FINAL EXAM, PHYSICS 1403
August 7, 2006, Dr. Charles W. Myles
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INSTRUCTIONS: Please read ALL of these before doing anything else!!!
PLEASE put your name on every sheet of paper you use & write on one side of the paper only!!
PLEASE DO NOT write on the exam sheets, there will not be room! Yes, this wastes paper, but it
makes my grading easier!
PLEASE show all work, writing the essential steps in the solutions. Write appropriate 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.
For answers which are very small or very large numbers PLEASE use scientific (power of 10) notation!
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 and put the
pages in numerical order, b) put the problem solutions in numerical order, 7 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: I HAVE 85+ EXAMS TO GRADE!!! PLEASE HELP ME GRADE
THEM EFFICIENTLY BY FOLLOWING THE ABOVE SIMPLE
INSTRUCTIONS!!! FAILURE TO FOLLOW THEM MAY RESULT IN A
LOWER GRADE!! THANK YOU!!
Problem 1 (Conceptual Questions) AND Problem 2 (Vibrations) ARE REQUIRED! Work any three (3) of
the other problems for five (5) problems total. Each problem is equally weighted & worth 20 points, for a
total of 100 points on this exam..
1. MANDATORY QUESTION!!! Answer briefly, in complete, grammatically correct English
sentences. Supplement answers with equations, but keep these to a minimum & EXPLAIN WHAT
THE SYMBOLS MEAN!! Answers which have only equations & no explanation will receive very
little, if any credit!
a. State Newton’s 1st Law of Motion (for Translation).
b. State Newton’s 3rd Law of Motion (for Translation).
c. State the Principle of Conservation of Mechanical Energy.
d. State the Law of Conservation of Linear Momentum.
e. State Newton’s 2nd Law for Rotational Motion. (∑F = ma will get ZERO credit!).
f. See Figure. The round objects roll without slipping down an inclined plane. The box slides
without friction down the slope. The round objects all have radius R &
mass M (also the box mass). Moments of inertia: Hoop: I = MR2, Cylinder:
I = (½)MR2, Sphere: I = (2MR2)/5. The objects are released, one at a
time, from the same height H. Which object arrives at the bottom with the
greatest (translational) speed V? Why? Which object arrives with the
smallest V? Why? What Physical Principle did you use to arrive at these
conclusions? (Note: I want most of the answer in WORDS!)
g. 5 Point Bonus!! During our rotational motion discussion, I did a demonstration to try to illustrate
the answer to part f. Briefly describe this demonstration. (If you were in class the day I did this
demonstration, likely will be able to answer this. If you “cut” class that day, as several of you have habitually
done this session, you probably won’t be able to answer it!) NOTE: I did several rotational motion
demonstrations that day. The one I’m referring to was specifically about objects rolling down an
incline. This was NOT the “rotating professor” demonstration!
NOTE: Problem 2 (Vibrations) is MANDATORY!
2. See figure. A mass m = 15 kg is attached to an ideal spring of spring constant
k. The mass is pulled a distance x = A from its equilibrium position & released
from rest. It undergoes simple harmonic motion. Observation shows that x as a
function of time is given by x(t) = Acos(ωt) = (1.5 m) cos(10t). That is, the
amplitude A = 1.5 m & the angular frequency ω = 10 s-1. (Note: Answers to this
problem which attempt to use the constant acceleration kinematic equations from Ch. 2
will get ZERO credit!) Neglect friction. Compute:
a. The frequency f and the period T of the motion.
CONTINUED ON NEXT PAGE!
b.
c.
d.
e.
f.
Problem 2 Continued!
The spring constant k.
The maximum speed vmax and the total mechanical energy E.
The maximum force on the mass & the maximum acceleration it experiences.
The potential energy, the kinetic energy and the mass’s speed v when x = +1.1 m.
The force on the mass & it’s acceleration when x = +1.1 m.
NOTE: Work any three (3) of Problems 3, 4, 5, 6, & 7!!
3. (Static fluid )
a. State Archimedes’ Principle (for the buoyant force on an object partially or completely submerged in a fluid).
For parts b to e, see figures. A rectangular block, mass m = 11 kg, is suspended by a wire
from a scale & immersed in oil (oil density ρo = 1.5  103 kg/m3). It’s free body
diagram is at the far right. FB is the buoyant force on the block due to the oil &
FT is the tension in the wire. The block’s horizontal faces have area A = 0.02 m2
& it’s vertical dimension is L = 0.11 m, so it’s volume is V = AL = 2.2  10-3 m3.
It’s top face is a distance y = 0.14 m below the oil surface. The system is static.
b. Compute the density ρB of the block.
Neglect the effect of atmospheric pressure & answer the following. Compute:
c. The oil pressure P1 on the top face of the block & the oil pressure P2 on it’s
bottom face. Use these results to compute the downward force F1 due to the
oil on the block’s top face & the upward force F2 on it’s bottom face. (Hint:
Use the definition of pressure in terms of force).
d. The upward buoyant force FB exerted by the oil on the block. What physical principle
did you use to compute this force?
e. The tension FT in the wire. What physical principle did you use to compute this force? The
magnitude of FT is the same as the scale reading. This is true because of what physical principle?
NOTE: Work any three (3) of Problems 3, 4, 5, 6, & 7!!
4. (Flowing fluid)
a. State Bernoulli’s Principle (for fluid flow). (Hint: Area of circle of radius r: A = πr2).
For parts b to e, see figure. A fluid of density ρ = 1.5  103 kg/m3 moves through
a horizontal circular pipe of radius r1 = 0.42 m at a speed of v1 = 2.2 m/s under a
pressure P1 = 2.7 x 105 N/m2, as on the left in the figure. The pipe narrows to
radius r2 = 0.16 m as on the right in the figure. Compute:
b. The volume flow rate of the fluid.
c. The speed v2 of the fluid in the narrow part of the pipe.
d. The pressure P2 in the narrow part of the pipe.
e. If a circular sheet of thin plastic of radius r = r1 = 0.42 m were placed inside the wider part of the
pipe (at the left) perpendicular to the direction of the fluid flow, it obviously would stop the flow.
The fluid flowing from the left of this sheet would then obviously exert a force to the right on it.
Compute this force. (Hint: Use the definition of pressure in terms of force.)
NOTE: Work any three (3) of Problems 3, 4, 5, 6, & 7!!
5. See figure. A pulley has mass M = 8.0 kg, radius R = 0.6 m & moment of inertia I = (0.35)MR2.
(This means it ISN’T a uniform disk & that the moment of inertia for a uniform disk& (½)MR2 is ISN’T
valid here!) A massless cord is wrapped around it & a constant force FT is applied tangentially as
shown. It starts from rest. After FT has been applied for 4.0 s, the angular speed has reached ω =
25 rad/s. Compute:
a. The linear (translational) velocity of a point on the rim of the pulley after 4.0 s.
b. The pulley’s rotational kinetic energy & angular momentum after 4.0 s.
c. The pulley’s angular acceleration & the linear (tangential) acceleration of a point on the rim.
d. The net torque acting on the pulley. What physical principle did you use to do this calculation?
e. Assuming that FT is the only force producing a torque, compute FT.
 
