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Midterm 2 PRS Questions

PRS questions from the lectures afterMidterm 1 but before Midterm 2

PRS Question. You want to launch arocket into space, and you want to

maximize its kinetic energy.Suppose that you can increase the

rocket’s mass or its launch velocity byabout the same amount, but you can’t

increase both. Which would youchoose?

1. I’d make the rocket moremassive

2. I’d make the rocket faster

If we race two equal-mass ballsdown these two tracks, which ball

will win the race?

1. The ball on the flat track2. The ball on the “V-shaped” track3. Neither! Both balls will reach the

finish line at the same time

Another delightfulinterlude from thegood folks at

PRS

What happens if I place a ball at the top of the“V” in the lower track and then let it go?

• The ball starts at rest with maximum gravitational potentialenergy (GPE) and zero kinetic energy (KE) because v = 0

• As gravity pull the ball toward the ground, the GPE isconverted to kinetic energy, and the ball rolls faster

• At the bottom of the “V”, it attains its minimum GPE andmaximum KE. This is where it rolls the fastest

• As it climbs back up the track, the KE is converted back intoGPE and the ball slows down

Because the v-shaped track converts more GPE into KE, theball on that track moves much faster than the ball on the flattrack for much of the race, and consequently it wins in the end.

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A Sun-like star puts out 9 x 1026 Joules everysecond. The speed of light is 3 x 108 m/s.How much mass does the star convert to

energy every second?1. 10 kg2. 100 kg3. 104 kg4. 108 kg5. 1010 kg

E = mcE = mc22

Hurray! PRS Question

Two types of nuclear reactionsthat release mass-energy

Fission FusionLess mass is present after than before the reaction...

E = mcE = mc22Human nuclearpower plants usefission (e.g., ofuranium or plutonium)

Cosmic power plants use fusion (e.g., two hydrogen atoms fusedto form one helium atom)

A nice cosmic powerplant: our Sun! Cosmic power plant

• mass-energy = E/c2

• c2 = (3 x 108 m/s)2 = 9 x 1016 m2/s2

• E = 9 x 1026 Joules• Therefore, mass = 1010 kg

E = mcE = mc22

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Atom 1: 92 protons, 143 neutrons, 92 electronsAtom 2: 92 protons, 143 neutrons, 91 electronsAtom 3: 91 protons, 143 neutrons, 91 electronsAtom 4: 92 protons, 144 neutrons, 92 electrons

Which of these atoms are isotopes?

1. 1 and 22. 2 and 33. 3 and 14. 1 and 45. 3 and 4

• A particular element always has thesame number of protons

• atomic number = # protons• atomic mass number = #protons +

#neutrons (aka “atomic weight”).• Isotopes are the same element but

with different atomic weights Ener

gy

Atom energy levels are often depicted in a simpleway as shown below. PRS Question! Atoms oftenspontaneously emit radiative energy (light). Which ofthe electron transitions shown below (A, B, C, D, or E)would cause the atom to emit light?

1. A2. B3. C4. D5. E6. A and B7. A and C8. A, B, C9. A, B, C, D10. All of them

not allowed

Ionization. Energyadded, not removed.

Excitation. Energy added, not removed.

Opposite charges attract, but similar charges repel eachother. The nucleus of helium contains two positiveprotons and two neutral neutrons. Why don’t the

similarly-charged protons in this nucleus push each otheraway?

1. There is a strong chemical bond inside thenucleus.

2. The attraction of the negatively-charged electronsholds the protons together.

3. There is a force that is even stronger than thecharge force that holds the nucleus together, butit only acts on short distance scales, i.e., whenparticles are quite close together.

Which of the following is least likely to beaccelerating?

1. A car driving down a winding, narrowmountain road.

2. A racecar driver.3. A car driving through Texas on the

interstate.4. A bumper car at a county fair.5. A planet orbiting a star.

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Newton’s Universal Law of Gravitation Between every two objects there is an attractive

force, the magnitude of which is directlyproportional to the mass of each object and inverselyproportional to the square of the distance betweenthe centers of the objects.

(G = the “gravitational constant”, a constant of nature)

Two equal masses separated by distance d exert a force F oneach other due to gravity. How large would the gravitational

attraction be if the distance between them was doubled?

