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EXAM III, PHYSICS 1403, July 29, 2015, Dr. Charles W. Myles
INSTRUCTIONS: Please read ALL of these before doing anything else!!!
PLEASE put your name on every sheet of paper you use and write on one side of the
paper only!! PLEASE DO NOT write on the exam sheets, there will not be room! This
wastes paper, but it makes my grading easier!
PLEASE show all work, writing the essential steps in the solutions. Write formulas first,
then put in numbers. Partial credit will be LIBERAL, provided that essential work is
show n. Organized, logical, easy to follow work will receive more credit than
disorganized work.
The setup (PHYSICS) of a problem will count more than the math of working it out.
PLEASE write neatly. Before handing in your solutions, PLEASE: a) number the pages
& put the pages in numerical order, b) put the problem solutions in numerical order, & c)
clearly mark your final answers. If I can’t read or find your answer, you can't expect me
to give it the credit it deserves.
NOTE!! The words “EXPLAIN”, “DISCUSS” & “DEFINE” below mean to answer
mostly in ENGLISH, NOT math symbols!
I HAVE 43 EXAMS TO GRADE!! PLEASE HELP ME GRADE THEM
EFFICIENTLY BY FOLLOWING THESE SIMPLE INSTRUCTIONS!!!
FAILURE TO FOLLOW THEM MAY RESULT IN A LOWER GRADE!! THANKS!
An 8.5’’ x 11’’ piece of paper with anything written on it & a calculator are allowed. NOTE: Question 1
is Required Conceptual Questions as usual. However, in contrast to previous exams, there are
only three (3) numerical problems. Further, EACH of them is REQUIRED! That is, you have
no problem choices this time! You must answer Question 1 and each of the 3 numerical
problems! Each Question /Problem contains sub-parts a, b, c, etc. Please answer all sub-parts for each!
Each of #1, #2, #3, #4 is equally weighted & worth 25 points, for 100 points on this exam.
1. CONCEPTUAL QUESTIONS!!! Answer briefly all parts in a few complete,
grammatically correct English sentences. Give answers using mainly ENGLISH WORDS,
NOT symbols or equations! If you insist on using symbols, DEFINE all symbols! NO credit
will be given for answers with ONLY symbols! If a part contains more than one question,
please answer each one!
Fig. 1
a. State Newton’s Universal Law of Gravitation. I prefer that you state it using
v
mostly English words. If you write a formula, DEFINE all symbols in it!
b. Fig. 1 shows a spherical planet with a small satellite in a circular orbit about it. The
r 
orbit radius is r and the satellite is moving at a constant speed v in its orbit. Briefly
and qualitatively discuss THE REASON that the satellite stays in orbit. That is,
what is THE PHYSICS behind it staying in orbit? (Hints: Because its moving in a
Circular
circle, it experiences a centripetal acceleration and a centripetal force. Tell me
Orbit!
what physical phenomenon CAUSES this centripetal force.) Note: For a numerical
application of this, see Problem 2a!
c. Briefly DEFINE: 1) Work Done by a Constant Force 2) Kinetic Energy
d. State the Work-Energy Theorem. (Note! This ISN NOT the same as the definition of
The work done by a constant force! Answers giving the definition of the work done by a
constant force will get ZERO credit!).
e. Note that the following is NOT in your book, but I talked about it in class! I stated that
the Work-Energy Theorem is one of Newton’s Laws of Motion, but expressed in WorkEnergy language rather than Force language. Fill in the blank: The Work Energy
Theorem is Newton’s ___________ Law of Motion in Work-Energy Language.
f. 2 BONUS POINTS! This was introduced & discussed yesterday: State The Principle of
Conservation of Mechanical Energy. (Hint: This IS NOT the same as The Law of
Conservation of Total Energy! Answers discussing that Law will get ZERO credit!)
NOTE: YOU MUST ANSWER all parts of PROBLEMS 2., 3. & 4!!
2. See Fig. 2. Note: YOU MUST use scientific (power of 10) notation to solve this problem.
PLEASE be careful in accounting for powers of 10! A satellite, mass m = 4,000 kg,
Fig. 2
is in a circular orbit at constant speed v around planet X, assumed to be a uniform
v
sphere of constant density. (Resemblance of planet X to Earth is coincidental!) The
radius of the orbit (measured from the planet’s center) is r = 8  107 m. The planet mass is
r 
M = 7.0  1024 kg. The gravitational constant is G = 6.67  10-11 (N m2)/(kg2).
a. Calculate the gravitational force between the satellite and the planet.
b. The satellite’s orbit is circular, so it experiences a centripetal acceleration aC and a
Circular
“centripetal force”. (Note: This problem assumes that you know, understand &
Orbit!
have stated the correct qualitative answer to Question 1 b on the previous page!)
Calculate the “centripetal force” on the satellite (Hint: You don’t need to know the
satellite’s speed to answer this!).
c. Calculate the centripetal acceleration experienced by the satellite. What is it’s direction?
(Hint: This will be very small! You don’t need to know the satellite’s speed to answer this!).
d. Calculate the speed of the satellite in orbit. (Note: Einstein told us that the largest speed
possible for any mass is the speed of light c = 3 × 108 m/s! If your speed is larger than c,
or even a significant fraction of it, you’ve done something wrong! But, v should be large
enough for the satellite to go the HUGE distance around the orbit in a reasonable time.
FYI: Earth satellites can make 2 or more full orbits per day. Typical speeds for them are
in the 1,000 m/s to 3,000 m/s range. If you find a v as slow as that of ordinary objects
moving on the Earth’s surface, such as, for example, 100 m/s, that’s much too slow &
you’ve done something wrong!).
e. Calculate the period of the satellite’s orbit. (Hint: This should be a reasonable period for
a satellite around a planet similar in size to Earth. For a typical period, see the hint for part d.)
