Final

Physics 101 Final Exam
Dec 2002 Prof L. Weinstein

There are 34 questions. Unless otherwise noted, please give a short explanation for all of your non-numerical answers. Show your work for all numerical answers.

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Two different objects have the same momentum. Do they have to have the same velocity?
1. yes
2. no
3. need more information
p = mv. One can have more mass and less velocity.
The primary coil of a step-up transformer has 100 turns and draws 100 W at 20 V. The secondary coil of the transformer has 10,000 turns. How much voltage does the secondary coil provide?
V1/100 turns = V2/10,000 turns therefore V2 = 100*v1 = 2,000 V. The wattage is irrelevant.
A big battery is connected to a lamp by means of a transformer. When the switch is pressed down and held closed for 5 minutes will the lamp stay lit for the entire time?
= 2.2in $\epsffile{transformer.ps}$
1. Yes, if the battery is powerful enough.
2. No.
3. Need more information.
No. Transformers only work with changing voltage. The battery puts out a constant voltage.
Electric railroad locomotives in the mountains use electric motors to turn their wheels when they go uphill. When they go downhill, is it possible to use the electric motor to slow them down (ie: as a brake)? Explain.
1. yes
2. no
3. need more information
The electric motor converts electrical energy to kinetic energy. You can always reverse it so that it converts kinetic energy into electrical energy.
Light bulbs A and B are identical in all ways except that B's filament is thicker than A's. Which bulb has more resistance?
= 1.2in $\epsffile{bulbs.ps}$
1. A
2. B
3. both the same
4. need more information
A thinner or longer wire has more resistance (it is harder for the electrons to get through it).
Light bulbs A and B are identical in all ways except that B's filament is thicker than A's. If screwed into 110-volt sockets, which bulb will be brightest?
1. A
2. B
3. both the same
4. need more information
Less resistance means more current will flow (I = V/R). Power = current * voltage so that more current means more power. 100 W light bulbs have less resistance that 60 W bulbs.
When I dropped a bar magnet through a vertical length of pipe in class, the bar magnet dropped VERY slowly because of magnetic induction. After the first half-second, it is moving at constant downward velocity. If the mass of the bar magnet is 0.15 kg and the mass of the pipe is 2 kg, what is the force exerted on the bar magnet by the pipe after the first half-second?
= 1.5in $\epsffile{pipe.ps}$ The weight of the magnet is 0.15 kg * 10 m/s^2 = 1.5 N. Since it is falling at constant velocity, the net force must be zero (Newton's 2nd Law). Therefore, there must be an upward magnetic force of 1.5 N. The weight of the pipe is irrelevant.
The space shuttle is in a circular orbit around the Earth travelling at 8 km/s. It can generate electrical power by induction by dragging a long wire through the Earth's magnetic field. It can then use this electrical power to operate its lights, computers, motors, etc. If the space shuttle does this, what will happen to its orbit?
= 1.2in $\epsffile{shuttle.ps}$
1. It will lose kinetic energy, slow down, and eventually hit the Earth.
2. Its kinetic energy will not change and its orbit will not change.
3. It will gain kinetic energy, speed up, and move further from the Earth.
4. Need more information.
The energy for the electrical power must come from somewhere. The only place it can come from is the Shuttle's kinetic energy.
I push a 0.2 kg bar magnet through a 250-turn, 3-kg coil of wire. It induces a current in the coil. If the coil exerts 2 N of force on the bar magnet, what force does the bar magnet exert on the coil?

2 N. Newton's 3rd Law.
A 2000 kg truck travelling at 30 m/s (about 65 mph) hits a stationary 1000 kg car. They stick together. = 1.2in $\epsffile{collision.ps}$
a) What is the total momentum of the truck plus car before the collision?

p = m1 v1 + m2 v2 = 2000 kg * 30 m/s + 1000 kg * 0 = 60,000 kg m/s

b) What is the total momentum of the truck plus car after the collision?

p(after) = p(before) = 60,000 kg m/s

c) What is the speed of the truck plus car after the collision?

v = p/m = p/(m1 + m2) = 60,000 kg m/s / (2000 kg + 1000 kg) = 20 m/s

d) What is the total kinetic energy of the truck plus car before the collision? (Use scientific notation.)

KE = KE1 + KE2 = 0.5*(2000 kg)*(30 m/s)^2 + 0 = 9*10^5 kg m^2/s^2 = 9*10^5 J

e) What is the total kinetic energy of the truck plus car after the collision? (Use scientific notation.)

