Question 1

As the speed of a particle approaches the speed of light, the momentum of the particle

Accepted Answer

The answer of As the speed of a particle approaches...

Question 2

A spaceship carrying a light clock moves at a speed of 0.96 c relative to an observer on Earth. Relative to a frame of reference that is fixed with respect to the earth, how long does it take the clock to advance 1 s?

Accepted Answer

Due to time dilation, the time observed on Earth is longer than the time on the spaceship. The time dilation factor is given by the Lorentz factor: γ = 1/√(1-v²/c²). For v = 0.96c, γ ≈ 3.57. Thus, 1 second on the spaceship corresponds to approximately 3.57 seconds on Earth.

Question 3

A spaceship approaches the earth with a speed 0.50 c. A passenger in the spaceship measures his heartbeat as 70 beats per minute. What is his heartbeat rate according to an observer that is at rest relative to the earth?

Accepted Answer

The answer of A spaceship approaches the earth with a...

Question 4

An object moves in a direction parallel to its length with a velocity that approaches the velocity of light. The length of this object, as measured by a stationary observer,

Accepted Answer

According to the theory of relativity, as an object approaches the speed of light, its length as measured by a stationary observer will appear shorter. This phenomenon is known as length contraction, and it is due to the time dilation effect. Therefore, as the velocity of the object approaches the velocity of light, the length of the object would approach zero.

Question 5

One 20-year-old twin brother takes a space trip with a speed of 0.80c for 30 years according to a clock on the spaceship. Upon returning to the Earth, what is his own age and the age of the Earth-based twin brother?

Accepted Answer

The answer of One 20-year-old twin brother takes a space...

Question 6

How fast should a moving clock travel if it is to be observed by a stationary observer as running at one-half its normal rate?

Accepted Answer

According to the theory of relativity, time dilation is given by the formula $ t' = t/\sqrt{1-v^2/c^2} $. For the clock to run at half its normal rate, $ \sqrt{1-v^2/c^2} = 1/2 $. Solving for $ v $, we find $ v = 0.87c $.

Question 7

A set of twins, Andrea and Courtney, are initially 10 years old. While Courtney remains on Earth, Andrea rides on a space ship which travels away from Earth at a speed of 0.6c for five years (as measured by Courtney), then turns around and comes back at 0.6c. When Andrea returns, Courtney is 20 years old. How old is Andrea upon her return?

Accepted Answer

Explanation:Time dilation is a phenomenon in which time passes slower for an observer who is moving relative to another observer. In this case, Andrea is moving relative to Courtney, so time passes slower for Andrea. When Andrea returns to Earth, she has only aged 5 years (as measured by her own clock), while Courtney has aged 10 years (as measured by her clock). Therefore, Andrea is 15 years old upon her return.

Question 8

An astronaut leaves Earth in a spaceship at a speed of 0.96 c relative to an observer on Earth. The astronaut's destination is a star system 14.4 light-years away (one light-year is the distance light travels in one year.) According to the astronaut, how long does the trip take?

Accepted Answer

The answer of An astronaut leaves Earth in a spaceship...

Question 9

A spaceship moves away from the Earth with a speed of 0.80c. The spaceship then fires a missile with a speed of 0.50c relative to the spaceship.
(a) What is the velocity of the missile measured by observers on the Earth if the missile is fired away from the Earth?
(b) What is the velocity of the missile measured by observers on the Earth if the missile is fired toward the Earth?

Accepted Answer

The answer of A spaceship moves away from the Earth...

Question 10

As the velocity of your spaceship increases, you would observe

Accepted Answer

The answer of As the velocity of your spaceship increases,...

Question 11

Suppose one twin takes a ride in a space ship traveling at a very high speed to a distant star and back again, while the other twin remains on Earth. The twin that remained on Earth predicts that the astronaut twin is

Accepted Answer

According to the theory of relativity, time dilation occurs as velocity increases. The closer an object's velocity is to the speed of light, the slower time will pass for that object relative to a stationary observer. Therefore, the twin traveling in the high-speed spaceship will experience time passing more slowly than the twin who stayed on Earth. As a result, when the traveling twin returns to Earth, they will have aged less than the twin who remained on Earth, making the twin on Earth older than the traveling twin.

Question 12

An object moves in a direction parallel to its length with a velocity that approaches the velocity of light. The width of this object, as measured by a stationary observer,

Accepted Answer

The answer of An object moves in a direction parallel...

Question 13

Relative to a stationary observer, a moving object

Accepted Answer

According to the theory of relativity, a moving object appears shorter along the direction of motion to a stationary observer, a phenomenon known as length contraction.

Question 14

The redshift due to the Doppler effect is caused by

Accepted Answer

The redshift due to the Doppler effect occurs when sources of light are moving away from the observer, causing the light's wavelength to stretch and shift towards the red end of the spectrum.

Question 15

Consider two spaceships, each traveling at 0.50c in a straight line. Ship A is moving directly away from the Sun and ship B is approaching the Sun. The science officers on each ship measure the velocity of light coming from the Sun. What do they measure for this velocity?

Accepted Answer

According to the theory of relativity, the speed of light in a vacuum is always measured to be exactly c, regardless of the observer's motion relative to the light source.

Question 16

As the speed of a particle approaches the speed of light, the mass of the particle

Accepted Answer

The answer of As the speed of a particle approaches...

Question 17

A spaceship takes a nonstop journey to a planet and returns in 10 hours according to a clock on the spaceship. If the speed of the spaceship is 0.80c, how much time has elapsed on the Earth?

Accepted Answer

The answer of A spaceship takes a nonstop journey to...

Question 18

The closest star to our solar system is Alpha Centauri, which is 4.30 light years away. A spaceship with a constant speed of 0.800c relative to the Earth travels toward the star.
(a) How much time would elapse on a clock on board the spaceship?
(b) How much time would elapse on a clock on the Earth?

Accepted Answer

The answer of The closest star to our solar system...

Question 19

You are a passenger on a spaceship. As the speed of the spaceship increases, you would observe

Accepted Answer

According to the theory of relativity, length contraction occurs in the direction of motion for an outside observer, but passengers on the spaceship would not notice any change in the length of their own spaceship.

Question 20

If you were to measure your pulse rate while in a spaceship moving away from the Sun at a speed close to the speed of light, you would find that it was

Accepted Answer

According to the theory of relativity, time dilation occurs at speeds close to the speed of light, but an observer moving with the spaceship would not notice any change in their own pulse rate. It would appear normal to them.

Quiz 36: Special Theory of Relativity