3. Fig 2 shows a boy pulling a
FN
wagon, mass m = 10 kg, along
Fig. 3
Ffr
a flat, horizontal sidewalk by
pulling on the handle with
force FP = 25 N at an angle
θ = 30° to the ground. Other
mg
forces acting on the wagon are
its weight mg, acting
vertically downward, the normal force FN acting vertically upward and a friction force Ffr =
10 N acting in opposite direction of the motion. The free body diagram for the wagon is
shown in the figure. The displacement of the wagon is d = 100 m in the horizontal direction.
a.
b.
c.
d.
e.
f.
Calculate: 1) The work done by the weight mg as the wagon moves through the displacement d
= 100 m AND 2) the work done by the normal force FN, in this process. (Hint: You ought to be
able to do this without knowing the numerical value of FN!)
Calculate: 1) The work done by the friction force Ffr during this process AND 2) the work done
by the pulling force FP during this process.
Use the results of parts a & b to calculate the net work done Wnet due to all forces acting on the
wagon during the process described above.
If the wagon starts from rest (v0 = 0) on the left of the figure, calculate it’s kinetic energy KE after
it has moved through the d = 100 m displacement. What Physical Principle did you use to do this
calculation?
Calculate the box’s speed after it has moved through the d = 100 m displacement.
2 BONUS POINTS! Calculate the normal force FN acting on the box in the vertical direction. Is it
equal & oppositely directed to the box’s weight in this case? What Physical Principle did you use
to do this calculation? (Hint: Doing this requires material from chapters previous to Ch. 6 on
Work & Energy!)
h
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NOTE: YOU MUST ANSWER all parts of PROBLEMS 2., 3. & 4!!
4. Note! Parts a, b & c are independent of parts d & e!
For parts a, b & c, see Fig. 4, which shows a car, mass
v1 =
v2 =
Fig. 4
15m/s
m = 1,500 kg, accelerating along a flat, horizontal road. At
35 m/s
the initial position in the figure, its velocity is v1 = 15 m/s.
At the final position in the figure, its velocity is v2 = 35 m/s.
During this process, the car moves through a displacement d = 100 m.
a. Calculate the car’s kinetic energy, KE, when its velocity is 15 m/s, its KE when its
velocity is 35 m/s and the change in its KE (ΔKE) in this acceleration.
b. Calculate the net (total) work Wnet done by all forces acting on the car as it accelerates
from 15 m/s to 35 m/s. What Physical Principle did you use to do this calculation?
c. Assuming that the net (total) force Fnet acting on the car to cause its acceleration from
15 m/s to 35 m/s is a constant, calculate that total force Fnet.
For parts d & e, see Fig. 5, which shows a mass m = 15 kg being
moved through a vertical displacement by a person’s hand from the
ground at y1 = 0 to a height y2 = h = 10 m above the ground. The free
body diagram is shown in the figure. The two vertical forces on the
mass are the force Fext from the person’s hand and its weight mg.
d. If the person moves the mass vertically and accelerates it at the
same time then, Fext will be greater than mg and the net vertical
force will be Fnet = Fext - mg. If Fext = 160 N calculate the net
work Wnet done by Fnet in moving the mass through the vertical
displacement h.
e. If the mass starts from rest ay y1 = 0, for the same Fnet as in part d, calculate its kinetic
energy KE and its speed v at height = h = 10 m. What Physical Principle did you use to
do this calculation?
5. BONUS QUESTIONS, 6 POINTS TOTAL!! For the extra points indicated, briefly answer
the following questions using a few complete, grammatically correct English sentences.
The answers to most of these are NOT in the book! If you were in class when I discussed
them, you likely will be able to answer them. If you skipped, as some often do, you likely
won’t be able to answer them.
a. 2 BONUS POINTS! When starting the Gravitation discussion, I said that Newton was
the first to do Gravitation Theory. I also said that he used his Gravitation Law (+ his 2nd
Law + Calculus!) to make predictions which were in Excellent Agreement with some
observations. Tell me, briefly, exactly what the observations were that Newton explained
with his theory. This result also eventually came to be called his “Greatest
Achievement”. It’s a major reason why he’s called “the Greatest Scientist who Ever
Lived”!. Correct answers should give some details of the problem he successfully applied
his Gravitation Law to. NOTE: Answers ONLY saying that he developed the Gravitation
Law aren’t sufficient (this is obvious!) & will get ZERO credit. The problem I’m
referring to here is NOT the same as his idea for putting objects into orbit around Earth.
Answers here that discuss that idea will get ZERO credit. I ask about that idea in part b!
b. 2 BONUS POINTS!!! Near the end of the Gravitation discussion, we talked about small
objects orbiting larger ones, like artificial satellites around the Earth. As a historical
comment, I mentioned that Newton himself was the first to suggest putting objects in
Earth orbit. Briefly describe his idea for HOW to launch such objects into orbit. Be specific!
c.
He didn’t know about rockets! Zero credit will be given for answers which talk about rockets. (He
had the physics correct for this, but the technology to actually do this didn’t exist in the 1600’s).
2 BONUS POINTS!!! Near the end of the Gravitation discussion, we discussed the “effective
weightlessness” concept & the fact that reporters are VERY wrong when they say things like “the
space shuttle has escaped the Earth’s gravity & is now in orbit.” In a few complete,
grammatically correct sentences, explain the reason that this statement is wrong. What would
happen if the shuttle didn’t experience the Gravitational force of the Earth?
h
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Fig. 5