Question 1

Your strange friend flies past you in a relativistic spacecraft holding a meterstick and a clock.The meterstick appears too _____ to you,and the clock appears _____ to you.

Accepted Answer

According to special relativity theory, as an object approaches the speed of light, its length appears shorter and time appears to slow down. This effect is known as time dilation and length contraction. Therefore, to the observer, the meterstick will appear shorter (length contraction) and the clock will appear to tick slower (time dilation). Choice A fits this description.

Question 2

Spaceship Julio passes spaceship Klara with a relative velocity of 0.8c.An astronaut aboard Julio finds that her heart is beating once every 0.0133 min (75 beats/min).The time between beats according to a sympathetic astronaut aboard Klara is

Accepted Answer

The answer of Spaceship Julio passes spaceship Klara with a...

Question 3

Our galaxy,the Milky Way,has a diameter of about 100 thousand light-years.How many years would it take a spacecraft to cross the galaxy if it could travel at 99% the speed of light?

Accepted Answer

The distance across the Milky Way, or its diameter, is given as 100,000 light-years. If a spacecraft could travel at 99% the speed of light (0.99c), we need to use the formula:

distance = (speed of light) x (time)

where distance is the diameter of the Milky Way and speed of light is 299,792,458 meters per second. Solving for time:

time = distance / (speed of light x 0.99)

time = 100,000 light-years / (299,792,458 m/s x 0.99)

time = 1.4 x 10^14 years

Using scientific notation, the answer is 1.4 x 10^14 (or 140,000,000,000,000) years. Therefore, the best choice is C.

Question 4

You observed that event A occurred before event B.Which of the following statements is false?

Accepted Answer

The answer of You observed that event A occurred before...

Question 5

A beam of unstable neutral pions is observed to travel on average 8 m before they decay.If their proper lifetime is 0.8 $\times$ 10^-8 s,then calculate how fast the beam is traveling.

Accepted Answer

The decay length $L$ in the lab frame is related to the proper lifetime $\tau_0$, the speed of the particle $v$, and the speed of light $c$ by the formula $L = v\gamma\tau_0$, where $\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$ is the Lorentz factor. Given $L = 8$ m and $\tau_0 = 0.8 \times 10^{-8}$ s, we can solve for $v$ by rearranging the formula to $v = \frac{L}{\gamma\tau_0}$. Since $L = v\tau$, where $\tau = \gamma\tau_0$ is the dilated lifetime, we find that $v = \frac{L}{\tau_0\gamma}$. Knowing that the pions travel 8 m before decaying and using the proper lifetime, we can infer that the speed must be such that the relativistic effects significantly increase the observed lifetime, allowing the pions to travel this distance. The correct speed that matches these conditions, given the options, is $0.96c$, which implies a significant relativistic time dilation allowing the pions to travel 8 m.

Question 6

Because the galaxies are moving away from us,the light they emit

Accepted Answer

This is known as redshift, which is caused by the Doppler effect. As an object moves away from an observer, the light waves are stretched out (wavelength is increased), causing the light to appear more reddish in color.

Question 7

An astronaut aboard a spacecraft enroute to Mars with a speed of 0.5c relative to Earth observes a meteor approaching head on at a speed of 0.9c.What is the speed of the meteor relative to Earth?

Accepted Answer

We can use the relativistic velocity addition formula to find the relative velocity of the meteor to Earth:

v = (v1 + v2) / (1 + v1*v2/c^2)

where v1 = 0.5c (velocity of the spacecraft relative to Earth) and v2 = -0.9c (velocity of the meteor relative to the spacecraft, with a negative sign indicating that it is approaching head-on). Plugging in the values, we get:

v = (0.5c - 0.9c) / (1 - 0.5c*(-0.9c)/c^2) = -0.73c

Therefore, the speed of the meteor relative to Earth is 0.73c, in the opposite direction to the spacecraft's motion.

Question 8

What is the difference in age between the mother and son after she returns back to Earth?

Accepted Answer

The mother was 30 years old when she left Earth, and her son was 10 years old. When she returned to Earth, her son was 37 years old. So the difference in age between the mother and son after she returned back to Earth is 37 - 30 = 7 years.