KE = 0.5*(2000 kg + 1000 kg)*(20 m/s)^2 = 6*10^5 J
An AC power supply is connected to a switch and a coil. An adjacent coil is connected to a voltmeter. When the switch is closed, the voltmeter reads 2 V. If an unmagnetized iron rod is inserted through both coils and left there, the voltmeter will read
= 1.5in $\epsffile{transformer2.eps}$
1. 0 V
2. between 0 and 2 V
3. 2 V
4. more than 2 V
5. need more information
There is a voltage induced in the secondary circuit by the changing magnetic field within the secondary coil. This changing magnetic field is due to the current in the first coil. If an iron rod is inserted through both coils, then the magnetic field in the second coil due to the current in the first coil will be much greater. This larger magnetic field will induce a much larger voltage in the secondary coil. (An alternate answer is: We did that in class.)
(No explanation needed) Two long parallel wires, and , are separated by 3 cm. They each carry a current of 5 A. What forces do they exert on each other (circle all that apply)?
= 1.1in $\epsffile{wires.ps}$
1. gravitational
2. magnetic
3. electrical
4. friction
5. tension
They exert gravitational forces on each other (but those are REALLY tiny). They also exert magnetic forces since the electric current in one wire makes a magnetic field that exerts a magnetic force on the current in the other wire. There is no electrical force because the two wires are both uncharged. There is no friction or tension force because the wires are not touching each other.
Can an electron at rest in a constant magnetic field be made to move by the magnetic field?
1. Yes
2. No
No, you need a changing magnetic field to exert a force on an electron at rest.
An electron is at rest. Can it be made to move by a changing magnetic field?
1. Yes
2. No
Yes. A changing magnetic field exerts a force on charged particles. We did this in class when I moved a magnet near a coil of wire and induced a current.
(no explanation needed) A wire placed in a region of constant magnetic field has a 20 A current through it. The magnetic field goes from left to right and the current in the wire goes from down to up (see figure). What direction is the force on the wire?
= 1.2in $\epsffile{wire.ps}$
1. into or out of the page
2. left or right $\leftrightarrow$
3. up or down $\updownarrow$
4. other
5. need more information
The magnetic force will be perpendicular to both the direction of the current and the direction of the magnetic field.
(no explanation needed) A bar magnet has a north pole and a south pole. I break the magnet in half. I now have
1. one north pole magnet and one south pole magnet
2. two smaller bar magnets, each with a north and a south pole
3. one magnet and one piece of unmagnetized iron
4. other
5. need more information
The wires in a circuit in my house can carry 20 A without overheating. The voltage is 110 V. My favorite lightbulb has 55 $\Omega$ .
a) How much current does one light bulb draw?

I = V/R = 110 V / 55 ohm = 2 A

b) How many light bulbs can I connect in parallel to this circuit without overheating the wires?

10 light bulbs
I have an ideal 1.5 V battery (ie: a battery that can deliver as much current as I want at 1.5 V) and fifteen 3- light bulbs. How many light bulbs should I connect in series to get the maximum amount of light?
1. 1
2. 2
3. 3
4. 15
5. need more information
The more bulbs I add, the greater the total resistance. This will decrease the current in the circuit. Since the power is I*V and V is constant, this will decrease the power. Therefore I should use only one bulb.
I paid the electric company $100 last month. They charge $0.10 per kiloWatt-hour. How many electrons did they send me that I got to keep? (Hint: your answer should be in Coulombs, not kW-hr.)

zero. I paid the power company for power, not for electrons. If I kept all those electrons, there would be a HUGE static electricity buildup in my home.
The electric field of the Earth is 100 N/C at the Earth's surface and points downward. George has a mass of 80 kg.
a) What is George's weight?

W = mg = 800 N

b) How much electric charge would have to be added to George so that the force from the Earth's electric field balanced his weight (ie: so he could fly)?

We want the electric force to equal the gravitational force. F = qE (charge times electric field) so that q = F/E = 800 N / 100 N/C = 8 C.
Two charged metal spheres are 3.9 m apart. If the distance between them doubles, then the electric force between them
1. quadruples
2. doubles
3. is unchanged
4. halves
5. quarters
6. need more information
F = k q1 q2 / d^2. If d doubles, then F gets four times smaller.
Two charged metal spheres are 3.9 m apart. If the distance between them doubles, then the gravitational force between them
1. quadruples
2. doubles
3. is unchanged
4. halves
5. quarters
6. need more information
F = G m1 m2 / d^2. If d doubles, then F gets four times smaller.
When I was zapped by a spark from the van de Graaf generator I did not die because
1. the spark had high voltage but low current
2. the spark had high current but low voltage
3. the spark had low current and low voltage
4. I did die but they forgot to put a wooden stake in my heart
5. other
Current kills, not voltage.
How much energy does 1 microCoulomb of charge gain when it passes through a 50,000 V potential difference?

The energy gained is charge times voltage: E = q V = 1*10^(-6) C * 5*10^4 V = 5*10^(-2) J = 0.05 J
Hepzibah is on a new planet. In order to determine the acceleration of gravity she drops a rock from a height of 30 m. It takes 3 s to fall.
a) What is the average speed of the rock during its fall?

