Which spool will reach the floor first? Explain your reasoning.?

Question

Two identical spools of radius R are held the same height above the floor. The thread from spool A is tied to a support, while spool B is not connected to a support. Both spools are released from rest at the same instant. The ×’s mark the spots directly below each of the spools. Which spool will reach the floor first? Explain your reasoning.

http://i617.photobucket.com/albums/tt253/bboyDP/q3.jpg?t=1241195354

Please solve and explain!

-Thank you!!

Answer 1

Spool B reaches the mark-x first.

First think of it in the terms of Energy. Well its obvious that when any of the spools reaches the ground, it has the same energy as the other = mgh; as there is no dissipative force. However spool A has rotational energy as well as the kinetic energy of falling. Spool B has only Kinetic Energy.

So,

Spool A; E = K + R

Spool B; E = K



Thus, spool B is faster at any time during the fall. It reaches first.





From the point of view of dynamics, the tension in the thread reduces the net force downwards on spool A. Its this force that causes it to rotate. But it results in smaller acceleration and slower falls.



is it okay?

Answer 2

Id say that B would reach the ground first. A will have tension in the thread which will put an extra upward force on the spool causing it to fall slower.

Answer 3

Do your own homework. The answer is basic, and even more so, is pure logic.