EXAM III, PHYSICS 1306
April 22, 2002, Dr. Charles W. Myles
INSTRUCTIONS: Please read ALL of these before doing anything else!!!
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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!
PLEASE show all work, writing down the essential steps in the solution of a problem. Write the
appropriate formulas first, then put in numbers. Partial credit will be LIBERAL, provided that the
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 clearly mark your final answers and write neatly. If I can’t read or find your answer, you
can't expect me to give it the credit it deserves.
You will lose credit if you don’t show the units of an answer or if the units are wrong .
PLEASE FOLLOW THESE SIMPLE DIRECTIONS!! THANK YOU!!
An 8.5’’ x 11’’ piece of paper with anything written on it and a calculator are allowed.
Problem 1 (Conceptual Questions) and IS REQUIRED! Work any 2 of the remaining problems for three
(3) problems total. Problem 1 is worth 34 points. Each other problem is equally weighted and worth 33
points, for a total of 100 points.
1. THIS PROBLEM IS MANDATORY!!! CONCEPTUAL QUESTIONS: 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 the conditions for static equilibrium. Explain the meaning of any symbols!
b. Define the terms: Elasticity, Stress, and Fracture.
c. See Figure to the right. A straw of length L is put into a fluid of density . A
finger is put over the top of the straw so that no air can get in or out, and then
the straw is lifted out of the fluid. The straw retains the fluid such that the
distance from the bottom of the finger to the top of the fluid is h. Does the air
in the space between the finger and the top of the fluid have a pressure P that
is 1) greater than, 2) equal to, or 3) less than the atmospheric pressure PA
outside the straw? Explain the reasoning you used to arrive at this answer!
d. State Archimedes’ Principle (for computing the buoyant force on an object
in a fluid). Explain the meaning of any symbols!
e. State Bernoulli’s Principle. Explain the meaning of any symbols! Using
Bernoulli’s Principle, explain qualitatively how a perfume atomizer works
(see Figure).
2. A uniform beam, length L = 20 m & mass m = 1,000 kg, rests with its ends on
vertical supports, as in the Figure. A machine, mass M = 10,000 kg, rests on the
beam, with its center a distance x = 15 m from the left end, as shown.
a. Compute the torque which the weight of the beam produces about an
axis which passes through the left end of the beam.
b. Compute the torque which the weight of the machine produces about
an axis which passes through the left end of the beam.
c. Write equations which describe the conditions for equilibrium of the
beam. This does not mean to just write the general abstract conditions
for equilibrium! It means to APPLY these conditions to the beam and to write the
equations which result from this application.
d. Find the values of the vertical support forces, F1 and F2, at the ends of the beam.
NOTE: WORK ANY TWO (2) OF PROBLEMS 2., 3., 4., or 5.!!!!!
3. See Figure. A uniform beam, length L = 5 m, mass m = 60 kg, is
mounted by a hinge on a wall. It is uniform, so its weight may be
taken as acting through its center of mass. It is held in a horizontal
position by a wire that makes an angle  = 37 with the horizontal, as
shown. From its end, it supports a mass M = 600 kg.
a. Compute the torque which the weight of the board produces
about an axis which passes through the hinge.
b. Compute the torque which the weight of the large mass produces about an axis
which passes through the hinge.
c. Write equations describing the conditions for equilibrium of the beam. This does
not mean to just write the general, abstract conditions for equilibrium! It means to
APPLY these conditions to the beam and to write the equations which result from
this application.
d. Determine the components FHx and FHy that the hinge exerts on the beam and the
components FTx and FTy of the tension in the supporting wire.
e. Compute the magnitude and direction of the hinge force FH.
4. See Figure. A balloon is filled with just enough helium so that, in air, it will lift a
load (excluding the mass of the helium, but including the mass of the empty balloon)
of mass m = 1500 kg. The density of air is air = 1.29 kg/m3 and the density of
helium is He = 0.18 kg/m3.
a. What volume V of helium is required?
b. What is the mass mHe, of helium required?
c. Using these results, calculate the buoyant force of the air on the
balloon (neglecting the volume of the load).
d. What physical principle (or whose principle) did you use to make the
calculations in parts a. and c.?
5. See Figure. Water at a pressure of P1 = 8 x 105 N/m2 at street
level flows into an office building at a velocity of v1 = 0.8 m/s
through a pipe of circular cross section with radius 0.3 m. The
pipe tapers down to a radius of 0.1 m by the top floor, a height h
= 30 m above the street. The density of water is  = 1,000 kg/m3.
a. What is the volume flow rate of water in the pipe?
b. What is the water’s velocity in the pipe at the top floor?
c. What is the water pressure on the top floor?
d. What physical principles did you use to answer a., b., and c.?