Physics 101
Fall 2012
NAME:
Quiz 5 - Solutions
Make sure your name is on your quiz, and please box your final answer. Because we will
be giving partial credit, be sure to attempt all the problems, even if you don’t finish them!
1. A bug slides back and forth in a bowl 11 cm deep, starting from rest at the top, as
shown in the figure. The bowl is frictionless except for a 1.5 cm wide sticky patch on
its flat bottom, where the coefficient of friction is 0.61.
(a) How fast is the bug moving at the
bottom of the bowl right before
he hits the sticky patch?
(b) How many times does the bug
completely cross the sticky region
(i.e., what is the whole number of
crossings)?
————————————————————————————————————
Solution
1. (a) The bug starts off at the top of the bowl, having only gravitational potential
energy, P Eg = mgh, where m is the mass of the bug. As he slides down the bowl
he picks up speed, changing his potential energy into kinetic energy, KE = 12 mv 2 .
At the bottom of the bowl, all of the potential energy has become kinetic energy,
and so
p
1
mgh = mv 2 ⇒ v = 2gh = 1.47 m/s.
2
(b) Every time that the bug crosses the sticky region, he loses energy due to the work
done by friction. Every time the bug crosses the sticky region he loses an energy
W = Ff D, where Ff = µk mg is the frictional force, and D = 0.015 m is the
width of the sticky patch. So, if he crosses N times, then the total work done is
W = N µk mgD. When he finally stops, then all of his initial potential energy is
lost to friction and so
mgh = N µk mgD
Solving for N gives
h
11
=
= 12.02,
µk D
0.61 × 1.5
and so he crosses the patch 12 times.
N=
1