EXAM II, PHYSICS 1403, July 25, 2012, Dr. Charles W. Myles
INSTRUCTIONS: Please read ALL of these before doing anything else!!!
1.
2.
3.
4.
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 shown. Organized,
logical, easy to follow work will receive more credit than disorganized work.
The setup (PHYSICS) of a problem will count more heavily 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.
5. NOTE!! The words “EXPLAIN”, “DISCUSS” & “DEFINE” below mean to answer
mostly in ENGLISH, NOT math symbols!
I HAVE 32 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, Conceptual Questions IS REQUIRED! You may work any three (3) of the remaining 4 problems
for four (4) problems total. (This means 4 complete problems, with all of their parts!). Each
problem is equally weighted & worth 25 points, for 100 points on this exam.
1.
MANDATORY CONCEPTUAL QUESTIONS!!! Answer briefly all parts briefly 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! For parts a & b: Newton’s Laws
are about forces. Complete statements of each Law MUST mention forces! If a part contains
more than one question, please be sure to answer each one!
a. State Newton’s 1st Law. How many objects at a time does it apply to?
b. State Newton’s 3rd Law. How many objects at a time does it apply to?
c. See Fig. 1. A hockey puck slides (to the right) at constant velocity v
across a flat, horizontal, frictionless ice surface. Which of the sketches in
the figure is the correct free body diagram for this puck? WHY? Explain
your answer using Newton’s Laws! (Hint: Is there a force in the
direction of the puck’s motion?) To answer correctly, you need to think
like Newton (300+ years ago) NOT like Aristotle (3,000+ years ago).
d. These questions are about a box of mass m, under two different conditions. In
both cases, it sits statically (not moving!) on a flat horizontal table. Fig. 2 is the
box’s free body diagram when the only forces acting on it are the normal force FN from
the table acting upward & it’s weight mg downward. Is the normal force FN in this case
equal in magnitude & opposite in direction to the weight? Which Newton’s Law of
Motion did you use to answer this? Fig. 3 is the free body diagram when, in addition to
the normal force FN & weight mg, an additional downward force FP = 40 N acts on it
when someone pushes on the top. Is FN in this case equal in magnitude & opposite in
direction to the weight? Which Newton’s Law of Motion did you use to answer this?
e. See Fig. 4. A ball of mass m is twirled at the end of a string in a circle of constant
radius r & constant speed v. The ball’s free body diagrams at the top & at the bottom of
the circle are shown. Is the tension FTA that the string exerts on the ball at the top of the
circle (point A) less than, more than, or the same as the tension FTB at the bottom of the
circle (point B)? WHY? Explain (in English!) your answer using Newton’s 2nd
Law with centripetal acceleration.
f.
State THE
THEME OF THE COURSE.
Fig. 1
Fig. 2
θ
Fig. 3
Fig. 4
NOTE: WORK ANY THREE (3) OF PROBLEMS 2., 3., 4., or 5.!!!!!
2. See figure. A carton is placed on a dolly by a stock clerk. He pushes on it with a force
F = 80 N which makes an angle θ = 37° BELOW the horizontal. The carton + dolly have
mass m = 23 kg. There is a friction force Ff between the dolly & the
floor, acting in the opposite direction of the motion. The coefficient of
kinetic friction between the box & floor is μk = 0.16. To solve this
problem, use the x & y axes shown.
a. Sketch the free body diagram of the carton + dolly, properly
Ff
labeling all forces. (Note: If you don’t make a sketch, you will lose
points!!) Don’t forget the weight mg and the normal force FN
which are NOT SHOWN in the figure!
b. Calculate the x & y components of the pushing force F.
c. Answer this qualitative question: Is the normal force FN in this problem equal in
magnitude & opposite in direction to the weight mg? WHY or WHY NOT? Explain!
Which Newton’s Law of Motion did you use to answer this? (Note: If you don’t answer
a 
θ
F
this, you will obviously lose points!!)
d. Calculate the weight mg of the carton + dolly and the normal force FN.
e. Calculate the friction force Ff that the dolly experiences as it moves to the right.
f. Use Newton’s 2nd Law to find the acceleration a experienced by the carton + dolly. What
forces cause this acceleration? (Answer in words!)
NOTE: WORK ANY THREE (3) OF PROBLEMS 2., 3., 4., or 5.!!!!!
