Download Physics 10 Sample Midterm #1a: The Tempest

Physics 10
Sample Midterm #1a: The Tempest
After getting caught in a terrible storm, you find yourself shipwrecked on a remote
island.
Fortunately, you are not entirely alone. There are two survivors of another shipwreck
who have lived on the island for many years now: an eccentric old man named
Prospero and his daughter Miranda. (With due apologies to William Shakespeare for
stealing his characters. His story about them was probably better than mine…)
Act I:
Please answer all the questions in this section.
If you like, you can always explain your answer, even on multiple-choice
questions. I'll take the explanation into account and possibly give partial credit if
your answer was wrong (or extra credit if your explanation was particularly
insightful.)
1) As you talk to your hosts, you find that Prospero is a classically trained philosopher
who got all his ideas about physics from Aristotle, Ptolemy, and that crowd. He has
never heard of Galileo or Newton, and is familiar with none of their discoveries. (He's
been on this island for a long time.)
This means that Prospero probably believes that: (circle all that apply.)
a)
b)
c)
d)
e)
e)
f)
The Earth is flat.
The Earth is a sphere.
The Sun orbits around the Earth.
The Moon orbits around the Earth.
The Earth orbits around the Moon.
Heavy objects always fall faster than light objects.
None of the above.
2) Miranda has read all of her father's books and learned about Aristotelean physics,
but is willing to consider other arguments. Describe a simple experiment you could do,
with materials available on a stereotypical shipwreck island, to show that Aristotle was
wrong.
3) When you try to convince Prospero that the Earth orbits the Sun, he scoffs. "What
force could keep an object as massive as the Earth in motion?" he asks. What do you
answer?
a)
b)
c)
d)
e)
Gravity
Support Force
Buoyant Force
No force is necessary to keep an object moving.
The Earth is orbiting the sun, but it is not actually moving.
Questions 4&5:
You are dragging a crate of salvaged tools across the sandy beach. When you get
tired and let go of the crate, it stops moving almost immediately.
4) According to Prospero, who is still a die-hard Aristotelean, why did the crate stop
moving?
a)
b)
c)
d)
e)
It is made of the element Earth, which cannot move.
If there is no force acting on an object, it will stop.
Friction from the sand caused the crate to accelerate.
The Earth's gravity caused the crate to stop accelerating.
When you stopped pushing on the crate, it gained kinetic energy.
5) If Miranda has been convinced by now that Galileo and Newton were correct, which
of the above answers will she give as to why the crate stopped moving?
Questions 6-8:
Due to a freakish cold snap, you find yourself and the crate stranded in the center of a
perfectly flat, frictionless patch of ice. No problem; you're the one who understands
Newton's laws. So you give the crate a good shove toward the north edge of the ice
patch, and you recoil toward the south edge.
Assume that your mass is twice the crate's mass.
6) While you were pushing on the crate, which was stronger: the force of the crate
pushing you south, or the force of you pushing the crate north?
a)
b)
c)
d)
The force of you pushing on the crate.
The force of the crate pushing on you.
Both forces were equally strong (and non-zero).
Both forces were zero.
e) There is no way to tell.
7) While you were pushing on the crate, which was greater: your acceleration or the
crate's acceleration?
a) Your acceleration was greater.
b) The crate's acceleration was greater.
c) Both accelerations were equal (and non-zero)
d) Both accelerations were zero.
e) There is no way to tell.
8) Once you let go of the crate and were sliding across the ice, which was greater:
your acceleration or the crate's acceleration? (Assume there is no friction or air
resistance.)
a)
b)
c)
d)
e)
Your acceleration was greater.
The crate's acceleration was greater.
Both accelerations were equal (and non-zero)
Both accelerations were zero.
There is no way to tell.
Now you want to lift that crate onto a high ledge. Inspired by her new understanding of
Newtonian Physics, Miranda builds a mechanical device to do the job. A fast-moving
river (flowing down from a mountain on the island) turns a water wheel, which by way of
various cogs and gears, causes a cable to lift the crate upward at a steady speed.
9) What form of energy is the crate definitely gaining as the machine lifts it?
a)
b)
c)
d)
e)
f)
g)
Gravitational potential energy.
Kinetic energy.
Chemical energy.
Sound energy.
Thermal energy.
None of the above; energy cannot be created.
All of the above; energy cannot be destroyed.
10) As the machine lifts the crate, is any form of energy being lost (by the crate itself,
or by any other object involved?) What form of energy? And why are you certain of
your answer?
11) As the cable lifts the crate, there are at least two forces acting on the crate: gravity,
and the tension of the cable. If the crate is rising at a steady speed, then which of
these forces is stronger?
a)
b)
c)
d)
e)
Gravity.
The tension in the cable.
They are both the same strength.
There is no way to tell, unless you know how fast the crate is moving.
