Black Holes Final

Kelly and Michael are astronauts on a mission to Mars. Kelly is exploring the planets surface while Michael orbits at 8 Martian radii in their spacecraft's command module. Each astronaut carries a very accurate atomic clock with them for their missions. What do they perceive about each other's clock? A. Michael thinks that Kelly's clock runs slow while Kelly thinks that Michael's clock runs fast. B. Kelly thinks that Michael's clock runs slow while Michael thinks that C. Kelly's clock runs fast. D. They both think the other's clock runs slow. E. They both think the other's clock runs fast.

A A is correct. Since Kelly is deeper in the gravitational potential of the planet, her clock does run slow relative to Michael's. Since Kelly thinks here clock runs normal, she perceives that Michael's clock is fast. Remember this is unlike time dilation in special relativity, where both observer's think the other's clock is slow.

Donald and Daisy are moving at constant velocity in their space ships. Suppose Donald is moving away from Daisy at 85 km/h. Donald throws a ball in Daisy's direction at a speed of 75 km/hr. According to Daisy, which of the following is going on? A. She sees him moving away from her at 85 km/hr and the ball moving away from her at 10 km/hr. B. She sees him moving towards her at 85 km/hr and the ball moving toward her at 75 km/hr. C. She see him moving away from her at 85 km/hr and the ball moving towards her at 75 km/hr. D. She sees him moving away from her at 85 km/hr and the ball moving toward her at 10 km/hr.

A From Daisy's point of view, Donal is moving away at 85 km/hr. Since the ball is moving at -75 km/hr from Donald, addition of velocities yields 10 km/hr from Daisy's point of view.

The gravity of the Earth is exerting a force on a man standing on the ground. Which of the following statements is implied by Newton's 3rd law? A. The gravitational force of the man on the Earth is equal and opposite to the gravitational force of the Earth on the man. B. The normal force of the ground on the man is equal and opposite to the gravitational force of the Earth on the man. C. The net force on the man must be zero because he is not being accelerated. D. The gravitational force on the man must be balanced by some equal and opposite force on the man.

A Newton's 3rd law deals with action - reaction pairs. It is important to remember that the forces in this pair act on different objects. Both b and d deal with two forces that are acting on the man so they do not represent action -- reaction pairs. Statement c deals with Newton's 2nd law. So, a is the only correct response.

An absorption line is observed in the lab to be at 1000 nm. If a star moves perpendicular to our line-of-sight at 1/1000 of the speed of light, what is the observed wavelength of the absorption line from this star? A. 1000 nm B. 1001 nm C. 1010 nm D. 990 nm E. 999 nm

A Since the star is moving perpendicular to our line of sight, we do not see a Doppler shift. Doppler shift requires the star to be moving towards or away from us.

Cosmic rays are particles in space that travel very close to the speed of light. Some cosmic rays are inferred to have Lorentz factors of γ = 106 (or even much higher). The Milky Way galaxy is about 100,000 light-years across meaning that it takes about 100,000 years for the cosmic ray to travel this distance from the point of view of a static observer. In the frame moving with the cosmic ray, how much time passes as it covers this distance? A. About a month B. About a day C. About a year D. About 10 years E. About 100,000 years

A Time dilation says that the passage of time in the frame of the cosmic ray is shorter by a factor γ = 106. Since 100,000 year equals 105 years, we find the time in the cosmic ray frame to be 105 years/106=0.1 years or about a month.

Examples of a freely falling observer include: A. An astronaut in orbit around the Earth. B. A skydiver who has just jumped out of an airplane. C. A man standing in an elevator that is going down at normal speed. D. A man standing in an elevator that is going up at normal speed. E. Ignore air resistance and choose all that apply.

A and B A is not a freely falling observer because gravity is not acting. D and E are not freely falling because the man is standing in the elevator so he is being supported against gravity by the normal force exerted by the floor of the elevator. Both B and C are freely falling observers if air resistance is negligible. B is a freely falling observer because orbit corresponds to falling with gravity at just the right rate to maintain circular (or elliptical) motion.

Which of the following are statements of one of Newton's laws of motion? A. For any force, there is always an equal and opposite reaction force. B. The square of an object's orbital period is proportional to the cube of the object's semi-major axis. C. An object moves with constant velocity if no net force is acting upon it. D. The acceleration of an object is inversely proportional to the net force acting upon it. E. The energy of an object is conserved. Choose all that apply.

A and C Both a and c express ideas that are restatements of Newton's laws of motion. Statement b deals with Newton's law of gravitation -- not motion. Statement d is close to one of Newton's laws, but states the wrong relation: acceleration is proportional to the net force -- not inversely proportional. Newton's law to not explicitly address energy conservation.

You start at point A and drive N at 60 mph for 1 hour, then E at 30 mph for 2 hours, and finally S at 60 mph for 1 hour, arriving at point B. What is your average velocity? A. 15 mph east B. 45 mph C. 45 mph east D. 45 mph west E. -15 mph west

A and E

You and Cooper are each next to each other in spaceships freely floating in empty space. Your rockets fire, causing you to accelerate, while Cooper's do not. You both perceive the other moving away with an increasing speed. Assuming your spaceship's artificial intelligence started the rockets without your knowledge, how can you tell that it is you who are accelerating and not Cooper? A. You cannot tell. The situation is symmetric because there is no preferred frame. B. You are pulled down towards the bottom of your spaceship while Cooper is not. C. Cooper is pulled down towards the bottom of his spaceship while you are not. D. You can see your clock running slower.

B

the Corner broadcasts close 100 MHz (106.1) on your radio dial. What's the wavelength of these radio waves? A. 30 cm B. 3 m C. 30 m D. 300 m E. 3 km

B

When it was first developed, what known anomaly could the theory of general relativity explain that Newtonian gravity could not? A. A displacement in angular position of background stars when observed close to the Sun. B. The observed rate of increase in distance between the Earth and the Moon. C. The rate of precession of the perihelion of Mercury. D. The variation in the speed of light with direction relative to Earth's motion.