3. See figure. A helicopter, mass M = 8.0  103 kg, moves vertically upward with

acceleration a. It lifts an object, mass m = 1.1  103 kg, which is

connected to its bottom by a massless cable. The upward force on the
FP = 1.4  105 N
5
helicopter exerted by the air on the rotors is FP = 1.4  10 N. The cable
tension, FT, of course, acts down on the helicopter & up on the object.
 a
The acceleration a & the tension FT are unknown. (Note: In this
 FT
problem, the numbers are large enough that I want you to give your
numerical answers using scientific, power of 10, notation! Each
Helicopter
correct answer which doesn’t use this notation will have one point
M = 8000 kg
 FT
deducted from the total credit for that answer.)
 a
a. Sketch the free body diagrams for the helicopter & the object,
properly labeling all forces. Don’t forget the weights of the
Object
helicopter & the object, not shown in the figure! (Note: If you
m
= 1100 kg
don’t make a sketch, you will lose points!!)
nd
b. Apply Newton’s 2 Law to the helicopter & to the object to find the 2 equations needed
to solve for a & FT. Writing them without substituting in numbers, will receive more
credit than writing them with numbers in them! (Hint: FT can’t possibly be equal to the
weight mg of the object!! If it were, the acceleration a would be zero!!)
c. Using the equations derived in part b, calculate a & FT. (Note: You MUST use the
algebra of 2 linear equations & 2 unknowns
to answer this! Attempts to answer it without using that algebra will get ZERO credit!).
d. When the cable becomes tight & the helicopter starts to lift the object, it is moving up at
velocity v0 = 10 m/s. Calculate it’s velocity a time t = 20.0 s later. (Hint: The motion is
vertical, but obviously, the acceleration is NOT g downward, it is a upward!!)
NOTE: WORK ANY THREE (3) OF PROBLEMS 2., 3., 4., or 5.!!!!!
4. See figure. A child, mass m = 45 kg, is on a Ferris wheel which moves her at
constant speed v = 2.5 m/s in a vertical circle of (unknown) radius r. The
period for this uniform circular motion is T = 50 s. The free body diagrams for
the rider at the top & at the bottom are shown. FN is the normal force
experienced by the rider (due to the seat pressing upward on her body). FN is not
necessarily the same at the top & at the bottom.
a. Calculate the radius r of the child’s circular path as the Ferris wheel
moves her around in a circle as the just described.
b. Calculate the centripetal acceleration aR experienced by the rider.
Calculate the “centripetal force” experienced by the rider. What are
the vector directions of this acceleration and force?
c. Answer this qualitative question: Is the normal force FN in this problem equal in
magnitude & oppositely in direction to the weight mg at either the top or the bottom
of the child’s circular path? WHY or WHY NOT? Explain! Which Newton’s Law of
Motion did you use to answer this question? (Note: If you don’t answer this, you will
obviously lose points!!)
d. Write the equation resulting from applying Newton’s 2nd Law in the vertical
direction to the rider when she is at the top of the Ferris wheel. Calculate the normal
force FN on the rider at that point.
e. Write the equation resulting from applying Newton’s 2d Law in the vertical
direction to the rider when she is at the bottom of the Ferris wheel. Calculate the
normal force FN on the rider at that point.
f. 5 POINT BONUS!! For a mass such as this child moving in a circle at a constant
speed, briefly discuss why it is incorrect to ever say that the mass experiences a
“Centrifugal Acceleration” and a “Centrifugal Force”.
NOTE: WORK ANY THREE (3) OF PROBLEMS 2., 3., 4., or 5.!!!!!
5. See figure. A ball, mass m = 3 kg, is attached to the end of a massless string of
length r = 0.5 m. A child holds onto the other end of the string and twirls the ball
in a perfect vertical circle of radius r at constant speed v = 4 m/s. The period for
this uniform circular motion is T = 40 s. The free body diagrams for the ball at
the top & at the bottom of the circular path. FT1 and FT2 are the tension in the
string at the top (point 1) and the bottom (point 2) of the circle.
a. Calculate the Centripetal Acceleration aR experienced by the ball
throughout its motion. Calculate the “Centripetal Force” the ball experiences.
b. Answer this qualitative question: What are the vector directions of the
Centripetal Acceleration and the “Centripetal Force” calculated in part a?
(Note: If you don’t answer this, you will obviously lose points!!)
c. Write the equation resulting from applying Newton’s 2nd Law in the vertical direction to
the ball when it is at the top of the circle. More credit will be given for first writing this
algebraically without putting in numbers for the known quantities than for writing it with these
numbers already in it. Calculate (numerically) the tension in the string FT1 on the ball at
that point.
d. Write the equation resulting from applying Newton’s 2nd Law in the vertical direction to
the ball when it is at the bottom of the circle. More credit will be given for first writing this
algebraically without putting in numbers for the known quantities than for writing it with these
numbers already in it. Calculate (numerically) the tension in the string FT2 on the ball at
that point.
e. 5 POINT BONUS!! For an object such as this ball moving in a circle at a constant speed,
briefly discuss why it is incorrect to ever say that the object experiences a “Centrifugal
Acceleration” and a “Centrifugal Force”.