FINAL EXAM, PHYSICS 1403
May 10, 2004
Dr. Charles W. Myles
INSTRUCTIONS: Please read ALL of these before doing anything else!!!
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4.
PLEASE put your name on every sheet of paper you use and write on one side of the paper only!!
Yes, this wastes paper, but it makes my grading easier! PLEASE DO NOT write on the exam sheets,
there will not be room!
PLEASE show all work, writing the essential steps in the problem solution. 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.
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, and 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.
Please write large enough that an old guy like me can read it!
NOTE: I HAVE 114 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!!
Three 8.5’’ x 11’’ pieces of paper with anything written on them and a calculator are allowed. Problem 1
(Conceptual Questions) IS REQUIRED! Work any 4 of the remaining problems for five (5) problems
total. Each problem is equally weighted and worth 20 points, for a total of 100 points.
1. THIS QUESTION IS MANDATORY!!! Answer briefly, in complete,
grammatically correct English sentences. Supplement answers with equations, but
keep these to a minimum and EXPLAIN WHAT THE SYMBOLS MEAN!!
a. State Newton’s 3 Laws of Motion.
b. State the Principle of Conservation of Mechanical Energy.
c. State the Principle of Conservation of Momentum.
d. State Newton’s 2nd Law for Rotational Motion. (∑F = ma will get ZERO credit!)
e. State the conditions for equilibrium.
f. Briefly define these terms for wave motion: period, wavelength, amplitude.
NOTE: Work any four (4) of Problems 2.,3.,4., 5., and 6.!
2. Note: Parts a & b are independent of parts c, d, & e!
a. State Archimedes’s Principle (for the buoyant force on an object
partially or completely submerged in a fluid). Explain the
meaning of any symbols!
b. State Bernoulli’s Principle (for a flowing fluid). Explain the
meaning of any symbols!
For parts c, d & e, see the figure. A fluid of density ρ = 800 kg/m3
moves through a horizontal circular pipe of radius r1 = 0.30 m at a speed
of v1 = 6.0 m/s under a pressure P1 = 2.5 x 105 N/m2, as shown on the
left of the figure. The pipe narrows to a radius r2 = 0.15 m as shown on
the right of the figure.
c. Compute the volume flow rate of the fluid.
d. Compute the speed v2 of the fluid in the narrow part of the pipe.
e. Compute the pressure P2 in the narrow part of the pipe.
NOTE: Work any four (4) of Problems 2.,3.,4., 5., and 6.!
3. See the figure. A pulley has mass M = 5.0 kg and radius R = 0.5 m. Assume
it is a uniform disk so that its moment of inertia is I = (½)MR2. A massless
cord is wrapped around it and a constant force FT is applied tangentially as
shown. It starts from rest. After FT has been applied for 5.0 s, the angular
speed has reached ω = 20 rad/s.
a. Compute the linear velocity of a point on the rim of the pulley after 5.0 s.
b. Compute the pulley’s kinetic energy and angular momentum after 5.0 s.
c. Compute the pulley’s angular acceleration and the linear (tangential) acceleration
of a point on the rim.
d. Compute 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.
4. See figures below. Use energy methods to solve parts a, b, c, & d! A mass m = 25 kg
is released from rest at the top of an inclined plane a height h = 3.0 m above a
frictionless horizontal surface. It slides down the inclined onto the surface. The
incline angle is 30º with respect to the horizontal.
h=0
v=?
h = 3.0 m
v=0
Before
After
a. Compute the gravitational potential energy of the mass at the top of the plane.
b. If the incline is frictionless, compute the kinetic energy, the velocity and the
momentum of the mass at the bottom of the plane.
c. Part b assumes no friction. Suppose that you test this assumption experimentally.
The velocity v that you measure for the mass after it has reached the bottom of the
incline is 6.0 m/s. This is less than the speed you (should have) computed in part
b. This means that friction can’t be neglected. How much work is done by friction
as the mass slides down the incline? (Hint: To answer this, you DON’T need to
know either the friction force or the coefficient of friction!)
d. Using the results of part c, compute the friction force between the block and the
incline. (Hint: To answer this, first use trigonometry to compute the distance
down the plane [along the hypotenuse] the mass has traveled in order to get to the
bottom, starting at height h = 3.0 m. You DON’T need to know the coefficient of
friction!).
e. Compute the normal force between the mass and the incline as the mass slides
down the plane (NOTE: I will give ZERO credit if you tell me that the normal
force is equal to the weight!)
NOTE: Work any four (4) of Problems 2.,3.,4., 5., and 6.!
5. See Figure. Fig. (a) shows an ideal, massless spring
which is hung vertically. A mass m = 0.5 kg is hung
from it. This causes it to stretch a vertical distance x0 =
0.150 m from its original equilibrium position in Fig.
(a) to the position in Fig. (b). Note that, in Fig. (b), the
mass is not moving, so that Fig. (b) is a STATIC
equilibrium situation. The position shown in Fig. (b) is
a new equilibrium position for the mass-spring
combination and any subsequent oscillations will be about this position. In Fig. (c),
the mass-spring combination is stretched an additional distance x = 0.100 m and
released from rest. Fig. (c) shows the mass at the beginning of its simple harmonic
motion. Calculate the following:
a. The spring constant k of the spring.
b. The amplitude A and the period T of the simple harmonic motion.
NOTE: In answering the following, NEGLECT the GRAVITATIONAL force and
potential energy! Calculate:
c. The total mechanical energy and the maximum speed of the mass.
d. The maximum force on the mass and the maximum acceleration it experiences.
e. The mass’s potential energy, the force on it, and its speed when x = 0.050 m
(measured from the position in Fig. (b)).
f. Write an expression for x as a function of time (x(t)). (Note: ZERO credit will be
given if you use a kinematic equation from Chapter 2!).
6. See figure. A block of mass m = 25 kg is pulled across a table by a
massless cord, to which is applied a force FP = 40 N, as shown. The cord
makes an angle of 30º with the horizontal. The mass remains on the
horizontal surface; there is no vertical motion. There is friction; the
coefficient of kinetic friction between the mass and the table is μk = 0.25.
a. Draw the free body diagram for the mass, properly labeling all forces.
b. Compute the horizontal and vertical components of the applied force FP.
c. Compute the normal force between the mass and the horizontal surface. (NOTE:
I will give ZERO credit if you tell me that the normal force is equal to the
weight!)
d. Compute the frictional force between the mass and the table.
e. Compute the acceleration of the mass.
f. If the mass starts from rest, compute its velocity and kinetic energy after 5 s.
7. BONUS QUESTION!!! During the semester, I did a few demonstrations. If you
were present at any one of those times, please write a few short, complete,
grammatically correct English sentences telling about ONE of these times. 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 and you will (probably) not be able to answer this.
Have a good summer and good luck in the future!