Download Physics 105a-2008 Practice Problems for Exam 2 IMPORTANT: This

Physics 105a-2008 Practice Problems for Exam 2
IMPORTANT: This is not a full-length practice exam. Instead, it is a set of questions
intended to give you a sense of the style of questions you may find on the actual exam. Of
course, the actual exam questions will not be on exactly the same topics as these questions.
Therefore, if you do well on these questions, that does not necessarily mean that you have
prepared adequately for the real exam. However, if you do poorly on these questions, that
does indicate that you need to review the associated material more thoroughly. Also, you
may find the problems on the actual exam to be harder or easier than these problems. You
should be able to complete each of these problems, including all sub-parts, in about fifteen
minutes.
1. A box of mass m sits on a surface with
coefficient of kinetic friction k, just barely
touching the end of a spring of spring
constant k, which is initially at its
equilibrium length. A distance d to the
right, there is a second box, of mass 2m.
The small box is then moved a distance x
to the left, as shown, compressing the
spring. The small box is then released. It
moves to the right (through a total distance
x + d) until it collides elastically with the larger box. This box moves on a surface with zero
friction, as shown. After moving horizontally for a short distance, it enters an upward curve with
radius of curvature R. What is the maximum height h that the box of mass 2m reaches?
Cv 2 A
2. Recall that the force from air resistance is given by Fdrag 
, where  is the density of
2
air (varies with altitude and humidity, but for this problem assume 1.20 kg/m3), C is the drag
coefficient, A is the cross-sectional area of the object, and v is the velocity of the object relative
to the air. A baseball of radius r = 3.69 cm (for which A   r 2 ) and mass 0.145 kg is dropped
from the Empire State Building (height = 381 m). For a baseball, C is about 0.4. Long before it
reaches street level, the ball has attained terminal velocity. A few meters above street level, the
baseball is swallowed by a pelican of mass 6.80 kg, initially travelling horizontally and due
North at 0.75 m/s. What is the velocity of the pelican (with the baseball in its belly) immediately
after it swallows the ball?
Practice problems continue on the next page
3. A steel plate of uniform thickness initially has a mass of
32 g, and measures 4 cm  2 cm. A hole of radius 0.5 cm is
then drilled in the plate, 1 cm to the right of center, as
shown. The plate is then glued onto the center of the top of
a rod of hexagonal cross-section having a height of 3 cm and
a mass of 40 g. Where is the center of mass of the
composite object? Hint: On problems like this, plugging in
numbers fairly early on is a good idea.
4.
Derive the law of conservation of momentum, i.e.
dP
Fnet ext 
(where P is the total momentum of a system),
dt
from Newton’s laws.
5. Many commercial satellites are in “geosynchronous” orbits, i.e. circular orbits above the
equator for which the period is 24 hours, so that the satellite is always above the same point on
the surface of the Earth. The mass of one such satellite is 675 kg. How much energy must be
provided to this satellite to move it infinitely far away from the Earth? (Ignore the gravity of the
Sun, the other planets, etc.) You may find that it saves effort to plug in numbers on some
intermediate results for this problem.
6. A garbage truck crashes head-on into a Volkswagen and the two come to rest in a cloud of
flies. Which experiences the greater force? Which experiences the greater change in momentum? Which experiences the greater acceleration? Explain your answer.
7. If the potential energy in a particular situation is U  A sin kx  Bxy , where A, B, and k are
constants, what is the force?