C A, B, and C all represent tests of general relativity, but only C was a known issue when Einstein started working on relativity. A was a prediction of the theory that was later confirmed and the precise measurement of the distance between Earth and Moon didn't occur until after the Apollo missions. So C is the correct answer.

Special relativity tells us that A. Different observers must agree on the order in which all events occur. B. Different observers must always agree on the order in which all events happen, but can disagree on whether they happen at the exact same time. C. Different observers must agree on the order events happen if the events occur in the same location. D. Different observers can disagree on the order of events even when the events are causally connected.

C Observers must always agree on the order of events that are causally connected. This is always applicable to events that occur at the same location and sometimes true of events that occur at different locations but are sufficiently close together in time. However, observers do not need to agree on the order of events that are not causally connected. This means that c is true but a, b and d are not true.

Consider two observers. Sebastian is traveling in a spaceship at ½ the speed of light. Belle is travelling in another spaceship moving perpendicular to Sebastian's at ¼ the speed of light. What do Belle and Sebastian perceive about each other's clocks? A. Both perceive each other's clocks to agree because they are moving perpendicular to each other. B. Belle thinks that Sebastian's clock runs fast. C. Sebastian thinks that Belle's clock runs fast. D. Sebastian thinks that Belle's clock runs slow. E. Belle thinks that Sebastian's clock runs slow. Select all that apply.

D and E Both perceive the other to be moving relative to their frame of reference. Hence both perceive the other's clock to run slow. This conclusion is independent of the orientation of their velocities.

Grass looks green because A. it emits green light and absorbs other colors. B. it absorbs green light and emits other colors. C. it reflects green light and absorbs other colors. D. it transmits green light and emits other colors.

C Grass emits its own light, but only in the infrared where we can see it. The light we do see is the reflected light. Grass appears green because it predominantly reflects green light.

From which objects' surface would the gravitational redshift of light be largest for an observer very far away? A. The Earth with M=6 x 1024 kg and R=6400 km B. The Sun with M=2 x 1030 kg and R=7 x 105 km C. A white dwarf star with M=2 x 1030 kg and R=6400 km D. A red giant star with M= 2 x 1030 and R=3 x 108 km

C The gravitational redshift goes like GM/(r c2). Since G and c are constants this means that redshift is proportional to M/r. The mass is the same for B, C, and D, so the object with the largest redshift is the one with the smallest radius, which is the white dwarf. Since the white dwarf star and the Earth have the same radius, but the white dwarfs mass is nearly a million times larger, it must have the largest redshift. So the answer is C.

You and a highway patrolman are driving at constant speeds in opposite directions on a straight highway. The patrolman is driving at 60 mph and his radar gun determines your relative speed (the magnitude of the difference between your velocities) to be 135 mph. What is your speed at the time of measurement? A. 60 mph B. 135 mph C. 75 mph D. 185 mph

C The magnitude of the difference between your velocities is 135 mph, but you are traveling in opposite directions so this corresponds to -135 mph relative to the patrolman's direction of travel. Adding -135 mph to 60 mph gives -75 mph. The fact that this is negative makes sense because you are traveling in the opposite direction. Your speed is the magnitude of this velocity or 75 mph.

Which of the following motivated Kepler to develop his laws of planetary motion? A. He wanted to show that Brahe's measurements were incorrect. B. He wanted to prove that Copernicus was wrong about the Sun being the center of the solar system. C. He believed that the motion of heavenly bodies should obey simple mathematical laws. D. He wanted to prove that Newton's law of universal gravity was correct.

C Kepler did believe that heavenly bodies should obey simple relations so c is correct. Kepler may have wanted to disprove Brahe's model, but he knew that Brahe's measurements were the most accurate and precise available and used them to derive his laws. Kepler favored the heliocentric model so he agreed with Copernicus. Newton was not yet living when Kepler formulated his laws.

Which object has the most kinetic energy? A. a 4-ton truck moving 50 km/hr B. a 3-ton truck moving 70 km/hr C. a 2-ton truck moving 90 km/hr D. a 1-ton truck moving 110 km/hr E. A, B, C, and D all have the same energy

C We need to use the KE=0.5 M v2 formula to evaluate the options. In this case, it is not necessary to change units because all examples are given with the same units. 4 * 502 = 10000, 3 * 702​ = 14700, 2 * 902​ = 16200, 1 * 1102​ = 12100. Since 16200, is largest, the answer is c.

How do we reconcile the driver and door operator's different conclusions about fitting? A. We can't reconcile them. Relativity is just strange. B. The driver's view is correct and the door operator's perception is an illusion C. The door operator's view is correct and the driver's perception is an illusion D. The driver and door operator disagree about whether the doors were shut simultaneously

D

If an astronaut landed on a planet that had twice the radius and twice the mass of the Earth, how would the gravitational force experienced by that astronaut compare to the force on Earth? A. it would be the same B. it would be higher by a factor of two C. it would be higher by a factor of four D. it would be lower by a factor of two E. it would be lower by a factor of four

D

Michell envisioned a scenario where light starts moving out, slows due to gravity and then falls back. Is this feasible? Why or why not? A. Yes. Photons are particles so gravity can slow them down. B. No. Light is a wave so gravity cannot affect it. C. Yes. Light is a wave so gravity can affect it. D. No. Photons always travel at the speed of light and cannot be slowed down by gravity.

