PHYS 202 General PhysicsFinal exam review sheet

Winter 2010

The final exam will be given on Wednesday, March 17, at 8:00 am. You may bring a3 × 5 card with appropriate equations (no text) written on it. Don’t forget to bring yourscientific calculator, as well.

A sample exam from a previous year is available online. The mix of problems is not quitethe same as this year, but it will give you an idea of the level of difficulty. The exam will becomprehensive.

Your lab notebooks will be available on Monday (March 15) for you to pick up andreview. Some sample questions are given here. These questions emphasize the later materialcovered 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 by5.0 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 fora 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 constantforce of 40 N tangent to the outside of the merry-go-round. The mass of the merry-go-round is 800 kg and its radius is 1.5 m. Assume it is a disk. There is a constantfrictional torque of 15 N-m. (a) How long does it take the child to accelerate the merry-go-round to an angular velocity of 0.50 revolutions/second? (b) What is the angularmomentum of the merry-go-round at this angular velocity? (c) Now, assume that thechild jumps onto the merry-go-round and sits 1.0 m from the center. How much timewill it take the merry-go-round to come to a stop? (Assume an initial angular velocityof 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 thereis no power applied: it is “coasting.” Someone drops a 100-gram lump of clay ontothe turntable, at a point 10.0 cm from the center. What is the angular velocity of theturntable 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 themiddle and with a radius equal to (1/3)R. I claim that I have lowered the rotationalinertia 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 onemeter long, tilted at an angle of 30 with the vertical asshown. What is the angular acceleration α of the stick?(Assume the bottom of the stick cannot slip.) What isthe speed of the ball when it hits the ground? Ignore themass 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 Obser-vatory in England, where g = 9.812 m/s2, is taken to Paris, where it loses 20 secondsa 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 thelength of this pendulum? [0.993 m] (b) If the amplitude of the swing is 5.00, whatis 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 whatpositions does this occur? Find this value in two different ways. [0.85 m/s2] (d) Whatwould the angular frequency and the period of this pendulum be on the moon, wherethe 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 aspring, sliding without friction on a30 incline. At the equilibrium posi-tion of the 1.5-kg mass, the spring is0.32 m longer than its unstretchedlength. (A) What is the spring con-stant of the spring? (23.0 N/m) (B)We can start the system oscillat-ing by giving the mass a little push.What would be the frequency of os-cillation? (0.62 Hz)

30

9. A 0.80-kg mass on a spring is oscillating with an amplitude of 0.12 m. The totalmechanical energy of the system is 0.360 J. (A) Find the spring constant. (B) Findthe vibrational frequency. (1.26 Hz) Note: there are at least two approaches to thisproblem.

10. Below is a diagram of a tube open on one end and closed on the other. It is 2.50m 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, firstharmonic, second harmonic, etc.) State whether you are drawing the pressure or thedisplacement pattern. (b) Determine the frequency of this standing wave assuming thespeed 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 tothe sound power level. Also, doubling I results in adding 3 dB to the sound powerlevel. (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 todetermine 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 discfastened to the end of a wire. The disc rotates back and forth, twisting the wire asit does so. This is just another example of oscillation, but of a type we have notexamined much. (A) What is the period of the system? (B) If we describe the motionas Θ = A sin ωt, what is the amplitude A and the angular frequency ω? (C) What isthe maximum angular velocity of the disc itself? What does this correspond to on thegraph?

13. Consider the circuit below. When the resistance of the nichrome wire is decreased,what happens to the brightness of each bulb?

A

B

3 V

Nichrome wire

-

+

14. Redraw the circuit at right to show more clearlythe series and parallel elements.(A) What happens to the current in resistor 3 ifresistor 1 is replaced by a wire? (Does it increase,decrease, or stay the same?) Explain.(B) What happens to the current in resistor 3 ifresistor 2 if replaced by a wire? Explain.

1 2 3

4

5

6

3

15. The circuits below show a diode in series with a 10- Ω resistor. The forward-bias voltageof this particular diode is 0.7 V. That means that when the diode is conducting, itsvoltage 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 Ω3.0 V

10 Ω3.0 V

(A) (B)

−

+

−

+

16. In the circuit below, you are given the current through three of the elements. Find thecurrent 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.

E

A

DC

B

F

1.80 A

0.8 A

0.6 A

10 V−

+

17. In the circuit below, (A) What is the total current supplied by the battery immediatelyafter the switch is closed? (B) What is the total current supplied by the battery a longtime after the switch is closed? (C) what is the voltage across the capacitor a longtime after the switch is closed? (D) What is the charge stored by the capacitor a longtime after the switch is closed?

100 Fµ

10.0 V

60

40

Ω

Ω

50Ω

150 Ω

−

+

4