There is no way to tell, even if you knew how fast the crate were moving.
12) When the crate has almost reached the ledge, Miranda adjusts the gearing of her
machine, and the crate begins to slow down. Now what answer would you give to the
previous problem?
13) Describe at least two other process, likely to happen on a typical day on the island,
in which one form of energy is converted into another. For each process, specify which
form of energy is being lost and which form is being gained.
14) Prospero has been hitting the fermented coconut juice again. During an inspired
rant, he makes the following statements:
a) There is an invisible, undetectable air spirit on the island.
b) There is a second invisible air spirit on the island, which sings Celine Dion songs if
you offer to share your fermented coconut juice with it.
c) Fermented coconut juice contains no alcohol.
d) Fermented coconut juice tastes better than squid.
e) Five times four is twenty.
"I don't think those were all scientific statements," comments Miranda.
Which, if any, of the statements were scientific? (You may choose more than one.)
Briefly explain your reasoning. (Hint: Think about Hewitt's definition of a scientific
statement, and the related discussions from class.)
15) When Prospero tries to stand up, he wobbles and falls over, directly toward a
nearby coconut tree. "You were right about gravity!" he exclaims, shooting the tree a
dirty look. "That tree's gravity pulled me over!"
Is he correct that the tree is exerting a gravitational force on him? Is it likely that the
tree's gravity caused him to fall over? Briefly explain your reasoning.
16) "Then it must have been an electrical force!" Prospero announces. "The tree
stole some electrons from me, and the damned thing still has them!"
If he is correct, what type of charge does Prospero have? What type of charge does
the tree have? What does this tell you about the electrical force acting on each of
them?
17) Enraged by the tree's continued defiance, Prospero charges at the tree (which is
much more massive than he is) and slams directly into it. During their collision, which
is greater: the force that Prospero exerts on the tree, or the force that the tree exerts on
Prospero?
18) If Prospero was running due south when he collided with the tree, which direction
did he accelerate during the collision? Which direction did the tree accelerate?
Whose acceleration was greater? Briefly explain your reasoning.
Act II:
The wind finally picks up again, and you and your companions reach land with no
further ado. Once there, you decide to publish a book about your adventures. Your
publisher tells you that to give your book proper Geek Cred, you should include an
explanation of at least two of the following issues:
(On separate papers, answer at least two of the following problems. You can
answer more than two if you like, but please choose two as your "main" answers,
and clearly label the others as "Extra Credit".)
Problem #1:
In Questions #9 and #10 of Part I, you began discussing the role of various types of
energy in Miranda's water-powered crate lifting device. Expand on this discussion, and
trace the history of the energy that is being given to the crate back through as many
steps as possible. (Remember that the device is powered by a fast-moving river that
just flowed down from a mountain top. You can make up any reasonable story about
how the water got to the mountain top in the first place…but try to trace its energy as far
back in time as you can.)
Does this energy ultimately come from the sun? Is there any form of energy that we
use which does not ultimately come from the sun?
Problem #2:
Continuing to analyze Miranda's crate-lifting machine, you measure that the crate has a
mass of 30 kg.
a) Approximately how strong (in Newtons) is the pull of the Earth's gravity on the
crate?
b) When the crate is first being lifted off the ground, and has not yet reached its full
speed, it was accelerating upward at 2 m/s2. How strong (in Newtons) was the force of
the cable's tension during this part of the trip?
c) Once it reached cruising speed, the crate was moving upward at a constant velocity
of 6 m/s. How strong (in Newtons) was the force of the cable's tension during this part
of the trip?
Problem #3:
When you were trying to convince Prospero that the Earth orbits the Sun, he raised
several additional objections. What answers would you give to each of his questions:
a) "If the Earth is moving, why doesn't it sweep out from under us every time we jump
off the ground for a moment?"
b) "So is it the Sun's gravity that keeps the Earth moving? If the Sun's gravity were
somehow to disappear, how would that affect the Earth's motion?"
c) "If gravity is pulling the Earth toward the Sun, why don't we fall into the sun?"
Problem #4:
Draw a diagram of the solar system as Propero (or most other pre-Copernican
philosophers) would have described it, and a diagram of the solar system as you
understand it. You don't have to get every detail right (for example, don't worry about
the names of all the planets), but try to show the important differences between the two
ways of thinking. Explain briefly the important points you're trying to illustrate.
Problem #5:
You and Miranda manage to build a seaworthy boat, and the three of you prepare to sail
away from the island. “We must navigate with care,” intones Prospero, “or we could fall
off the edge of the Earth.”
Miranda rolls her eyes. “You don’t actually believe that,” she tells her father. “No one
has believed that for centuries.”
Help her convince PRospero that the Earth is a sphere. When did humans first
manage to measure the size and shape of the Earth? What was some of the evidence
that convinced them? Are there any observations you could make on your island that
would directly prove the earth is a sphere?