D

Now consider the path of light in an elevator that is being accelerated upward. How will this look to the observer? A. straight line pointing upward B. straight line pointing downward C. curved path curving upward D. curved path curving downward

D

Now imagine a spaceship travelling at V = 0.5 c launches a space torpedo with velocity v = 0.9c relative to the spacecraft's motion at another space ship which is sitting still. What is the velocity with which the space torpedo approaches its target from the point of view of the target spacecraft's observers. A. 1.4 c B. greater than c, but not as high as 1.4 c C. c D. less than c E. scenario is not possible because the spacecraft can only launch with v

D

What about accelerating frames? If you are in an accelerating frame, what do you think you would see for time dilation of observers moving relative to you based on what we inferred for gravity? A. You would see no time dilation because special relativity does not apply B. The equivalence principle suggests you should see moving clocks runs slow but never fast C. The equivalence principle suggests you should see moving clocks runs fast but never slow D. The equivalence principle suggests you should see moving clocks runs slow or fast

D

What makes the concept of a four dimensional spacetime useful for understanding relativity? A. One can treat transformations between the coordinate systems carried by different observers as analogous to rotations of coordinate systems in three dimensional space. B. The theory of general relativity treats gravity as arising from spacetime curvature. C. Observers do not have to agree on the properties of space alone or properties of time alone, but they do have to agree on the properties of spacetime. D. All of the above E. Only A and C.

D

Why is a rose red? A. the rose absorbs red light B. the rose transmits red light C. the rose emits red light D. the rose scatters red light E. all of the above

D

If you have a 75 watt light bulb, how much energy does it use each minute? A. 75 joules B. 450 joules C. 4500 watts D. 4500 joules E. 450 watts

D A minute corresponds to 60s and a watt is a joule/second so we need to multiply 60s by 75 watts to obtain 4500 joules. Remember that joules is the unit of energy -- not watts which measures energy per unit time (or power).

Rose and Dimitri are traveling on trains passing each other in exactly opposite directions, both travelling at constant velocity. Which of the following is true? A. Rose and Dimitri agree on the length of her traincar along the direction of travel. B. Rose and Dimitri agree on the time between events. C. Rose and Dimitri agree on which events are simultaneous. D. Rose and Dimitri agree on the width of her traincar perpendicular to direction of travel.

D A, B, and C are all observer dependent quantities in special relativity. In contrast, length contraction only applies for lengths along the direction of travel. Lengths perpendicular to the direction of motion are measured to be the same by two observers.

The acceleration of gravity on Earth is approximately 10 m/s2 (9.8 m/s2). If you drop a bowling ball off a cliff, how fast will it be falling after 4 seconds? A. 400 m/s2 B. 400 m/s C. 40 m/s2 D. 40 m/s E. 4 m/s F. 4 m/s2

D Acceleration is the rate of change is velocity. So assuming the rock starts from rest (you drop it), we have vf = a t = (10 m/s2) ( 4 s) = 40 m/s so the answer is d. Pay attention to units.

Can a particle that has mass (equal to m) ever reach the speed of light? A. Yes. You just need to give it an amount of energy equal to mc2. B. Yes, but it will require a much larger amount of energy than mc2. C. No, because a massive particle travelling at the speed of light would have energy equal to 0.5mc2 which is more than its rest mass energy. D. No, because a massive particle travelling at the speed of light would have infinite energy and would therefore require an infinite amount of energy to accelerate.

D Answer D is correct. As v gets closer to c, the g factor continues to increase, eventually becoming infinite at v=c. Since energy is proportional to g, it also must be infinite. Hence infinite energy must be provided to the particle, but we believe the energy of the universe must be bounded (less than infinity).

A leading candidate for dark matter are weakly interactive massive particles (WIMPs) -- the idea that our galaxy is filled with such particles which are difficult to detect but have mass and contribute to the galaxy's gravity. One way of detecting these particles is via their interaction with Xenon. Where do scientists place such experiments? A. On satellites orbiting the Earth. B. On top of mountains. C. At sea level. D. In mines deep below the Earth's surface.

D As discussed in this week's blog reading, the experiments for liquid Xenon are done in mines deep below the Earth. They are placed deep below the Earth to eliminate other particles (for example cosmic rays) that might also interact with the Xenon but will be absorbed at the Earth's surface.

A neutron star is a very dense type of star. The gravitational fields at the surface of a neutron star are almost a trillion times larger than on Earth. How would yellow light emitted from the surface of the neutron star appear to an observer very far from the star. A. It would experience a small blueshift. B. It would experience a large blueshift. C. It would experience a small redshift. D. It would experience a large redshift. E. It would be observerd at the same wavelength of yellow light as it was emitted.

D Light deep in a gravitational potential appears to be redshifted to an observer who is farther out in the potential. Since the gravity of a neutron star is very large, the redshift is very large so D is the correct answer.

If you are travelling at a large fraction of the speed of light (v = 0.99c) down a city street and facing forward in the direction in which you are moving, what would you see? A. Nothing abnormal, but everyone would seem to move really slowly. B. Buildings would be shorter along the direction of motion, but would otherwise look normal. C. The shapes of buildings would be distorted and colors would be unchanged. D. The shapes of buildings would be distorted and the colors would be redshifted. E. The shapes of buildings would be distorted and the colors would be blueshifted.

E Due an effect called relativistic aberration, the appearance of objects is significantly distorted as speeds close to the speed of light. Furthermore, since objects appear to be coming toward you at large velocity, they are relativistically Doppler shifted towards short wavelengths (i.e. blueshifted).

An evil physicist decides she wants to blow up the Earth by detonating an antimatter bomb in the center of the planet. She estimates that this will take about 2 x 1032 Joules (the gravitational binding energy of the Earth). Since only half the of the bomb needs to be anti-matter (the other half can just be normal matter at the center of the Earth), how much anti-matter does she need to create for her bomb. (One metric ton = 1000 kg.) A. one metric ton B. one thousand metric tons C. one million metric tons D. one billion metric tons E. one trillion metric tons

E We know that E=mc2 so we need to solve for m = E/c2=(2 x 1032 J)/(3 x 108 m/s)2 = 2 x 1015 kg = 2 x 1012 metric tons but we divide by 2 since only half needs to be antimatter. 1012 corresponds to one trillion so E is correct. This is a very large amount of antimatter.

