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Unformatted text preview: Problem #1: Ranking (15 points) Lacking anything better to do at the moment, a librarian places four identical books
against a wali, then applies a 50—Newton force to each book. The direction of this applied
force is different for each book, as shown below. All four books remain at rest, not
accelerating up or down the wall. The only forces acting on any of the books are gravity, the normal force from the wall,
static friction with the wall, and the librarian’s applied force. E a) Rank the four books according to the magnitude of the normal force which the wall exerts on them, from strongest normal force to weakest. Indicate any ties Brieﬂy
explain the reasoning behind your answer. {One or two sentences is fine.) b) Rank the four books according to the magnitude of the static friction force between
the book and the wall, from strongest friction force to weakest. Indicate any ties. Brieﬂy explain the reasoning behind your answer. c) What is the mass of one book? Problem #2: True / False (18 points) Two simple pendulums are set up as shown below (the diagram is not necessaril},r to I
scale.) You can assume that as they oscillate, the angle they make from equilibrium is
always much smaller than one radian (so that the smalluangle apprommation always applies.) Mark each statement as True or False. lf the statement is false, then moori‘y it (by
adding, remo vlng, or changing a few words) so theta becomes true. 1) If m, is nine times greater than m9, then the frequency of pendulum #1 is one third
the frequency of pendulum #2. 2) if L, is nine times Iongerthan L2, then the frequency of pendulum #1 is one third
the frequency of pendulum #2. 3) if m, is nine times greater than my, then the amplitude of pendulum #1 is nine
times the amplitude of pendulum #2. 4) Suppose pendulum #1 is at rest when a moving blob of clay strikes the
pendulum hob and sticks to it. Since the collision is inelastic, some of the clay blob’s
initial momentum is converted into heat. 5) Suppose the two pendulums are identical, exce pt that pendulum #1 is oscillating
with twice the amplitude of pendulum #2. Both pendulums will then have the same
frequency. 8) Suppose the two pendulums are identical, exce pt that pendulum #1 is on Earth,
while pendulum #2 is on a planet whose gravityr is nine times stronger than Earth’s.
Then the period of pendulum #1 will be nine times longer than the period of
pendulum #2. Problem #1: (12 points) Four Inass—sprin g systems are set up on frictionless surfaces. Each mass is initially sitting
at its equilibrium position, but is then given a sharp “kick” which sets it in motion with
the initial velocities given below. As you would expect, all four systems then continue to
oscillate back and forth about their equilibrium points. a) Rank the four situations shown above according to the frequency to of their
oscillations, from highest to to lowest. Indicate any ties. la 991L354” a _ ) le‘lL
DU Lt) b) Rank the four situations shown above according to the amplitude of their oscillations,
from highest amplitude to lowest. Indicate any ties. lﬂ ighfﬁi‘. lowed Sanity Check: Ocean’s 4st (20 points) Do not set up this problem and solve it. ( Unless you want to try for extra credit, as
described at the end.) Instead, you’ll use various sanit}r checks to deoide which, if any, of
the proposed answers might be correct. The problem: Ajewel thief whose mass is M wants to steal a safe of mass as, without stopping on the
ﬂoor (it’s alarmed.) She stands on a shelf of height H above the floor, and attaches a
cable of length L with a grappling hook to the ceiling. She pauses for time I to radio her
co—conspirators, then steps off the shelf and swings downward on the cable. At the
lowest point in her swing, she grabs the safe, then continues to swing upward. ‘I What is the maximum height. it that she reaches after grabbing the safe? a) What should be the units of it? Which equation(s), it any, does this eliminate? b) lithe safe’s mass m approaches zero (max M), how should it behave? Which equation(s), if any, does this eliminate? } c) if you’ve reasoned correctly in parts (a) and (b), you should still have more thar
one possible answer left. Desoribe another sanity check and explains how it
eiiminates at least one of the remaining equations. d) Which equation(s), if any, might be the correct answer to this problem? Extra Credit (use the back of the facing page):
Go ahead and actualiy soiye this problem using whatever physical principles you
