Exam 1 practice problems.pdf

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Physics 194 Exam #1 practice problems 1. A small electrically charged aluminum sphere (mass 20.0 𝑔, charge −5.00 𝜇𝐶) is placed on a plastic tabletop. Your

goal is to set up an electric field that will result in the sphere accelerating upwards at 13.0 𝑚 𝑠 . over a distance of 1.00 𝑚.

a. Draw a force diagram for the sphere while it is in motion.

b. Determine the magnitude and direction of the E-field required to make the sphere move in this particular way. c. What assumptions did you make in part b.?

2. “High voltage” power lines are often seen suspended high above the ground. Two of these power lines are suspended above a physics professor who is out for a walk. The power line on the left carries a current out of the page; the power line on the right carries a current into the page.

a. What is the direction of the magnetic field produced by the two currents at the location of the physics professor? He is on the ground halfway between the two wires. Draw a diagram illustrating your reasoning. Hint: Determine the direction of the magnetic field produced by each current separately, then add them together.

b. The physics professor has been shuffling his feet on the ground as he walks to the right which has made him become negatively charged. Determine the direction of the magnetic force (if any) exerted by the magnetic field on him. Explain your reasoning.

c. Does the power line on the left exert a force on the power line on the right? Explain your reasoning. If you think it does, determine its direction.

3. Your friend is heating some food in the microwave. The two lights in the kitchen are off. You join your friend in the kitchen and turn the lights on as you enter. Your friend says “Since you turned the lights on I’ll have to leave the pizza in the microwave longer.” You’re not so sure about this, but your friend tries to explain. They take out a piece of paper and draw the circuit shown. “When you turned on the lights you closed the switch in the circuit. This means the current from the power supply is being split between the microwave and the two lights. Since the power output of a device is 𝑃 = 𝐼∆𝑉 and the current through the microwave is now lower, the power output of the microwave will be lower and the pizza will take longer to cook.”

a. You’re pretty sure you’ve never noticed having to heat something longer in the microwave if the lights were on. Explain the problem with your friend’s reasoning.

b. Assuming the circuit drawn by your friend’s is the way the kitchen is wired, determine the power output of the power supply when just the microwave is on. Then, determine the power output of the power supply when the microwave and two lights are on.

4. An advanced materials lab uses strong magnetic fields to investigate the properties of new compounds. During a particular experiment the magnetic field in the lab is supposed to do the following, in sequence:

• Stage 1: Remain at 0.030 T for 1.0 s.

´

Microwave

Light Light Power supply

to kitchen

120

V V

D =

9.6

R= W

192 R= W

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• Stage 2: Increase to 0.600 T over the next 0.5 s. • Stage 3: Remain at 0.600 T for 1.0 s.

• Stage 4: Decrease back to 0.030 T over the next 0.5 s. • Repeat the above steps a second time.

A circular wire coil (100 windings, 0.20 m radius, 5.0 W resistance) connected to an ammeter is placed in the lab so the above magnetic field points perpendicularly through the coil. This coil will be used to determine if the magnetic field in the lab is what it’s supposed to be.

a. Is it possible to use the ammeter reading to decide if the magnetic field in the lab is consistent with the above sequence? Explain your reasoning.

b. Sketch a graph of the current in the coil as a function of time for the above 6 second sequence. The graph should numerically precise along the horizontal axis. It does not need to be numerically precise along the vertical axis. c. Determine the magnitude of the current in the coil during the first time interval that the current is present. d. For each time interval that a current is present in the coil draw a labeled diagram showing its direction and also

the direction of the induced magnetic field. In the diagram(s) you draw, the coil should be in the plane of the page and the magnetic field produced by the lab equipment should point out of the page.

5. For each of the statements below, if true, write a response to convince Mike that the statement is true. If not true, write a response to convince Mike that the statement is not true.

a. As you take your jacket off you hear cracking sounds coming from the long sleeves of the shirt you are wearing. You then bring your arm close to some dust on the floor. The dust leaps through the air and sticks to your shirt sleeve. This means the dust was electrically charged.

b. A toy car has a positively charged glass sphere attached to its roof. A second toy car has a negatively charged plastic sphere attached to its roof. The two cars are released from rest and roll towards each other. The electric potential energy of the two-car system increases with time because they are getting closer.

c. A single light bulb is connected to a battery. The power output of this light bulb is 10 W. A second identical light bulb is added in series with the first. The power output of each light bulb will be significantly less than 5 W.

6. Two plastic spheres are hanging from plastic threads as shown. A glass rod that has been rubbed with silk (removing electrons from the rod) is brought nearer and nearer sphere #1 from the left. Sphere #1 swings toward the rod as it gets close. Sphere #2 does the same, but swings less. The rod is then used to “paint” sphere #1, which means touching all parts of the sphere with the rod. Once this is done and the rod is moved far away, the two spheres swing towards each other and remain touching.

a. Explain in detail what is happening microscopically during this sequence of events and why the spheres behaved in the way they did. Use diagrams to illustrate your explanation.

b. The two plastic spheres are replaced by metal spheres. Everything happens the same except for:

• When the rod is brought near, the two spheres swing toward it more dramatically.