Among these five pairs of objects, rank them from weakest to strongest gravitational force assuming the same distance separating each pair. (Remember to set the < signs when doing the ranking.) -asteroid - asteroid -Sun - asteroid -Earth - asteroid -asteroid - astronaut -Moon - asteroid

asteroid - astronaut < asteroid - asteroid < Moon - asteroid < Earth - asteroid < Sun - asteroid Since the problem does not say anything about distance, you are free to assume that they are all at the same location. Otherwise, there would be no way to answer the problem. Then, the force is simply equal to the product of the masses. Since one of the masses (asteroid) is the same for all choices, you simply need to order them by the mass of the second object, from smallest to largest.

Rank the following parts of the electromagnetic spectrum for shortest wavelength to longest wavelength. -gamma rays -infrared -visible light -radio -ultraviolet -X-rays

gamma rays < X-rays < ultraviolet < visible light < infrared < radio

Match the physical situations with the type of light and matter interaction.

-white light hits a white piece of paper - scattering -visible light meets clear glass - transmission -blue light hits a red sweatshirt - absorption -light is is produced by a computer screen - emission

How do we make the escape velocity from an object very larger? A. We give it a larger mass and a smaller radius B. We give it a larger mass and a larger radius C. We give it a smaller mass and a smaller radius D. We give it a smaller mass and a larger radius

A

Many astrophysical objects have material falling onto them. Which of the following must be true? A. The material loses gravitational potential energy so this energy can be released in other forms B. The material gains gravitational potential energy so this energy can be released in other forms C. The material loses gravitational potential energy so this energy must be provided for the material to fall in D. The material gains gravitational potential energy so this energy must be provided for the material to fall in

A

Special relativity suggests that both twins see the other age more slowly during the non-accelerating parts of the trip. What happens when Mary-Kate accelerates at the star? (Note that when Mary-Kate turns around, her acceleration points towards Ashley.) A. Mary-Kate thinks Ashley ages more quickly. Ashley thinks Mary-Kate ages more slowly B. Mary-Kate thinks Ashley ages more slowly. Ashley thinks Mary-Kate ages more quickly C. Both think the other ages more quickly. D. Both thin the other ages more slowly.

A

The Earth orbits the Sun with a mean orbital speed of about 30 km/s. If we approximate Earth's orbit as a circle, what is the acceleration required to keep Earth in orbit around the Sun? A. 6×10^−3m/s2 B. 6×10^−9m/s2 C. 6×10^−3m/s D. 6×10^−9m/s

A

When Mary-Kate is turning around at the destination star what direction is her acceleration pointing when she is (1) slowing down towards the star (2) speeding up for her return to Earth? A. (1) toward Earth; (2) toward Earth B. (1) toward Earth; (2) away from Earth C. (1) away from Earth; (2) toward Earth D. (1) away from Earth; (2) away from Earth

A

Why is Newton's version of Kepler's thrid law so useful to astronomers? A. It tells us that all planetary orbits are elliptical B. It allows us to calculate distances to objects C. It allows us to calculate masses of distant objects D. It allows us to calculate the rotation rates of stars

C

Gravity's effect on light is best described by which of the following statements? A. Gravity bends the path of light just like it bends the path of a massive object. B. Gravity has no effect on the path of light because light is made up of massless particles (photons). C. General relativity predicts that gravity could bend light but the effect is too small to yet measure so it is only hypothetical. D. The bending of light by gravity is forbidden because the speed of light is constant.

A A is the only correct statement. Light is bent by gravity and the effect is quite easy to observer with modern astronomical instrumentation. Light from distant galaxies is frequently bent by galaxies along our line of sight to these background galaxies.

In relativity, two observers share the same frame of reference only if A. they are not moving relative to each other. B. they are both located in the same place and are stationary. C. they agree on the laws of nature. D. they are both located in the same place regardless of motion. E. they are both located in the same place and are traveling at the same speed.

A As discussed in lecture 7, reference frames are defined in terms of relative motion. The position of an observer plays no role in defining the frame. Observers have the same reference frame if and only if they have the same velocity.

In 2018, NASA's Solar Probe Plus is expected become the fastest man made object ever, reaching velocities of 200 km/s. By what factor γ will clocks seem to run slow at this velocity? A. 1.0000002 B. 1.0003 C. 1.02 D. 2.1 E. 3.5

A Clocks run slow by the Lorentz factor γ. To compute γ, we first compute v/c = (200 km/s)/(300,000 km/s) = 0.00067. Then we use the formula γ = 1/sqrt(1-(v/c)2) to find γ = 1.0000002. Remember, time dilation only becomes large when velocities get very close to the speed of light.

Rank these people by their gravitational potential energy relative to Earth from lowest to highest. (Remember to set the < signs when doing the ranking.) -A woman flying in an airplane -A woman standing on the ground a sea level -A woman in deep space, far from Earth -A woman in low Earth orbit

A woman standing on the ground a sea level < A woman flying in an airplane < A woman in low Earth orbit < A woman in deep space, far from Earth We could use the formulat PE = -GMm/r. Since r is the only thing changing, we can see that potential energy will increase (become less negative) as r increases. Or we make an analogy with the roller coaster, where the furthe from the Earth (higher), the more gravitational potential energy that you have. So, the correct order is: woman at sea level, woman in airplane, woman in low Earth orbit, and woman in deep space far from Earth.

Einstein's Field Equations state that the source of spacetime curvature can include: A. mass B. pressure C. electric fields D. magnetic fields Choose all that apply.

