Name:
PHYSICS 231
MOCK MIDTERM
Instructor: P. Q. Hung
THIS IS ONLY A MOCK EXAM. IT DOES NOT COVER ALL THE CHAPTERS FOR THE 3RD MIDTERM. ALLOW YOURSELF 40 MINUTES AND NO MORE!
1) A cylindrical shell of mass 7 kg and radius 40 cm initially at rest rolls
down a plane inclined at 
with the horizontal and 7 m long. Use energy
conservation to calculate the angular velocity of the shell at the bottom
of the ramp. Assume a rolling motion without slipping.
SOLUTION:
Let l be the length. Energy conservation (the work done by friction
is zero) gives
With 
and 
(cylindrical shell), one gets
which gives 
.
2) A particle of mass m moves in a circular orbit of radius r under the influence of the gravitational force due to a body of mass M. Calculate the total energy of the particle as a fumction of r.
SOLUTION:
For a circular orbit, one has
which gives
The total energy is
after we have sustituted for 
.