V_average = d/t = 30 m / 3 s = 10 m/s

b) What is the acceleration of the rock during its fall? (Hint: average speed is not instantaneous speed.)

V_average is the average of the starting speed and the ending speed. Since the starting speed is zero, the ending speed must be twice the average speed (since V_average = [V_start + V_end]/2). Therefore it went from 0 m/s to 20 m/s in 3 s.

a = change in v / time = 20 m/s / 3 s = 6.7 m/s^2.
Early bicycles had a huge front wheel, often as tall as a person. Which has more rotational inertia, a 5 kg wheel with a large radius (eg: 1 m) or a 5 kg wheel with a smaller radius (eg: 0.5 m)?
1. the larger wheel
2. both the same
3. the smaller wheel
4. need more information
rotational inertia goes as mass*radius^2. If you increase the radius, you will increase the rotational inertia.
The gravitational acceleration at the Moon's surface is about 1.6 m/s . Let's say that you can apply a maximum force of 400 N (about 90 lbs).
a) If you apply your force vertically, could you lift a 50 kg block on the Moon? Could you lift it on Earth?

The weight of a 50 kg block on the moon would be W(moon) = 50 kg * 1.6 m/s^2 = 80 N. You could easily lift it.

The weight of a 50 kg block on Earth would be W(earth) = 50 kg * 10 m/s^2 = 500 N. You could not lift it.

b) If you apply your force horizontally, what acceleration would the block have on the moon (ignore friction)?

a = F/m = 400 N / 50 kg = 8 m/s^2. It doesn't matter where it is (as long as you can ignore friction).
The hang time of a basketball player who jumps a vertical distance of 2 feet (0.6 m) is about 2/3 of a second. What will be the hang time if the player reaches the same height while jumping 4 feet (1.2 m) horizontally?
1. less than 2/3 s
2. the same (ie: 2/3 s)
3. more than 2/3 s
4. need more information
Horizontal speed does not affect vertical motion.
(no explanation needed) I can accumulate a net negative charge on myself in the winter by scuffing my feet on a wool carpet. If I do this, then the carpet becomes
1. less positively charged
2. equally positively charged
3. more positively charged
4. negatively charged
5. need more information
A bicycle has one (or more) large gears attached to the pedals and one (or more) smaller gears attached to the back wheel. The two gears are connected by a chain. The front gear has a radius of 6 cm and the rear gear has a radius of 3 cm. The bicyclist pedals so that the front gear makes one revolution per second.
How many revolutions per second does the rear gear (and hence the rear wheel) make?

= 1.in $\epsffile{gear.ps}$ The two gears are connected by the chain so that they have the same linear (ie: tangential) velocity at their rims. The small gear has half the radius of the larger gear so it must make two revolutions for each revolution of the larger gear in order to have the same linear velocity.
In the previous problem, if the bicyclist wants to go faster without pedalling faster, she should use a
1. smaller rear gear
2. same size rear gear
3. larger rear gear
4. the rear gear size does not change the bike's speed
5. need more information
If the rear gear is smaller, then it will have to rotate even faster to have the same linear speed as the large gear. Try it at home (turn the bike upside down and turn the pedals with your hands)
A child dropped his marbles on the floor of the school bus when it was stopped at a traffic light. When the bus accelerates forward, the marbles
1. roll toward the back of the bus
2. stay where they are
3. roll toward the front of the bus
4. need more information
Inertia. The marbles try to stay where they are, the bus moves forwards.
My 1000 kg car can decelerate (ie: brake) at 3 m/s . If I am driving at 15 m/s (about 30 mph), I can stop my car in a distance of 37.5 m. If I am driving at 30 m/s (about 60 mph), then the distance I need to stop my car
1. decreases
2. stays the same
3. doubles
4. quadruples
5. need more information
Twice the speed means you need four times the stopping distance. There are two ways to look at this: 1) doubling the speed quadruples the kinetic energy (KE=0.5 mv^2) so you need to do four times the work to stop. If the force is the same, W= fd so you need four times the distance. 2) Since the time to stop is t = v/a, if you double the speed, then you need twice as much time to stop. However, since you have twice the starting velocity, you will have twice the average velocity. Twice the time and twice the velocity means you need four times as much distance.
If you think of the Earth as a giant magnet, then the North Pole of the Earth is actually
= 1.2in $\epsffile{earth.eps}$
1. the south pole of the magnet
2. the north pole of the magnet
3. the east pole of the magnet
4. other
The north pole of a magnet is points north. Therefore, it is attracted to the North Pole of the Earth, therefore the Earth's North Pole is actually the south pole of a magnet.

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2003-12-02