A, B, C, and D Mass and energy are closely related in special relativity. General relativity extends this relationship so that almost any type of energy can act as a source gravity. Since all of the above are associated with energy, they all act as a source of gravity. Since gravity is caused by spacetime curvature in GR, they are all sources of spacetime curvature.

Why do you suppose this equation (Kepler's 3rd law) is so useful to modern day astronomers? (Choose the best answer.) A. it allows us to constrain the orbital period of distant objects B. it allows us to compute the value of G C. it allows us to constrain the mass of distant objects D. it allows us to constrain the orbital semi-major axis of distant objects E. it allows us to prove the Sun is at the center of the solar system

C

Choose all of the following items that are accelerating. A. A car moving on a curved road at a steady 50 km/hr B. A car moving on a straight road at a steady 100 km/hr C. A golf ball at the peak of its flight through the air D. A rock falling off a cliff

A, C, and D

In 1905, Albert Einstein published papers describing which of the following phenomenon? A. theory of special relativity B. theory of general relativity C. the photoelectric effect D. proof of the wave nature of light E. theory of the random motion of particles Select all that apply.

A, C, and E The wave nature of light had long been demonstrated. Einstein did not publish work on the theory of general relativity until several years later.

An absorption line occurs at 100 nm when measured in the lab at Earth. If a star is moving towards Earth at 1% of the speed of light, what is the observed wavelength of this absorption line in the star's spectrum? A. 1 nm B. 99 nm C. 100 nm D. 101 nm E. 1000 nm

B

Consider an object moving in a circle with constant speed. The acceleration of this object is: A. zero B. constant in magnitude only C. constant in direction only D. constant in direction and magnitude E. neither constant in magnitude nor direction

B

In analogy with with the rocket, climbing out of the gravitational potential, what do you think happens to light? If I shine a laser up to the sky, what happens to the photons in that laser? A. nothing, since gravity does not affect light B. the light has to lose energy so its frequency decreases C. the light has to lose energy so its frequency increases D. the light has to gain energy so its frequency decreases E. the light has to gain energy so its frequency increases

B

In the late 1800's, most physicists believed that light travelled through a hypothetical medium called the aether because A. they thought the speed of light was much smaller than it actually is. B. they believed light was a wave and all other examples of waves travelled through some medium. C. Michelson and Morley had incorrectly claimed that they had measured the variation of light's velocity relative to the aether. D. Newton had incorrectly postulated the existence of the aether and everyone assumed Newton was correct because of his success explaining the laws of motion and gravity.

B

Now, assume your spaceship's artificial intelligence locked you in the ship and cutoff your view of the outside world. Your only way to tell where you are is by the forces you feel on yourself. Since you seem to be floating freely in your spacecraft, can you safely assume gravity isn't pulling on you? A. yes, you are floating so there is no gravitational force B. no, the same would be true if gravity was pulling you and the spacecraft isn't firing its rockets

B

The acceleration due to gravity at the Earth's surface is approximately constant and the same for all objects. What does this imply about the gravitational force? The gravitational force on an object is: A. independent of its mass B. larger for a more massive object C. smaller for a more massive object D. zero

B

The mass of a free neutron is slightly larger than the mass of a free proton. Reactions can occur that convert a neutron into a proton. Which of the following must be true? A. These reactions require energy to happen B. These reactions release energy when they occur C. No energy is required for these reactions to occur, nor is energy released

B

Think about a triangle on the surface of a sphere. What is the sum of the angles? A. 180o B. greater than 180o C. less than 180o

B

What does this imply about gravity's effect on light? A. Nothing. Light is not a particle so gravity cannot affect it. B. The equivalence principle suggests that gravity should bend light just like an accelerating frame does. C. The equivalence principle suggests that gravity should not bend light since light travels on a straight path in an inertial frame.

B

Which skier has larger kinetic energy? A 60 kg woman traveling at 30 m/s or a 90 kg man going at 24m/s? A. Man B. Woman C. Identical

B

Why was it important that the apparatus in the Michelson and Morely experiment could rotate? A. Rotation allowed them to compensate for the Earth's rotation B. They were looking for a change in the signal as the paths from the mirrors to the beam splitter change orientation relative to the Earth's motion through the aether. C. They needed rotation to change the path lengths between the mirrors and the beam splitter. D. Rotation was required because the detector needed to be rotating relative to the beam splitter.

B

What is the longest straight line ocean voyage one can take without hitting land? A. Australia to Argentina B. Eastern United States to Antarctica C. Eastern Russia to Pakistan D. Western United States to Australia E. Madagascar to Chile

C

Why are some physicists still searching for theories of gravity that are alternatives to general relativity? A. There are small but significant discrepancies between existing tests of general relativity and the predictions of the theory. B. The observed acceleration of the universe is not consistent with the predictions of general relativity unless we invoke the existence of some unknown "dark energy". C. The theory of general relativity can explain existing tests but is not mathematically self-consistent. D. Observations of the motion of galaxies in clusters of galaxies indicate that gravity is much weaker than expected given the amount of mass that is observed in these galaxies.

B A is incorrect because general relativity is consistent with all existing precision tests. C is incorrect because the theory is mathematically self-consistent. D sounds sort of like the evidence for dark matter, but remember that the gravitational force appears to be stronger than expected from the observed matter, driving the need for additional dark matter. B is correct because the universe is observed to be accelerating and this is inconsistent with general relativity unless we posit the existence of some very strange unknown field that physicists call dark energy. This leads some physicists to consider alternative theories of gravity.

Why do astronomers want to build the Thirty Meter Telescope on the summit of Mauna Kea? A. It is one of the best sites in the southern hemisphere for astronomical observing B. It is one of the best sites in the northern hemisphere for astronomical observing C. It is the best site other than the Canary Islands but they can't build it in the Canary Islands due to local opposition there. D. It is the best site other than Chile but they can't build it in the Chile due to local opposition there.