• After the rod is used to “paint” sphere #1 and the rod is moved far away, the spheres swing towards each other, touch, then quickly swing away from each other, eventually coming to rest angled away from each other.

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Explain in detail what is happening microscopically that causes the metal spheres to behave differently in these two parts of the experiment. Use diagrams to illustrate your explanation.

7. Two parallel metal plates are charged oppositely creating a uniform electric field of magnitude 6.00 × 107𝑁 𝐶 as shown. A beam of charged particles (could be positively or negatively charged) is fired with speed 𝑣 = 2.00 × 10:𝑚 𝑠 into the electric field region. You realize these particles will be deflected from traveling in a straight path by the electric field. But, you then realize that it is possible to add a magnetic field to this region so that the particles will travel in a straight path anyway.

a. Explain how this is possible. On the diagram show the magnetic field that will accomplish this.

b. Determine the magnitude of this magnetic field.

8. A pair of light bulbs is connected to a pair of batteries as shown. a. Predict the power output of each light bulb.

b. Light bulb 2 is removed from the circuit and replaced with an ordinary length of wire. Your friend says “Light bulb number 1 will remain just as bright because

and the potential difference hasn’t changed since it’s still 3 volts total, and the resistance of the bulb hasn’t changed.” You’re not so sure about this… Explain the problems with your friend’s reasoning, then make a numerical prediction for what the power output of bulb 1 will become.

9. Two parallel wires are carrying currents as shown in the diagram. The electrons that make up the current move at a very slow average speed, in this case approximately .

a. Draw a B-field line diagram of the magnetic field generated by . b. What is the magnitude and direction of the magnetic force, if any,

that is exerted on one of the moving electrons in the wire on the right. If this force is zero, explain why.

10. Nuclear fusion is a highly sought-after alternate energy source because it is environmentally friendly and uses very abundant fuels. However, it is a technical challenge to get two atomic nuclei to fuse. One way to get two nuclei to fuse is to strip off their electrons then accelerate the nuclei to high speed and collide them together. Using this idea it is possible to fuse two deuterium nuclei into helium which results in a release of energy. Deuterium is an isotope of hydrogen, having one proton and one neutron in its nucleus.

a. If the two deuterium nuclei need to get within of each other for them to fuse into helium, determine what speed they must be fired at from far away to get that close.

b. Describe any assumptions you made. 2

P

=

D

V R

2 I

5

6.9 10´ - m s

1

I

15

1.3 10

´

-

m

+ + + + + + + + + + + + + + + +

-E

!

1

1.50

V

e

=

e

2 =1.50V

1 5.00 R = W 2 10.0

R = W

10.0

cm

1

2.00

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c. Determine the electric field at the halfway point between the two nuclei when they are apart. Show your work/explain your reasoning.

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-CONVERSION FACTORS

Length

1 in = 2.54 cm

1 m = 39.4 in = 3.28 ft

1 mi = 5280 ft = 1609 m

1 km = 0.621 mi

1 angstrom (Å) = 10-10 m

1 light year = 9.46 : 1015 m

Volume

1 liter = 1000 cm3

1 gallon = 3.79 liters

Speed

1 mi/h = 1.61 km/h = 0.447 m/s

Mass

1 atomic mass unit (u) = 1.660 : 10-27 kg

(Earth exerts a 2.205 lb force on an object with 1 kg mass)

Force

1 lb = 4.45 N

Work and Energy

1 ft•lb = 1.356 N

#

m = 1.356 J

1 cal = 4.180 J

1 eV = 1.60 : 10-19 J

1 kWh = 3.60 : 106 J

Power

1 W = 1 J/s = 0.738 ft

#

lb/s

1 hp (U.S.) = 746 W = 550 ft

#

lb/s

1 hp (metric) = 750 W

Pressure

1 atm = 1.01 : 105 N/m2= 14.7 lb/in2

= 760 torr

1 Pa = 1 N/m2

PHYSICAL CONSTANTS

Gravitational constant on Earth g 9.81 N/kg

Universal gravitational constant G 6.67 : 10-11 N

#

m2/kg2

Mass of Earth 5.97 : 1024 kg

Average radius of Earth 6.38 : 106 m

Density of dry air (STP) 1.3 kg/m3

Density of water (4°C) 1000 kg/m3

Avogadro’s number NA 6.02 : 1023 particles (g atom)

Boltzmann’s constant k 1.38 : 10-23 J/K

Gas constant R 8.3 J/mol

#

K

Speed of sound in air (0°) 340 m/s

Coulomb’s law constant k 9.0 :910 N

#

m2/C2

Speed of light c 3.00 : 108 m/s

Fundamental electric charge e 1.60 : 10-19 C

Electron mass me 9.11 : 10-31 kg

= 5.4858 : 10-4 u

Proton mass mp 1.67 : 10-27 kg = 1.00727 u Neutron mass mn 1.67 : 10-27 kg

= 1.00866 u Planck’s constant h 6.63 : 10-34 J

#

s

Magnetic

Constant

𝑘

<

= 2.00 × 10

=7

𝑇 𝑚 𝐴

=

𝜇

@

2𝜋

Vacuum

Figure

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References

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