther than the hand pulling on the block?
Thus making the spool require more work over the distance (higher KE due to rotational + translational).

 

[haruspex]

So the spool's string will unwind and the hand pulling on it will move farther than the hand pulling on the block?
Thus making the spool require more work over the distance (higher KE due to rotational + translational).

Yes.