Question

A half section of thin circular pipe of mass m and radius 'r' is released from rest in the position shown. Pipe rolls without sliding. The change in potential energy of pipe after it has rolled through 90° :

Answer 1

Answer:0.0424753604

Explanation:

Answer 2

Given:

A half section of thin circular pipe of mass m and radius 'r' is released from rest in the position shown. Pipe rolls without sliding. The change in potential energy of pipe after it has rolled through 90°

To Find:

find the change in the potential energy

Solution:

Initial Position:

potential energy = mgh (h = height of the center of mass)

here , h = r (thin shell )

initial potential energy = mgr

Final Position:

potential energy = mgh

as we know that the center of mass of half section of the pipe has center of mass at 2r/π from the center of the pipe. Hence from the bottom it will be , h = r-(2r/π)

final potential energy = mg(r-2r/π)

change in potential energy = final energy- initial energy

                                              =mg(r-2r/π)-mgr

                                              =-2mgr/π

Hence the potential energy reduces by 2mgr/π from initial position to final position.