FB FT
 

mg

NOTE: Work any three (3) of Problems 3, 4, 5, 6, & 7!!
6. See figures. Use energy methods to solve parts a, b, & c! A mass m = 25 kg is released from rest (left
figure) at the top of a frictionless inclined plane a height h above a frictionless horizontal surface. It
slides down the inclined onto the surface. At the bottom (middle figure), its speed is v2 = 8 m/s. It
continues to the left & has a collision with a second mass M = 37 kg, which is initially at rest. They
stick together after the collision & continue to the left with velocity V' (right figure).
M
V=0
m
y1 = h = ?
v1 = 0
a.
b.
c.
M
V=0
m
 v2 = 8 m/s
y2 = 0
M+m
 V' = ?
Compute the kinetic energy & the momentum of m at the bottom of the incline (middle figure).
Compute the initial gravitational potential energy & the initial height h of m at the top of the
incline. What Physical Principle did you use to do this calculation?
Partway down the incline, m has reached a speed of 5 m/s. At that point, compute it’s kinetic
energy, gravitational potential energy, & it’s height y. (Note: Answers which set KE = PE at the same
point will get ZERO credit!)
d.
e.
The collision between m & M at the bottom is inelastic, since they stick together. Compute their
momentum & their speed after the collision. What Physical Principle did you use to do this
calculation?
Compute their kinetic energy after the collision between m & M. Is kinetic energy conserved in
This collision? Explain briefly in a few complete, grammatically correct English sentences.
NOTE: Work any three (3) of Problems 3, 4, 5, 6, & 7!!
7. See figure. A helicopter, mass M = 8.0  103 kg, moves up with acceleration a = 1.0 m/s2. It is lifting
an object of mass m = 1.5  103 kg, which is connected to it’s bottom by a massless cable. The upward
force, FP, on the helicopter exerted by the air on the rotors is unknown. So is the tension in the cable,
FT, which, of course, acts down on the helicopter & up on the object. (Hints: The
motion is vertical, but the acceleration is obviously NOT g downward, but a upward! If it were
g downward, the object would be in free fall & FT would be zero! Also, FT can’t possibly be =
mg, or a would be zero!).
a.
b.
c.
d.
Sketch the free body diagrams for the helicopter & the object, properly labeling
all forces. Don’t forget the weights of the helicopter & the object, which aren’t
shown in the figure!
Apply Newton’s 2nd Law to the helicopter & the object to find the two equations
needed to solve for FP & FT. Writing these without substituting in numbers, will
receive more credit than writing them with numbers substituted in!
Using the equations from part b, calculate FT & FP.
If the helicopter is moving upward at velocity v0 = 7 m/s when the cable becomes
tight & starts to lift the object, compute the distance the helicopter has traveled
time t = 6.0 s later.
8. BONUS!! During the session, I did some demonstrations. If you were present at any one of those,
please write a few short, complete, grammatically correct English sentences telling about ONE of
them. (You cannot discuss the same demonstration as you did in Problem 1, part g!) Tell me what
demonstration I did AND what physical principle I was trying to illustrate. If you do this, I will add
five (5) points to your Final Exam grade as a small reward for attending class. If you missed class on
demonstration days, you will (probably) not know what demonstrations I did & you will (probably) not
be able to answer this. Have a good rest of the summer and good luck in the future!
FT


FT


FP
 a