Work Done on Rotational Motion Homework Problem

[Fisicks]

Homework Statement

A puck of mass m is attached to a cord that passes through a hole in a horizontal frictionless surface. The puck is originally moving in a circle of radius r and speed v. The cord is then slowly pulled from below, decreasing to a circle with radius r1. What is the work done by the person pulling the string?

Homework Equations

W=Fd
Iw=Iw conservation of rotational momentum
F=ma

The Attempt at a Solution

I need to show that W is equal to the change in rotational kinetic energy. So I did W=FD.
F=m(v^2)(r^2)(1/R^3) where R is an arbitrary radius from r to r1. Thus I integrated what I set F equal too and multiplied by D=(r-r1). My answer is off by a factor of 1/4 b/c I calculated the change in rotational kinetic energy. Any tips?

 

[anathema]

It seems like you are on the right track with your approach. However, there are a few things that could be adjusted to get the correct answer.

Firstly, when calculating the work done by the person pulling the string, it is important to consider the change in velocity of the puck as the radius decreases. This can be done by using the equation F=ma and substituting in the appropriate values for mass and acceleration.

Secondly, the equation you used for F is not entirely correct. It should be F=m(v^2)/r, where r is the radius of the circle at any given point. This accounts for the change in radius as the puck moves along the circular path.

Lastly, when integrating to find the work done, make sure to use the correct limits of integration. The limits should be from r to r1, not from 0 to r1.

Overall, your approach is correct, but there are a few adjustments that need to be made to get the correct answer. Keep up the good work!