Practice Midterm 3

Physics 218 - Exam P3
April 17th , 2015
Please read the instructions below, but do not open the exam until told to do so.
Rules of the exam:
1. You have 75 minutes to complete the exam.
2. Formulae are provided on the last page. You may NOT use any other formula sheet.
3. You may use any type of handheld calculator. However, you MUST show your work. If you do
not show HOW you integrated or HOW you took the derivative or HOW you solved a quadratic
or system of equations, etc, you will NOT get credit.
4. Cell phone use during the exam is strictly prohibited.
5. Be sure to put a box around your final answers and clearly indicate your work.
6. Partial credit can be given ONLY if your work is clearly explained and labeled. NO credit will
be given unless we can determine which answer you are choosing, or which answer you wish us to
consider. If the answer marked does not follow from the work shown, even if it is correct, you will
not get credit for the answer.
7. You do not need to show work for the multiple choice questions.
8. Have your TAMU ID ready when submitting your exam to the proctor.
9. Check to see that there are 6 pages + 1 formula sheet.
10. If you need extra space, use the reverse side to complete your work and indicate/mark on the main
page of the problem that you are continuing on the reverse side.
11. DO NOT REMOVE ANY PAGES FROM THIS BOOKLET.
Sign below to indicate you understanding of the above rules.
Name : ..................................................................................
Section Number : ..................................................................................
Instructor’s Name : ..................................................................................
Signature : ..................................................................................
Short Problems (Circle the correct option - NO PARTIAL CREDIT)
[20 Points]
A) [5 points] A hollow sphere (a), a solid sphere (b), and a thin hoop (c) all with the same mass and
radius are having a race. They roll without slipping down a 30° incline starting at a height h. Rank
the time it takes each of them to roll down the hill from greatest to least.
i) ta > tb > tc
ii) ta > tc > tb
iii) tc > ta > tb
iv) tc > tb > ta
v) tb > tc > ta
vi) tb > ta > tc
vii) The correct answer is not shown.
B) [5 points]
A 2 kg rock has a horizontal velocity of 12 m/s when it is at the point P (x, y, z) =
√
(−6 3, 6, 0). At this point, what is the magnitude of its angular momentum relative to the origin?
i) 17 kg m2 /s
ii) 144 kg m2 /s
√
iii) 106 3 kg m2 /s
iv) 297 kg m2 /s
v) 9001 kg m2 /s
vi) The correct answer is not shown.
C) [5 points] Merril Lehrl (70 kg) sits on the midpoint of a board protruding horizontally from a wall.
The board has a length of 17 m and a mass of 140 kg. The board is also attached to the wall via
a string stretching from the wall to the opposite end of the board such that it makes an angle θ at
their intersection. If the tension in the string is measured to be 2060.1 N, what is θ?
i) 0°
ii) 30°
iii) 45°
iv) 60°
v) 90°
vi) 297°
vii) The correct is not shown.
D) [5 points] A loose cannon Dutch cop who refuses to play by the rules jumps from a levee with an
initial horizontal velocity v0 . After gracefully soaring a horizontal distance D, he reaches out and
grabs a windmill. The blade has a radius R and is perfectly horizontal. Assuming the windmill was
initially at rest, calculate its new angular momentum just after the collision in terms D, R, v0 , the
mass of the cop m, and constants.
i) L =
mgv0
DR
ii) L =
v0
mgDR
iii) L =
mgDR
v0
iv) L =
mg
v0 DR
v) The correct answer is not shown.
vi) The correct answer is never shown.
Problem 2
[20 Points]
Biggie recently installed a pool beneath his Goat Tower. So Biggie walks out on to the diving board
and does a front flip off the board. He starts out with his front and hind legs straight, so we can treat
him like a solid cube with a mass mb = 20 kg and side length l = 2 m, rotating about its center of mass1
with an angular speed of ω0 = 4 rev/s.
a) He then curls up into a solid ball of radius rb = 2 m.2 What is his new angular speed?
b) Suppose he curls up into the sphere at the very peak of his jump, 15 m above the pool. How many
revolutions does he complete before he strikes the water?
1I
cm
2
=
I=
ml2
for a cube.
6
2mr2
5
Problem 3
[20 Points]
Tiny the goat sits atop a uniform ladder of length l and of mass ml resting on a freshly painted wall
such that the base of the ladder makes an angle θ with the horizontal. The fresh paint makes the surface
of the wall very slippery, so friction between the ladder and the wall can be ignored. Tiny, unlike Biggie,
HAS been going to the gym and has a mass mt . To ensure that Tiny doesn’t fall to his death, what is
the minimum coefficient of static friction between the base of the ladder and the ground?
Problem 4
[20 Points]
Biggie the goat has just unveiled his latest ‘art’ installation! It is a kinetic sculpture that consists
of two alfalfa pies stuck together and hung vertically from a wall. The outer pie has a radius RD and
is firmly fixed onto the inner pie of radius RA such that the two pies have a common axis. About this
axis, the pies have moments of inertia ID and IA respectively. The pies are free to rotate about their
common center. A massless cord is wrapped around the inner pie and attached to a tin can of mass
m1 . A similar cord is wrapped around the outer pie in the opposite direction and attached to a potato
of mass m2 . Assuming the cords do not slip, find the acceleration of the potato.
Problem 5
[20 Points]
Biggie the goat decided to dig to center of the Earth one day. After he had dug a quarter of the
way there, he took a break. Then his friend, Tiny the goat, dropped a flowerpot of mass mp = 300 g on
Biggie for laughs. For reference, the mass of the earth is mE = 5.97∗1024 kg, its radius is RE = 6.37∗106
m, and air resistance is negligible.
a) Knowing that the density of the Earth is roughly constant (ρ = 5.51 ∗ 103 kg/m3 ), get an expression
for the force of gravity as a function of r felt by the flowerpot as it falls through the Earth. HINT:
the only mass that matters is that which is ’below’ the flowerpot, so we’re going to need to calculate
the fraction of mass that’s below the flowerpot at a radius r.
b) Supposing the flowerpot is dropped from rest, calculate the velocity of the flower pot when it strikes
Biggie. Will it hurt?
c) Furious, Biggie launches the flowerpot so hard that it reaches escape velocity. With what velocity
did Biggie throw the flower pot?3
3 As
a reminder, escape velocity is defined as when an object’s final potential and kinetic energy go to zero.