PHYS 202 General Physics
Final exam review sheet
Winter 2010
The final exam will be given on Wednesday, March 17, at 8:00 am. You may bring a
3 × 5 card with appropriate equations (no text) written on it. Don’t forget to bring your
scientific calculator, as well.
A sample exam from a previous year is available online. The mix of problems is not quite
the same as this year, but it will give you an idea of the level of difficulty. The exam will be
comprehensive.
Your lab notebooks will be available on Monday (March 15) for you to pick up and
review. Some sample questions are given here. These questions emphasize the later material
covered this term. You should also look over the review sheets for the Midterm exams.
Selected problems will be worked out at a review session at 12:00 noon on Monday
in Room 104.
1. A hoop of mass 2.0165 kg and radius 0.75 m rolls down a hill, decreasing in altitude by
5.0 m by the time it reaches level ground. Use conservation of energy to determine (a)
the speed of the hoop at the bottom of the hill, and (b) its angular velocity. Repeat for
a ball of the same mass and radius. Which is faster at the bottom? Explain. [Hoop:
7.0 m/s. Ball: 8.37 m/s]
2. A child of mass 40.0 kg accelerates a playground merry-go-round by exerting a constant
force of 40 N tangent to the outside of the merry-go-round. The mass of the merrygo-round is 800 kg and its radius is 1.5 m. Assume it is a disk. There is a constant
frictional torque of 15 N-m. (a) How long does it take the child to accelerate the merrygo-round to an angular velocity of 0.50 revolutions/second? (b) What is the angular
momentum of the merry-go-round at this angular velocity? (c) Now, assume that the
child jumps onto the merry-go-round and sits 1.0 m from the center. How much time
will it take the merry-go-round to come to a stop? (Assume an initial angular velocity
of 0.50 rev/sec.) Do this two ways: (1) using Newton’s second law, angular form, and
(2) using the impulse-momentum principle, angular form. [63 s; 2800 kg-m2 /s; 197 s]
3. A phonograph turntable may be treated as a 1.2-kg disc with a radius of 16.0 cm.
Suppose the turntable is turning at 3.50 rad/s (its normal playing speed) and there
is no power applied: it is “coasting.” Someone drops a 100-gram lump of clay onto
the turntable, at a point 10.0 cm from the center. What is the angular velocity of the
turntable after this?
4. Suppose I have a disk of radius R, made of a material of uniform density and thickness.
It has some rotational inertia I. Now I take a ”plug” out of the disk, centered in the
middle and with a radius equal to (1/3)R. I claim that I have lowered the rotational
inertia by less than 1.5%. Am I right or not? Show how you know.
1
5. Suppose a heavy ball is on the end of a light stick one
meter long, tilted at an angle of 30◦ with the vertical as
shown. What is the angular acceleration α of the stick?
(Assume the bottom of the stick cannot slip.) What is
the speed of the ball when it hits the ground? Ignore the
mass of the stick. [4.9 rad/s2 ; 4.1 m/s]
30˚
6. A simple pendulum that has a period of exactly 2.000 seconds at the Greenwish Observatory in England, where g = 9.812 m/s2 , is taken to Paris, where it loses 20 seconds
a day. What is the acceleration due to gravity in Paris? [9.807 m/s2 ]
7. A simple pendulum has a period of 2.00 seconds on the Earth. (a) What is the
length of this pendulum? [0.993 m] (b) If the amplitude of the swing is 5.00◦ , what
is the maximum speed of the pendulum bob? Determine this in two different ways.
[0.272 m/s] (c) What is the maximum acceleration of the pendulum bob, and at what
positions does this occur? Find this value in two different ways. [0.85 m/s2 ] (d) What
would the angular frequency and the period of this pendulum be on the moon, where
the acceleration of gravity is 0.165 that of Earth? [1.28 rad/s, 4.92 seconds]
8. At left is a diagram of a mass on a
spring, sliding without friction on a
30◦ incline. At the equilibrium position of the 1.5-kg mass, the spring is
0.32 m longer than its unstretched
length. (A) What is the spring constant of the spring? (23.0 N/m) (B)
We can start the system oscillating by giving the mass a little push.
What would be the frequency of oscillation? (0.62 Hz)
30
9. A 0.80-kg mass on a spring is oscillating with an amplitude of 0.12 m. The total
mechanical energy of the system is 0.360 J. (A) Find the spring constant. (B) Find
the vibrational frequency. (1.26 Hz) Note: there are at least two approaches to this
problem.
10. Below is a diagram of a tube open on one end and closed on the other. It is 2.50
m long. (a) On the diagram, the node-antinode pattern for the second harmonic.
(This is two harmonics up from the fundamental mode: the series is fundamental, first
harmonic, second harmonic, etc.) State whether you are drawing the pressure or the
displacement pattern. (b) Determine the frequency of this standing wave assuming the
speed of sound to be 340 m/s. [170 Hz ]
2
11. We know that if we increase the intensity I by a factor of 10, we just add 10 dB to
the sound power level. Also, doubling I results in adding 3 dB to the sound power
level. (a) Using only these facts and knowing that 10−12 W/m2 corresponds to 0 dB,
find the sound power level corresponding to 5.0×10−7 W/m2 . (b) Use this method to
determine I for a sound with power level of 43 dB. (c) Repeat for 84 dB.
12. Shown below is a graph of the motion of a torsional pendulum, consisting of a disc
fastened to the end of a wire. The disc rotates back and forth, twisting the wire as
it does so. This is just another example of oscillation, but of a type we have not
examined much. (A) What is the period of the system? (B) If we describe the motion
as Θ = A sin ωt, what is the amplitude A and the angular frequency ω? (C) What is
the maximum angular velocity of the disc itself? What does this correspond to on the
graph?
13. Consider the circuit below. When the resistance of the nichrome wire is decreased,
what happens to the brightness of each bulb?
A
+
B
3V
-
14. Redraw the circuit at right to show more clearly
the series and parallel elements.
(A) What happens to the current in resistor 3 if
resistor 1 is replaced by a wire? (Does it increase,
decrease, or stay the same?) Explain.
(B) What happens to the current in resistor 3 if
resistor 2 if replaced by a wire? Explain.
Nichrome
wire
2
1
4
5
6
3
3
15. The circuits below show a diode in series with a 10- Ω resistor. The forward-bias voltage
of this particular diode is 0.7 V. That means that when the diode is conducting, its
voltage drop is 0.7 V, nearly independed of the current. For each diagram, determine
(a) the voltage drop across the resistor, and (b) the current supplied by the battery.
+
+
10 Ω
3.0 V
10 Ω
3.0 V
−
−
(B)
(A)
16. In the circuit below, you are given the current through three of the elements. Find the
current through the elements A, E, and D, as well as the current through the battery.
In each case draw an arrow to indicate the direction of the current.
0.8 A
10 V
A
B
+
E
−
0.6 A
F
D
C
1.80 A
17. In the circuit below, (A) What is the total current supplied by the battery immediately
after the switch is closed? (B) What is the total current supplied by the battery a long
time after the switch is closed? (C) what is the voltage across the capacitor a long
time after the switch is closed? (D) What is the charge stored by the capacitor a long
time after the switch is closed?
60 Ω
50 Ω
100 µF
+
10.0 V
−
40 Ω
4
150 Ω