Copyright © Michael Richmond.
This work is licensed under a Creative Commons License.

##
Physics 211, Quiz 14A

Question 1:
Two ramps are the same size and shape.
Ramp A is frictionless; a block of mass **M**
slides down it.
Ramp B has friction; a ball of mass **M**
rolls down it.
Which item reaches the bottom of its ramp first?

Answer: The block slides down without friction. All the gravitational
potential energy it gains is turned into translational kinetic
energy.
0.5 * M * v^2 = GPE
2 * GPE
v^2 = -------
M
The ball rolls down. Some of the gravitational potential energy
energy is turned into translational kinetic energy, but some
is turned into rotational kinetic energy. Thus, it has
less translational kinetic energy, and so must be moving
more slowly.
0.5 * M * v^2 + 0.5 * I * (omega)^2 = GPE
2 * GPE - (I * omega^2)
v^2 = -----------------------
M
So the ball is moving more slowly.

Copyright © Michael Richmond.
This work is licensed under a Creative Commons License.