B B is correct because Mauna Kea is one of the best sites in the Northern (not Southern) Hemisphere and possibly the absolute best. Any other potentially comparable sites are too undeveloped or remote to utilize at this time. Many sites in Chile are actually better than Hawaii, but Europe is already building the ELT in Chile and astronomers would prefer to have large telescopes in both the northern and southern hemisphere. There is not significant opposition to building new telescopes in Chile.

Which of the following does special relativity say inertial observers must agree on? A. the order of events at different locations. B. the observer's relative speed C. the observer's lengths D. the time between events

B In special relativity, observers must agree on their relative speed. All of the other quantities listed are dependent on the observer's reference frame.

Mary-Kate is an astronaut who leaves Earth to travel at a large fraction of the speed of light to a nearby star and then returns to Earth. During the trip, 25 years pass for her twin Ashley on Earth, but Mary-Kate is only 4 years older upon her return. How can this aging difference be reconciled with the concept that different inertial observers in relative motion each perceive the other observer's clock to run slow? A. It cannot be reconciled. This scenario is not allowed by special relativity. B. Special relativity does not apply because Mary-Kate is not an inertial observer during this trip. C. Special relativity only says that inertial observers in relative motion perceive each other's clocks to run slow. It does not require their clocks to run slowly by the same amount. D. Special relativity does not apply when the velocities are close to the speed of light.

B Special relativity only applies to observers in inertial reference frames. Mary-Kate experiences large accelerations during her trip: first when she leaves Earth, then when she arrives at her destination, again when she leaves her destination, and then finally when she returns to Earth. These accelerations mean that she is not an inertial observer and account for the difference between her and Ashley.

Mary-Kate is an astronaut who leaves Earth to travel at a large fraction of the speed of light to a nearby star and then returns to Earth. During the trip, 25 years pass for her twin Ashley on Earth, but Mary-Kate is only 4 years older upon her return. How can this aging difference be reconciled with the concept that different inertial observers in relative motion each perceive the other observer's time to run slow? A. It cannot be reconciled. This scenario is not allowed by special relativity. B. Special relativity does not apply because Mary-Kate is not an inertial observer during this trip. C. Special relativity only says that inertial observers in relative motion perceive each other's clocks to run slow. It does not require their clocks to run slowly by the same amount. D. Special relativity does not apply when the velocities are close to the speed of light.

B Special relativity only applies to observers in inertial reference frames. Mary-Kate experiences large accelerations during her trip: first when she leaves Earth, then when she arrives at her destination, again when she leaves her destination, and then finally when she returns to Earth. These accelerations mean that she is not an inertial observer and account for the difference between her and Ashley.

Assume Jupiter's orbit is circular (a good approximation). If Jupiters orbital speed is 13 km/s and its orbital radius is 7.78×1011m, what is Jupiter's orbital acceleration? A. 1.67×10−8m/s2 B. 2.17×10−4m/s2 C. 2.17×10−2m/s2 D. 1.67×10−4m/s2

B We compute the acceleration using the formula for circular motion a = v2/r. To get consistent units we need to convert km/s to m/s. Since there are 1000 m in a km, we have 13 km/s = 13,000 m/s. Then we can compute a = (1.3 x 104 m/s)2/(7.78 x 1011)=2.17 x 10-4 m/s2.

You start at point A and drive N at 60 mph for 1 hour, then E at 30 mph for 2 hours, and finally S at 60 mph for 1 hour, arriving at point B. What is your average speed? A. 15 mph B. 30 mph C. 45 mph D. 60 mph E. not enough information

C

About how long would the Sun last if it was burning gasoline (and thus made entirely of gasoline)? A. fraction of a second B. 10 minutes C. 10 thousand years D. 10 million years E. more than 10 billiion years

C

From the muons' perspective (or an observer travelling at the same speed as the muons), why can so many muons decay before reaching the ground? A. Time runs slow for the muons because they are traveling close to the speed of light. B. Time runs normal for the muons in their own frame so most of the muons actually do decay before reaching the ground (from their perspective). C. Neither A nor B is correct.

C

Han and Greedo are two individuals in a galaxy far, far away who have shot at each other, with Han killing Greedo. Most eye witnesses claim Han shot first. But, one witness named George says Greedo shot first. Knowing nothing else about the circumstances, could both George and the other eyewitnesses be right? A. No, Han definitely shot first B. No, Greedo definitely shot first C. Yes, the answer could depend on George's velocity relative to the other eyewitnesses. D. Yes, the answer could depend on George's position relative to the other eyewitnesses.

C

If gravity causes the redshift of light moving to higher gravitational potential, what does this imply about time dilation effects? A. nothing since they are unrelated B. clocks higher in a gravitational potential run slower than clocks deeper in a gravitational potential C. clocks deeper in a gravitational potential run slower than clocks higher in a gravitational potential D. it requires clocks to keep the same time regardless of whether they are higher or lower in the gravitational potential

C

If muons are produced with v/c = 0.992 what is the corresponding Lorentz factor γ? This is the factor by which their clock "runs slow" from the perspective of an observer on the ground. A. 1 B. 3 C. 8 D. 100 E. 1000

C

If the spaceship is travelling with velocity V and instead fires a laser with v = c what is v', the velocity of the laser as perceived by the stationary target? A. V+ c B. V/ (1 + v/c) C. c D. (V+ c) / c E. (V+ c) / (1 + c)

C

Imagine you build a giant spherical shell and cover the inside with perfectly reflecting mirrors. You then continuously shine light inside the shell so that a huge number of photons build up inside. Does the presence of the photons in the shell increase the gravitational force you feel outside the shell? A. yes, it is proportional to the total mass of the photons B. no, because the photons have no mass C. yes, because photons have energy D. no, because the photons have no rest mass energy

C

What are orbits like far from a black hole (1000s of times RS or larger)? A. Orbits are unstable and you would fall into the black hole after a few orbital periods. B. Orbits are identical to Newtonian orbits. C. Orbits are similar to Newtonian orbits with only small differences. D. Orbits are similar to Newtonian orbits with only small differences, but only circular orbits are stable.