Question 9

Alpha Centauri is not only the closest star system to us (it is actually a triple star system)but it also seems to be an excellent place to look for extra-terrestrial life.It is about 4.3 light-years away from Earth.If an astronaut claims her journey there and back only took 6.3 years,then how fast was she traveling? (Assume she made a fast turnaround once she arrived there!)

Accepted Answer

The correct answer is D.The astronaut's journey there and back took 6.3 years. So, the time taken for the journey to Alpha Centauri is 6.3/2 = 3.15 years. The distance to Alpha Centauri is 4.3 light-years. So, the speed of the astronaut is 4.3/3.15 = 1.36 light-years per year. This is equivalent to 0.81c.

Question 10

A star system is 100 light-years away.If a spacecraft travels to the star system at 97% the speed of light then what is the ratio of the time for the journey measured by an observer left on Earth divided by the time measured by the astronaut?

Accepted Answer

4.1The time dilation effect described by Einstein's theory of relativity explains that time passes at different rates for observers in different inertial frames. For an observer on Earth, the spacecraft's journey appears to take slightly over 100 years because it's traveling close to the speed of light (100/0.97 ≈ 103.1 years). For the astronaut on the spacecraft, however, the journey's duration is significantly shorter due to time dilation. The time dilation factor (gamma) can be calculated using the formula γ = 1 / sqrt(1 - v^2/c^2), where v is the velocity of the spacecraft and c is the speed of light. Plugging in 0.97c for v gives γ ≈ 4.1, meaning the astronaut experiences time at a rate 4.1 times slower than the observer on Earth. Thus, the ratio of the time for the journey measured by an observer on Earth to the time measured by the astronaut is approximately 4.1.

Question 11

Two electrons are ejected in opposite directions from atoms in a sample of radioactive material.Each electron has a speed,as measured by a laboratory observer,of 0.6c.What is the speed of one electron as seen from the other electron?

Accepted Answer

According to the relativistic velocity addition formula, the velocity of one electron as seen from the other electron is:
v' = (v - u) / (1 - uv/c^2)
where v is the speed of one electron relative to the laboratory, u is the speed of the other electron relative to the laboratory, and c is the speed of light. 
Since the electrons are ejected in opposite directions, their relative speed in the laboratory frame is 2v = 1.2c. Thus, we have:
v' = (0.6c + (-0.6c)) / (1 - (0.6c)(-0.6c)/c^2) 
v' = 1.2c / (1 + 0.36)
v' = 0.882c
Therefore, the speed of one electron as seen from the other electron is 0.882c, which corresponds to choice B.

Question 12

What is the total distance traveled according to the biologist? Give your answer in light-years.

Accepted Answer

The total distance traveled is the sum of the distance from Earth to Proxima Centauri and back, plus the distance from Proxima Centauri to Barnard's Star and back.

According to the passage, the distance from Earth to Proxima Centauri is 4.24 light-years, and the distance from Proxima Centauri to Barnard's Star is 5.39 light-years.

So the total distance traveled is:

(4.24 + 4.24) + (5.39 + 5.39) = 18.26 light-years

Rounding to two decimal places, the answer is 4.39 light-years.

Question 13

Use the following scenario for the next three questions.
A 26-year-old biologist makes a trip to study alien life forms in a distant planet 10 light-years away.The round trip including a stay of 1 year in the distance planet takes 21.5 years according to the clock on earth.The biologist's son is 3-year-old when he left.Assume that the planet is not moving with respect to Earth,and the speed is the same for both outbound and inbound part of the journey.
-How fast is the spaceship traveling?

Accepted Answer

The answer of Use the following scenario for the next...

Question 14

At rest,pions have a proper lifetime of 26 ns.What is the speed of a beam of pions if their observed lifetime were measured to be 64 ns ? (This is a real experiment that has been performed and found to be consistent with Special Relativity.)

Accepted Answer

The answer of At rest,pions have a proper lifetime of...

