Rotational Kinematics of a spool of mass

[nahanksh]

Homework Statement

http://online.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?courses/phys211/oldexams/exam3/fa08/fig10.gif
A spool of mass M = 1 kg sits on a frictionless horizontal surface. A thread wound around the spool is pulled with a force T = 4 N as shown below. The total moment of inertia about the center of mass of the spool is I = 0.8 kg·m2, its outer radius is R = 1 m and its inner radius is r = 0.5 m. The spool starts from rest.

When the center-of-mass of the spool has traveled 2 m,
the net work done on the spool is 8 J.
(True/False Question)

Homework Equations

The Attempt at a Solution

I simply thought the net work done here is only by the tension force..
And i vaguely remember that the force given to the center of mass or the outer part of the edge would have the same acceleration "Acm".(Not sure if it's correct)

So i used the given tension 4N and into 2 meters which gives me 8J.

But it turns out that the answer is FALSE...

What's wrong in my thought?

Could someone help me out here...?

 

[tiny-tim]

Hi nahanksh!

Go back to the definition of work done …

work done = force "dot" displacement, where "displacement" means "the change in position of the point at which the force is applied."

How far does the point where the string leaves the spool move? ​

 

[vela]

You're forgetting that T exerts a torque on the spool.