C

What are the constraints on the worldline of a massive object? A. there are no constraints on the worldline B. the worldline must be straight C. the worldline must always point between vertical and 45 degrees D. the worldline must always point between horizontal and 45 degrees

C

Given that we observe stars from the surface of the Earth, do we observe stars to appear exactly the same as an observer freely floating out in deep space would? A. Yes. There is nothing special about our place in the universe. B. No. Since we are on the Earth's surface, the light from distant stars is redshifted by a very small amount by the time it reaches us. C. No. Since we are on the Earth's surface, the light from distant stars is blueshifted by a very small amount by the time it reaches us. D. Yes. The light could be blueshifted or redshifted, but the equivalence principles says it is by the same amount for us as the observer out in space.

C All light coming towards Earth from very far away experiences a very small blueshift. In contrast, radiation coming from the surface of the Earth appears redshifted to observers far from Earth. D is incorrect because a freely floating observer in space is not equivalent to a static observer in a gravitational field on Earth.

Tina and Amy are astronauts headed on an interstellar mission to Proxima B. To escape the pull of the Sun's gravity, they are accelerating in their spacecraft at a constant rate. Amy is stationed at the front of the rocket while Tina is near the back. How does Tina's atomic clock compare to Amy's atomic clock? A. Both clocks must agree because they are travelling with the same velocity. B. Tina's clock appears to run faster than Amy's clock because it is accelerating in the direction of Amy's clock. C. Amy's clock appears to run faster than Tina's clock because it is accelerating in the direction away from of Tina's clock. D. Both clocks seem to run slow.

C C is correct. Remember that being in an accelerating frame is equivalent to being in a gravitational field, with being closer to the front of the spacecraft being analogous to being higher in the gravitational potential and being near the back like being deeper in the gravitational potential. Hence Tina's clock runs slower than Amy's clock. See lecture 14 and the pdf notes on collab for more discussion.

How is peer review used by scientists? A. Peer review is used to determined whether articles reporting research results should be published in scientific journals. B. Peer review is used to prioritize which research proposals should receive federal funding. C. Both A and B. D. Neither A nor B.

C Peer review is used by scientists in two primary ways. To determine whether articles reporting scientific results should be published in scientific journals and to prioritize which research proposals should be given federal funding.

Which of the following examples describes a situation where a car is experiencing a net force? A. The car is moving at constant velocity. B. The car is stopped on a hill. C. The car is making a gradual turn. D. The car is stopped on a level pavement.

C Remember an object has a net force when the sum of all forces acting on it down cancel. Newton's first law says that any object experiencing a net force has an acceleration so we can identify cases that are accelerating. Cases a, b, and d are not experiencing an acceleration so they do not have a net force. In c there is an acceleration so there is a net force.

The equivalence principle implies that: A. Freely falling in a gravitational field is equivalent to being accelerated in a rocket. B. Being static in a gravitational field is equivalent to floating freely in space where gravity is negligible. C. Freely falling in a gravitational field is equivalent to floating freely in space where gravity is negligible. D. Energy is equivalent to mass times the speed of light squared.

C The equivalence principle is a statement about the relationship between freely falling frames and frames where acceleration is zero. It says that an observer who is freely falling in a gravitational field doesn't "feel" her own gravity. She would experience weightlessness just as if she were floating in space without any acceleration. A good example of this is an astronaut in orbit around the Earth.

A baseball player hits a baseball so that it travels 50 mph relative to the ground in the same direction as moving train travelling 45 mph. What is the speed of the baseball as perceived by an observer on the train? A. 50 mph B. 95 mph C. 45 mph D. 5 mph E. 0 mph

D

Brand watches Cooper fall into a "frozen star" from very far away. What best describes what Brand sees with her eyes as Cooper approaches r = RS? A. Cooper appears to be slightly bluer and his time appears to run somewhat slow but never stops. B. Cooper appears to be slightly redder and his time appears to run somewhat slow but never stops. C. Cooper appears to be slightly redder and his time appears to stop when he reaches r = RS. D. Cooper's time runs slower and slower while he reddens and gradually disappears right before reaching r = RS. E. Cooper falls in quickly and abruptly disappears when he reaches r = RS.

D

Rick and Ilsa are travelling rockets heading in opposite directions. As they fly by each other, they exert very small forces on each other to measure each other's mass and then compare these to measurements that were made when they were not moving relative to each other. (Since the forces are small, you can ignore non-inertial effects caused by their acceleration.) Which of the following are true? A. Rick thinks Ilsa's mass increased but she thinks his decreased when moving. B. Ilsa thinks Rick's mass increased but he thinks hers decreased when moving. C. Both find that the other's mass stayed the same when moving. D. Both think that the other's mass increased when moving. E. Both think that the other's mass decreased when moving.

D By now, it should be clear that special relativistic effects are symmetric so both observers see the same effect. Hence, neither A nor B could be correct. As discussed in lecture, moving masses increase relative to non-moving masses so D is correct.

A skinny physicist has been hitting the gym and lifting weights to try to increase his mass but he just can't manage to gain any. Knowing a little relativity, he decides to measure his mass in a spaceship travelling very close the speed of light. Does he see his mass increase? A. Yes. The mass of moving objects increases. B. No. The mass of objects is independent of their motion. C. No. The mass of moving objects decreases. D. No. From his standpoint, he is not moving so he measures the same mass as always.