choose. Does your answer agree with the one (if any) that you chose in part (d)? Problem #3 at 1 (25 points) A steel block of unknown mass M rests on a level, frictionless surface, connected to a
spring of unknown spring constant k, as shown below. The block is initially at rest, and
the spring is at equilibrium. A rubber ball of mass e: = 2 kg, moving to the right with speed 12,, = 20 ml s, makes a
perfectly elastic collision with the block. The instant after the collision, the ball is
moving left with speed vf: 10 mils. r.» ,.+. a) What iﬁ the block’s mass M? b) The instant after the collision, what is the block’s velocity v3? Now that the block has been set into motion by the collision, you observe that it is
oscillating back and forth (driven by the spring) with frequency f: 3 cycles I second. c) What is the spring constant k? d) Calculate the amplitude of the block’s oscillations. (Remember: the reason the block
began oscillating in the ﬁrst place is because of the collision you analysed in parts a 8: b.: Problem #ﬁ 5 n’ (30 points) A helicopter uses a steel cable to tow a sled of mass at = 100 kg across a frozen lake. The
cable, which has constant tension FFIZUO Newtons, makes an angle 6: 30” from the horizontal, as shown below. The coefﬁcient of kinetic friction between the ice and the
sled is Ink = 0.2. a) Draw a free—body diagram showing all forces on the sled.
h) Calculate the normal force between the sled and the ice.
c) Calculate the x— and y—contponents of the sled’s acceleration. d) If the sled started from rest at t = 0, then how far from its starting position is it located
at t: 10 seconds? e) Now we repeat the experiment. but this time the helicopter pulls twice as hard on the
cable; Fri22400 Newtons. What are the new answers to parts (b), (c), and (d)? A firecracker ef mass M = 50 g is ﬂying threugh the air. It is at altitude h : 45 m aheve
the greund when it suddenlyr eapledes inte three fragments. The instant befere the
explesien, the firecracker is meving tn the right at speed v,1 = 25 mi“ s The instant after
the explesien, ene fragment, with mass m, = 20 g, is running directly left with speed a, :
5 rnfs. A secend fragment, with mass mg: 10 g, is meving directly dewnward with spee
v2 = 20 mts. a) The instant after the cellisien, what is the speed and directien ef the third fragment? h} is the kinetic energy ef thethree fragments after the explesien greater than, less than,
er the same as the kinetic energ}r ef the firecracker befere the explesien‘? c) Hew de yen reeencile yeur answer te part (b) with the law ef energy censervatien? (If kinetic energy was gained, where did it ceme frem‘? If kinetic energy was lest, where
did it ge?) d) Cheese any ene ef the three fragments (tell me which ene yen picked), and calculate
hew much time passes between the expiesien and the mement when year chesen
fragment hits the greund. Neglect air resistance. Problem #37 :— . i ' (20 points) Your lab instructor challenges you to try to slide a coin of mass m = 3 grams aeross a
level table and land it in a eup on the floor below. The height of the table is it = 1.2
meters, and the cup is a distance 5 = 0.8 meters from the table. You have to release the
eoin at a distance L = 0.6 meters from the ed go of the table, and the coefficient of kinetic
friction between the table and the eoin is to = 0.2. a) How fast do you want the coin to be moving as it leaves the edge of the tabte‘ir (Point
B in the diagram.) ' b) How fast should the coin be moving when you ﬁrst release it? (Point A in the
diagram.) e) Suppose you double the mass of the coin to 6 grams. How do your answers to parts
{at and I'h‘t ﬂiiﬁl‘lﬂﬁ ‘? Problem #1: Spacewalk An astronaut on a spacewalk is connected to her spaceship by a massless cable of
length b = Si] m. She is moving in a circle around the spaceship, and completes
one revolution every 20 s. The astronaut and all the equipment she is carrying
have a combined mass m = 100 kg; assume the spaceship is so massive that it
remains essentially at rest as the astronaut circles it. I i.” an:
I” "
r Li I
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{SHIP FriJr“
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\\ ‘—I .. I" f, a) What is the astronaut's speed? s b) What is the tension in the cable? Problem #2: Planetfall The astronaut has now landed on an unfamiliar planet. She would like to know the
local gravitational acceleration g on this world. a) She ties small rock of mass m = 0.2 kg to a massiess string of length L = 0.5 m.
