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EXAM III, PHYSICS 1403
April 26, 2004, Dr. Charles W. Myles
INSTRUCTIONS: Please read ALL of these before doing anything else!!!
1. PLEASE put your name on every sheet of paper you use and write on one side of the
paper only!!
2. PLEASE do not write on the exam sheets, there will not be room!
3. 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.
4. The setup (PHYSICS) of a problem will count more heavily than the math of
working it out.
5. 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.
6. 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 Newton’s 2nd Law for Rotational Motion. Explain the meaning of any
symbols! (Note: The answer ∑F = ma will receive ZERO credit!)
b. State the conditions for static equilibrium. Explain the meaning of any symbols!
c. State Archimedes’ Principle. Explain the meaning of any symbols!
d. See figure: The round objects roll without slipping down an inclined plane, each
starting at height H above the horizontal. The box slides without friction down
the plane. All round objects have the same radius R. All objects, including the
box, have the same mass M. The moments of inertia are: Hoop: I = MR2,
Cylinder: I = (½)MR2, Sphere: I = (2MR2)/5. The four
objects are released, one at a time, from the height H. Which
object arrives at the bottom with the greatest speed? Why ?
Which arrives with the smallest speed? Why? What physical
principle did you use to arrive at these conclusions? (If you
write equations, explain the meaning of the symbols. Most of
the answer should be WORDS!)
NOTE: WORK ANY TWO (2) OF PROBLEMS 2., 3., or 4. !!!!!
2.
The figure is a free body diagram for this problem. A ladder, mass m =
20.0 kg and length L = 5.0 m, leans against a wall at a point 4.0 m
above the floor, as shown. (By geometry, xo in the figure is xo = 3.0
m.) The ladder is uniform, so its weight acts through its center of
mass. The wall is frictionless, so that the only force between it and the
ladder is FW, acting horizontally to the right. The ground is not
frictionless, so the force FG between the ladder and the ground has both
horizontal and vertical components, FGx and FGy.
a. Compute the torque which the weight of the ladder, acting alone, produces about
an axis passing through the contact point between the ladder and the ground.
b. Write equations describing the conditions for equilibrium of the ladder. This does
not mean to write the general, abstract conditions for equilibrium! It means to
APPLY these conditions to the ladder and to write the equations which result
from this application.
c. Determine (in any order!) the unknown force FW and the two unknown force
components FGx and FGy.
d. Compute the magnitude and direction of the force FG between the ground and the
ladder.
3. See figures below. A SPHERE, radius R = 0.5 m & mass M = 6.0 kg, rolls without
slipping from a flat, horizontal surface up onto an inclined plane. At the bottom of the
plane, the linear speed of the sphere’s center of mass is V = 8.0 m/s. It rolls up the
plane and stops a height H above the bottom of the plane. The sphere’s moment of
inertia is I = (2MR2)/5. The angle θ is not needed to solve this problem!
V = 8 m/s
ω=?
y=0
Before
y=H=?
V=0
ω=0
After
a. Compute the translational kinetic energy of the sphere’s center of mass at the
bottom of the plane.
b. Compute the angular velocity ω of the sphere at the bottom of the plane.
c. Compute the rotational kinetic energy of the sphere at the bottom of the plane.
At the same point, compute the angular momentum of the sphere about an axis
passing through the center of mass.
Use energy methods to answer parts d. and e.!
d. Compute the gravitational potential energy of the sphere at its final position.
e. Compute the final height H when the sphere has stopped at the top of the plane.
NOTE: WORK ANY TWO (2) OF PROBLEMS 2., 3., or 4. !!!!!
4. See figures. A crown of volume V and density ρC is weighed in
air, as in Fig. 1, and is found to weigh 150 N. That is, the reading
on the scale is FT = 150 N. The same crown is completely
submerged in water, as in Fig. 2, is weighed again, and is found
to weigh 130 N. That is, the reading on the scale is now FT´ = 130
N. As is shown in Fig. 2, the water produces an upward buoyant
force FB on the crown. The water’s density is ρH20 = 1,000 kg/m3.
(Hint: To answer questions b. and c. below, you must use BOTH
Archimedes’ Principle and a condition for static equilibrium.
Answers which attempt to use ONLY the definition of density
in terms of mass and volume are WRONG and will receive ZERO
Fig. 1
Fig. 2
credit!). Compute (in any order):
a. The mass of the crown.
b. The buoyant force FB and the volume V of the crown.
c. The density ρC of the crown.
Note: The following questions are (obviously!)
independent of the previous parts! See figure. Part of an
irrigation system is shown. At the left, in the lower pipe at
point 1, the water is flowing in a 6 cm diameter (radius r1
= 0.03 m) pipe at a velocity v1 = 5.0 m/s. The water
pressure there is P1 = 1.5  105 N/m2. The pipe bends
upward until it levels off again at point 2, 2.0 m above
point 1. The pipe at point 2 has narrowed to a 4 cm diameter (radius r2 = 0.02 m).
The density of water is ρH20 = 1,000 kg/m3. Compute (in any order):
d. The volume flow rate of water in the pipe and the velocity of water at point 2.
e. The water pressure at point 2.
f. What Physical Principle (or whose Principle) did you use to find the answer to
part e.?