FINAL EXAM, PHYSICS 1403
December 13, 2004
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!!
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 120 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
(to be done in 2.5 hours!). 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 1st, 2nd, and 3rd 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 static equilibrium.
f. State Archimedes’ Principle (for the buoyant force on an object partially or
completely submerged in a fluid).
g. State Bernoulli’s Principle (for a flowing fluid).
2. See Figure. A hollow sphere of volume V = 10 m3, is completely submerged in water.
It is filled with just enough of a liquid of unknown density ρ so that it will float
statically with a load (including that of the empty sphere) of mass m = 2,000 kg. (Not
including the mass m´ of the liquid itself.) Density of water: ρw = 1,000 kg/m3.
a. If the top of the sphere is a distance h = 3 m below the surface of the water,
compute the pressure at that point.
b. Compute the buoyant force FB the water exerts on the sphere (neglecting the load
volume).
c. Compute the density ρ of the liquid. (Hint: To answer this, you MUST use BOTH
Archimedes’ Principle AND a condition for static equilibrium! Answers attempting to
use ONLY the definition of density in terms of mass & volume will get ZERO credit!).
d. Compute the mass m´ of the liquid which is required.
NOTE: Work any four (4) of Problems 2.,3.,4., 5., and 6.!
3. See Figure. A fluid of density ρ = 900 kg/m3 moves
through a circular pipe, radius r1 = 0.30 m, at speed
v1 = 3.0 m/s under pressure P1 = 3.0 x 105 N/m2, as
shown on the left at point 1. The pipe bends
upwards a vertical distance h = 0.4 m, as shown in
the middle. It then narrows to a radius r2 = 0.1 m as
shown on the right at point 2. Area of a circle of radius r: A = πr2.
a. Compute the average force exerted by the fluid to the left of point 1 on the fluid
to it’s right. (Use the relation between force, cross sectional area, and pressure).
b. Compute the volume flow rate (in m3/s) of the fluid in the pipe.
c. Compute the speed v2 of the fluid in the narrow part of the pipe.
d. Compute the pressure P2 in the narrow part of the pipe.
4. See Figure. A compound wheel consists of two disk-shaped wheels
of radii r1 = 0.3 m and r2 = 0.5 m attached to each other on an axle
passing through their centers. The total mass is M = 5.0 kg. Two
equal forces, F1 = F2 = 40 N, are applied, directed as shown. F1 is
tangent to the inner wheel. F2 is directed at an angle of 60° with
respect to the radial direction. The moment of inertia of this
compound wheel is I = (½)M[(r1)2 + (r2)2]. It starts from rest at t = 0.
a. Compute the torques about the rotation axis produced by F1 and
F2 and the total torque produced by them together. (Hint: Don’t
forget to account for the signs! Pick a sign convention and stick with it!)
b. Compute the angular acceleration experienced by the wheel. What Physical
Principle did you use to do this calculation?
c. Using the results of part b, compute the linear acceleration of a point on the inner
rim at r1 and of a point on the outer rim at r2.
d. Compute the rotational kinetic energy and angular momentum of the wheel when
it’s angular velocity has reached ω = 10 rad/s.
e. Compute the wheel’s angular velocity and it’s angular displacement after 5 s. At
this same time, compute the linear velocity of a point on the inner rim at r1 and of
a point on the outer rim at r2.
NOTE: Work any four (4) of Problems 2.,3.,4., 5., and 6.!
h
5. The figure is a track that marbles can be rolled down. The loop radius is R = 0.6 m. The right
end of the track rises to height h = 0.5 m above the horizontal. The left part of the track,
including the entire loop, is frictionless. There is friction on the track from the end of the loop
to the right end of the track. A marble, mass m = 0.1 kg, is put on the track and released from
rest at height H at the left of the figure.
a. Compute the minimum velocity the marble
A
must have at the top of the loop (point B in
B
the figure) to make it around the loop
R
without falling off. (Hint: Use Newton’s
nd
2 Law along with what you know about
centripetal force!)
b. Compute the gravitational potential energy of the marble when it reaches the top
of the loop (point B in the figure).
c. Compute the height H from which the marble must be released from rest (point A in the
figure) in order for it to reach the top of the loop with the velocity of part a. (Hint: Use
energy!)
d. If the marble is released from rest at the height H of part c, compute it’s kinetic
energy and velocity when it has moved down to height y = 1.0 m above the
bottom. This will occur before it reaches the loop!
e. When the marble is released from the height H found in part c, it’s velocity at the
end of the ramp (the right of the figure) is measured and found to be 3.6 m/s. Compute
the work done by friction as the cart moves from the bottom of the loop to the end of the
track.
6. See figure. Two boxes, masses m1 = 20 kg and
m2 = 15 kg, are put on a horizontal frictionless
surface. They are connected by a massless cord.
Another massless cord is attached to m1 and
someone pulls on it with a horizontal force FP =
30 N. The boxes are therefore given an acceleration (the same for both!) a to the right.
a. Draw the free body diagrams for the boxes, properly labeling all forces (label the tension
in the cord between the boxes FT).
The unknowns are the acceleration a of the two boxes and the tension FT in the cord between
them.
b. By applying Newton’s 2nd Law to the two boxes, write the equations needed to solve for
a and FT. (I don’t mean to just write the abstract Newton’s 2nd Law equations! I mean to
write the equations which result when Newton’s 2nd Law is APPLIED to the boxes!)
c. Using the equations from part b, calculate a and FT (in any order).
d. If the boxes start from rest, after the force FP has acted for 5 s compute their velocity v
and the distance x they have traveled.
7. BONUS!!! During the semester, 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 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 holiday season and good luck in the future!
h