Question 15

You measure the length of a passing Imperial Starcruiser spacecraft to be 100 m.If the Starcruiser is moving at 80% the speed of light,what would be its length if it was at rest relative to you?

Accepted Answer

The answer of You measure the length of a passing...

Question 16

The light emitted by an object traveling at high speed toward Earth would

Accepted Answer

This is known as the Doppler Effect where the light waves from a moving object appear shifted toward the blue end of the spectrum if the object is moving toward the observer, and shifted toward the red end if the object is moving away.

Question 17

You place two clocks that you consider to be synchronized on a road 100 m apart.Your friend drives by at speed V and observes the clocks to be out of sync by an amount T.When you place the clocks 200 m apart and your friend drives by at speed 2V,by what amount will your friend claim the clocks to be out of sync?

Accepted Answer

The time dilation formula is:$$T' = \frac{T}{\gamma}$$where:* $T'$ is the time interval measured in the moving frame* $T$ is the time interval measured in the stationary frame* $\gamma$ is the Lorentz factor, which is given by:$$\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}$$where:* $v$ is the speed of the moving object* $c$ is the speed of lightIn this problem, we are given that the clocks are 100 m apart and that your friend drives by at speed $V$. We are also told that your friend observes the clocks to be out of sync by an amount $T$. This means that:$$T' = T - \frac{100 m}{V}$$We are then asked to find the amount of time by which your friend will claim the clocks to be out of sync when the clocks are 200 m apart and your friend drives by at speed $2V$. This means that:$$T'' = T - \frac{200 m}{2V}$$Substituting the first equation into the second equation, we get:$$T'' = T - \frac{100 m}{V} - \frac{100 m}{2V}$$$$T'' = T - \frac{200 m}{2V}$$$$T'' = T - \frac{100 m}{V}$$Therefore, the amount of time by which your friend will claim the clocks to be out of sync when the clocks are 200 m apart and your friend drives by at speed $2V$ is $T$.

Question 18

A clock has a period of exactly 1 second when at rest.If you were to measure a period of 1.5 seconds for the same clock,how fast is it moving relative to you as a percentage of the speed of light?

Accepted Answer

The answer of A clock has a period of exactly...

Question 19

Spaceship Solange passes spaceship Hari with a relative velocity of 0.6c.An astronaut aboard Hari observes the length of Solange to be 30.5 m.The astronauts aboard Solange claim that the length of their spaceship is

Accepted Answer

The length contraction formula is L = L0 * sqrt(1 - v^2/c^2). Given L = 30.5 m and v = 0.6c, solving for L0 gives approximately 38.1 m.

Question 20

An earthbound radar monitors a spaceship moving at 0.9c that is being followed by a second ship moving at 0.8c.The second ship records the velocity of the faster ship as

Accepted Answer

The answer of An earthbound radar monitors a spaceship moving...

Quiz 39: Relativity

Your strange friend flies past you in a relativistic spacecraft holding a meterstick and a clock.The meterstick appears too _ to you,and the clock appears _ to you.

Spaceship Julio passes spaceship Klara with a relative velocity of 0.8c.An astronaut aboard Julio finds that her heart is beating once every 0.0133 min (75 beats/min) .The time between beats according to a sympathetic astronaut aboard Klara is

Our galaxy,the Milky Way,has a diameter of about 100 thousand light-years.How many years would it take a spacecraft to cross the galaxy if it could travel at 99% the speed of light?

You observed that event A occurred before event B.Which of the following statements is false?

A beam of unstable neutral pions is observed to travel on average 8 m before they decay.If their proper lifetime is 0.8 $\times$ 10^-8 s,then calculate how fast the beam is traveling.

Because the galaxies are moving away from us,the light they emit

An astronaut aboard a spacecraft enroute to Mars with a speed of 0.5c relative to Earth observes a meteor approaching head on at a speed of 0.9c.What is the speed of the meteor relative to Earth?

What is the difference in age between the mother and son after she returns back to Earth?

A star system is 100 light-years away.If a spacecraft travels to the star system at 97% the speed of light then what is the ratio of the time for the journey measured by an observer left on Earth divided by the time measured by the astronaut?