1. 1/4 F2. 1/2 F3. The force would be the same.4. 2 F5. 4 F

If the Sun suddenly collapsed into a black hole withthe same mass but 10 times smaller diameter, how

would the Earth’s orbit change?1. It would become 10 times smaller.2. It would become 100 times smaller.3. The Earth would plunge into the black hole.4. The Earth would spiral into the black hole.5. Nothing would change.

PRS question.True or False: When a rocket

blasts off, it pushes off theground in order to launch itself

into the air.1. TRUE2. FALSE

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(1) (2)

(3)

The NASAPegasus rocket

You are a shuttle astronaut returning to the shuttle after attemptingto fix the International Space Station with a hammer. As you arejetting back to your shuttle, your lifeline breaks, your jets run outof fuel, your radio goes dead, and you miss the shuttle. To getback safely, you should:

1) use a swimming motion with your arms and legs2) throw the hammer at the shuttle to get someone’s attention3) throw the hammer away from the shuttle4) make a hammering motion in the direction of the shuttle5) make a hammering motion away from the shuttle

PRS Question

Escape VelocityIf the mass of the Earthwere increased by afactor of 10, what wouldthe new escape velocity be?

1. 1/4 its current value2. 1/3 its current value3. the same as its current value4. 3 times the current value5. 4 times the current value

Escape VelocitySuppose that you couldchange a planet’s properties.To make it easier to launch spacecraft off this planet, youwould:

1. Decrease the radius of the planet2. Decrease the mass of the planet3. Both of the above4. Can’t answer -- need more information

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PRS question.

True or False: To steer abicycle, you just move the

handlebars.1. TRUE2. FALSE

Actually, to steer a bicycle you must lean to move your bodyweight and manipulate the angular momentum in the spinningbicycle wheels.

Two angles - right ascensionand declination - indicate the

location of an object in the sky.

• One can imaginemoving a telescope onthe ground to thedesired angles.

• But how is the HubbleSpace Telescope movedto look at an object?

PRS question.Which part of Newton’s physics of motioncould be used to point the Hubble Space

Telescope at an interesting object?

1. Newton’s 1st Law2. Newton’s 2nd Law3. Newton’s 3rd Law4. Conservation of linear momentum5. Conservation of angular momentum

This could be accomplished various ways, but a frequently used method is to employ:

Three balls in space near a planet

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Three balls in space near a planetSuppose an astronaut places three equal mass balls next to each other out in spaceabove some planet as shown on the previousscreen. The balls are initially at rest. After some time, the balls will1. still be the same (i.e., nothing will have changed).2. all be falling toward the planet at the same speed.3. all be falling toward the planet with ball 3 moving

fastest.4. all be falling toward the planet with ball 1 moving

fastest.

Three balls in space near a planet

F = m a

The same effect causes tides.

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Survey question -- tides withoutoceans

Tides are readily apparent in the oceans because liquid water flows more readilythan rock. Can tidal effects be observedeasily on planets that have no water?

1. No, tidal effects are too subtle if there aren’toceans.

2. Yes.

Jupiter’s moon Io is the mostvolcanically-active object in the solar

system

Io is constantly stetched by tidal force in different directions as it orbits Jupiter. This generates frictioninside Io, which heats its interior! “Tidal friction”

Every seven days, Io, Jupiter,Europa, and Ganymede line upas shown at right. The sum ofthe gravitational tugs at this timepulls Io into an elliptical orbit.

This alignment effect is an example of an orbital resonance.

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Four fundamental forces.Astronomy??

1. The force of gravity2. Electromagnetic force3. The strong nuclear force4. The weak nuclear force

PRS question. Which of the forces drives the ejection of water geysers out of Enceladus?

Waves in waterWhat happens when a wave moves through a pond from the left side tothe right side?

1. The water molecules move from the left sideto the right side.

2. The wave moves from left to right, but thewater particles move from right to left

3. The wave moves from left to right and thewater molecules move up and down butdon’t move sideways.

PRS Question:A movie theater works on

the principle of

1. Specular reflection2. Diffuse reflection

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Specular reflection vs. diffusereflection (aka scattering)

• In specular reflection,the angle of incidence= angle of reflection

• In diffuse reflection,photons are reflectedin semi-randomdirections

Reflection vs.Scattering

Reflection: angle of incidence =angle of reflection

Scattering: angle of scattering is random