This improvised pendulum takes twenty seconds to make five small oscillations
about equilibrium. What is the value of g on this planet? {'7 Still standing on the same planet, the astronaut picks up a rock and throws it with initial speed v0 = 30 ms at an angle a: 600 above the horizontal, as shown below.
pieair at lli.~;;_,l,+
J... _'— "".__
...—I— ._\_H_ R b) When the rock reaches the peak of its flight, what are its horizontal and vertical
distances, ﬁx and fey, from its launch point? c) What are the magnitude and direction of the rock‘s velocity,( at the peak of its
flight? Problem #3: After a while, you don't even miss the gravity The astronaut is back on board her spaceship. it's a zerogravity environment, so
she has a couple of practical problems to solve. a) She brought back a rock from the planet she visited, and needs to know its
mass. On Earth, she would just measure its weight and divide by 9, but here in
deep space, the rock is weightless. (Or at least, its weight is far too smalt for her to
measure.) She does have a spring, one end of which is attached to a wall, and the
other end of which has a convenient hook for attaching it to rocks. She also has
clocks, rulers, and any other common measuring device she might want. How can she measure the rock's mass? (Describe in reasonable detail; exactly
what would she do, what measurements would she make, and what calculations
would she carry out?) p) Later, the astronaut falls asleep while working, and wakes to realize she is at
rest in the center of her ship‘s cargo bay, far from the wails, ceiling, or floor. Since
there's no gravity, she is effectively stranded in the center of the room until she can
think of a way to reach the wall. She is carrying an assortment of generic tools
(hammers, wrenches, etc.) What is the easiest way for her to reach the wall? Deity
a ' E”
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9 {mm was...
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 Problem #5: Shaken, not squished. Superspt’ James Bland, whose mass M: 80 kg, is standing on the roof of a
building a distance y: 50 m above the ground. To reach the ground safely, he
grabs hold of a rope, which is connected by a massless, frictionless pulley to a box
of mass m = 75 kg on the ground, and steps off the roof. The stunt proceeds as planned, and Mr. Bland descends to the ground, while the
box is pulled upward an equal distance. err: l” A Tier 1 a) How fast is the spy moving as he reaches the ground? (Note: you can set this
up as an Atwood machine, solve for the acceleration, and use kinematics
equations to reach the answer. But there is an easier way.) b) Suppose, instead, that the pulley is notquite frictionless, and as a result, Bland
hits the ground with only half the speed you calculated in part a. How much work
was done by the nonconservative) friction in the pulley? c) What actually happened to the "missing" energy in part b? (Has some energy
vanished from the universe? It not, what form(s) of energy has it most likely been
converted into?) Problem #8: The Physicists' obsession with springs continues... Suppose that you attach one end of a spring to a wall, and attach a mass m = 4 kg
to the other end. You pull the mass a distance L = 0.1 m from equilibrium, and you
find that it takes a force F = 160 N to hold the mass there, at rest. Throughout this problem, neglect friction and air resistance. uILf :diM: i r“ i4.. sawsr“(we—— /\ (instin Scalel.) a) What is the spring constant k? You new release the mass, and as expected, it oscillates back and forth about
equilibrium. \
b) What is the frequency of these oscillations? c} What’fsth‘eiampfitud’e" of'the oscillations?" d) What is the highest speed that the block reaches during each cycle of
oscillation? (Note: there are at least two quick ways to solve this. Can you think of
both?) ...
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 Fall '07
 Graham
 Friction, Mass, James Bland, eoin, smalluangle apprommation, remo vlng

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