Two electrons are ejected in opposite directions from atoms in a sample of radioactive material.Each electron has a speed,as measured by a laboratory observer,of 0.6c.What is the speed of one electron as seen from the other electron?

What is the total distance traveled according to the biologist? Give your answer in light-years.

At rest,pions have a proper lifetime of 26 ns.What is the speed of a beam of pions if their observed lifetime were measured to be 64 ns ? (This is a real experiment that has been performed and found to be consistent with Special Relativity.)

You measure the length of a passing Imperial Starcruiser spacecraft to be 100 m.If the Starcruiser is moving at 80% the speed of light,what would be its length if it was at rest relative to you?

The light emitted by an object traveling at high speed toward Earth would

A clock has a period of exactly 1 second when at rest.If you were to measure a period of 1.5 seconds for the same clock,how fast is it moving relative to you as a percentage of the speed of light?

Spaceship Solange passes spaceship Hari with a relative velocity of 0.6c.An astronaut aboard Hari observes the length of Solange to be 30.5 m.The astronauts aboard Solange claim that the length of their spaceship is

An earthbound radar monitors a spaceship moving at 0.9c that is being followed by a second ship moving at 0.8c.The second ship records the velocity of the faster ship as

Quiz 39: Relativity

Your strange friend flies past you in a relativistic spacecraft holding a meterstick and a clock.The meterstick appears too _____ to you,and the clock appears _____ to you.

Spaceship Julio passes spaceship Klara with a relative velocity of 0.8c.An astronaut aboard Julio finds that her heart is beating once every 0.0133 min (75 beats/min) .The time between beats according to a sympathetic astronaut aboard Klara is

Our galaxy,the Milky Way,has a diameter of about 100 thousand light-years.How many years would it take a spacecraft to cross the galaxy if it could travel at 99% the speed of light?

You observed that event A occurred before event B.Which of the following statements is false?

A beam of unstable neutral pions is observed to travel on average 8 m before they decay.If their proper lifetime is 0.8 ×\times× 10-8 s,then calculate how fast the beam is traveling.

Because the galaxies are moving away from us,the light they emit

An astronaut aboard a spacecraft enroute to Mars with a speed of 0.5c relative to Earth observes a meteor approaching head on at a speed of 0.9c.What is the speed of the meteor relative to Earth?

What is the difference in age between the mother and son after she returns back to Earth?

A star system is 100 light-years away.If a spacecraft travels to the star system at 97% the speed of light then what is the ratio of the time for the journey measured by an observer left on Earth divided by the time measured by the astronaut?

Two electrons are ejected in opposite directions from atoms in a sample of radioactive material.Each electron has a speed,as measured by a laboratory observer,of 0.6c.What is the speed of one electron as seen from the other electron?

What is the total distance traveled according to the biologist? Give your answer in light-years.

At rest,pions have a proper lifetime of 26 ns.What is the speed of a beam of pions if their observed lifetime were measured to be 64 ns ? (This is a real experiment that has been performed and found to be consistent with Special Relativity.)

You measure the length of a passing Imperial Starcruiser spacecraft to be 100 m.If the Starcruiser is moving at 80% the speed of light,what would be its length if it was at rest relative to you?

The light emitted by an object traveling at high speed toward Earth would

A clock has a period of exactly 1 second when at rest.If you were to measure a period of 1.5 seconds for the same clock,how fast is it moving relative to you as a percentage of the speed of light?

Spaceship Solange passes spaceship Hari with a relative velocity of 0.6c.An astronaut aboard Hari observes the length of Solange to be 30.5 m.The astronauts aboard Solange claim that the length of their spaceship is

An earthbound radar monitors a spaceship moving at 0.9c that is being followed by a second ship moving at 0.8c.The second ship records the velocity of the faster ship as

Your strange friend flies past you in a relativistic spacecraft holding a meterstick and a clock.The meterstick appears too _ to you,and the clock appears _ to you.

A beam of unstable neutral pions is observed to travel on average 8 m before they decay.If their proper lifetime is 0.8 $\times$ 10^-8 s,then calculate how fast the beam is traveling.