D It is true that the mass of a moving object increases, but only from the standpoint of an observer in relative motion. From the physicists own standpoint in the spacecraft, he is not moving and the rest of the universe is moving by him. Hence, he observes no increase in his own mass.

In general relativity, which of the following paths corresponds to a geodesic? A. The path followed by freely falling objects. B. The path followed by light. C. The path followed by planets in orbit around the Sun. D. All of the above. E. Only A and C.

D Light and freely falling objects both follow paths called geodesics. Since planets in orbit are freely falling (accelerating under gravity), they also follow geodesics. So all three statements are correct.

Cooper is an astronaut who leaves Earth to travel at a large fraction of the speed of light to a nearby star and then returns to Earth. During the trip, 76 years pass for Cooper's daughter, but Cooper is only a couple of years older upon his return. How can this aging difference be reconciled with the concept that different inertial observers in relative motion each perceive the other observer's clock to run slow? A. It cannot be reconciled. This scenario is not allowed by special relativity. B. Special relativity does not apply when the velocities are close to the speed of light. C. Special relativity only says that inertial observers in relative motion perceive each other's clocks to run slow. It does not require their clocks to run slowly by the same amount. D. Special relativity does not apply because Cooper is not an inertial observer during this trip.

D Special relativity only applies to observers in inertial reference frames. Cooper experiences large accelerations during his trip: first when he leaves Earth, then when he arrives at his destination, again when he leaves his destination, and then finally when he returns to Earth. These accelerations mean that he is not an inertial observer and account for the difference between him and his daughter.

The gravitational time dilation due to Earth's gravitational fields is best described as: A. A very small effect, which is so small that we cannot measure it. B. A very small effect, which we have only been able to measure in the last 10 years. C. A fairly large effect, but one which we do not notice because we don't move far from Earth's surface. D. A very small effect, but one that is essential to account for in the operation of the global positioning system (GPS).

D The gravitational time dilation effect at Earth's surface is small, but large enough that the clocks on orbiting satellites (that our far from Earth) must account for it if their clock are to stay synched with those on Earth's surface. Without correcting for relativity, GPS would be much less accurate because accurate clocks are need to measure light travel time from the satellite to the Earth's surface. So D is the correct answer.

A spaceship travels at speed V=0.5c relative to its target. The spaceship then launches a rocket at v=0.5c directly at its target. What is the speed of the rocket from the point of view of the target? A. 0.5 c B. c C. 1.25 c D. 0.8 c E. 0.667 c

D We solve this problem using the expression for the addition of velocities v' = (v+V)/(1+vV/c2). The numerator v+V=c. The denominator is 1+1/2*1/2 = 1+ ¼ = 5/4. Dividing numerator by denominator, we obtain 1 c/ (5/4) = 4/5 c = 0.8c.

Anna and Etienne are traveling on trains passing each other in opposite directions, both travelling at constant velocity. Which of the following are true? A. Anna thinks that Etienne's traincar is longer than Etienne does. B. Etienne thinks that Anna's traincar is longer than Anna does. C. Anna and Etienne both agree on the length of their respective traincars. D. Anna thinks that Etienne's traincar is shorter than Etienne does. E. Etienne thinks that Anna's traincar is shorter than Anna does. Choose all that apply.

D and E Length contraction means that we always perceive moving objects to be shorter in their direction of travel than an observer who is moving with the object. Since Etienne sees Anna's traincar moving, he must perceive it to be shorter than Anna, who moves with the car. Likewise, Anna sees Etienne's traincar moving, so she must perceive it to be shorter than Etienne who is moving along with the car. Hence D and E are both true but A, B, and C are all incorrect.

Rank the following US federal funding agencies from lowest to highest in terms of how much funding they provide for astronomy and astrophysics research. (Remember to set the < signs when doing the ranking.) -National Science Foundation -National Aeronautics and Space Administration -Department of Energy

Department of Energy < National Science Foundation < National Aeronautics and Space Administration

Consider two observers. Edward is on a train that is travelling at 40 mph and Bella is standing on the ground next to the train. What do Edward and Bella perceive about each other's clocks? (Assume that each has a good view of the other's clock.) A. Bella thinks thinks that Edward's clock is slow. Edward thinks that Bella's clock is fast. B. Edward thinks that Bella's clock is slow. Bella thinks that Edward's clock is fast. C. Both think that Bella's clock is slow and that Edward's clock is correct. D. Both think that Edward's clock is slow and that Bella's clock is correct. E. Both think that the other person's clock is slow

E

The most common frame we think about is the surface of the Earth. Is the surface of the Earth an intertial frame? A. yes, it is an inertial frame B. no, it is not an intertial frame because the Earth rotates C. no, it is not an inertial frame because the Earth orbits the Sun D. no, it is not an inertial frame because the solar system orbits the galactic center E. b, c, and d are all correct

E

What do physicists mean when they say that energy is conserved? A. Energy is not wasted. B. The energy of a closed system can go up or stay the same, but never decrease. C. The energy of a closed system can go down or stay the same, but never increase. D. The forms of energy in a closed system must remain the same. E. The forms of energy in a closed system can change, but the sum of all forms of energy must remain the same.

E

Based on Newton's law of universal gravitation, what is the acceleration due to gravity at the surface of the Earth in terms of Newton's constant G, the mass of the Earth ME, and the radius of the Earth RE

See notes

Based on the cartoon image of a roller coaster, answer the following questions.

The point of maximum potential energy is: - (a) The point where kinetic energy is increasing is - (b) The point of maximum kinetic energy is: - (c) Gravitational potential energy is largest and the maximum distance from the Earth (a in the picture). At point (b) the kinetic energy is increasing as potential energy is converted to kinetic energy. At point (c) kinetic energy is at a maximum.