Question 1

The captain of spaceship A observes enemy spaceship E escaping with a relative velocity of 0.48c,as shown in the figure.A missile M is fired from ship A,with a velocity of 0.72c relative to ship A.What is the relative velocity of approach of missile M,observed by the crew on ship E?

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Question 2

A spaceship approaching an asteroid at a speed of 0.60c launches a rocket forward with a speed of 0.40c relative to the spaceship.At what speed is the rocket approaching the asteroid as measured by an astronaut on the asteroid?

Accepted Answer

The speed of the rocket as measured by the astronaut on the asteroid can be calculated using the relativistic velocity addition formula: $v = \frac{v_1 + v_2}{1 + \frac{v_1v_2}{c^2}}$, where $v_1 = 0.60c$ is the speed of the spaceship relative to the asteroid, $v_2 = 0.40c$ is the speed of the rocket relative to the spaceship, and $c$ is the speed of light. Plugging in the values, we get $v = \frac{0.60c + 0.40c}{1 + \frac{(0.60c)(0.40c)}{c^2}} = \frac{1.0c}{1 + 0.24} = \frac{1.0c}{1.24} = 0.81c$.

Question 3

In a certain particle accelerator,a proton has a kinetic energy that is equal to its rest energy.What is the speed of the proton relative to the accelerator?

Accepted Answer

When a proton's kinetic energy equals its rest energy, its total energy is twice its rest energy. According to the theory of relativity, the relationship between total energy (E), rest energy (E_0), and kinetic energy (K) can be expressed as E = E_0 + K. If K = E_0, then E = 2E_0. The speed of the proton can be found using the formula for total energy: $E = \gamma E_0$, where $\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$. Solving for $v$ when $E = 2E_0$ leads to $\gamma = 2$, which corresponds to $v \approx 0.87c$.

Question 4

Three spaceships A,B,and C are in motion,as shown in the figure.The commander on ship B observes ship C approaching with a relative velocity of 0.78c.The commander also observes ship A,advancing in the rear,with a relative velocity of 0.31c.What is the velocity of ship C,relative to an observer on ship A?

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Question 5

A spacecraft is measured by an observer on the ground to have a length of 53 m as it flies toward the earth with a speed 1.7 × 10⁸ m/s.The spacecraft then lands and its length is again measured by the observer on the ground,this time while the spacecraft is at rest on the launchpad. What result does he now get for the length? (c = 3.00 × 10⁸ m/s)

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Question 6

Consider three galaxies,Alpha,Beta and Gamma.An observer in Beta sees the other two galaxies each moving away from him in opposite directions at speed 0.70c.At what speed would an observer in Alpha see the galaxy Beta moving?

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Question 7

In an "atom smasher," two particles collide head on at relativistic speeds.If the velocity of the first particle is 0.741c to the left,and the velocity of the second particle is 0.350c to the right (both of these speeds are measured in Earth's rest frame),how fast are the particles moving with respect to each other?

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Question 8

How much work must be done to accelerate a particle of mass 2.1 × 10^-14kg from a speed of 1.5 × 10⁸m/s to a speed of 2.5 × 10⁸m/s? (c = 3.00 × 10⁸ m/s)

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Question 9

At what speed relative to the lab will a 0.272-kg object have the same momentum as a 1.30-kg object that is moving at 0.515c relative to the lab?

Accepted Answer

We know that momentum (p) is given by:

p = m*v

where m is the mass of the object and v is its velocity.
Let's denote the velocity of the 0.272 kg object as v1 and the velocity of the 1.3 kg object as v2. In this case, we want to find v1 such that:

p1 = p2

or

m1*v1 = m2*v2

Substituting the given values, we get:

0.272*v1 = 1.3*(0.515c)

Solving for v1, we get:

v1 = (1.3*0.515c)/0.272 = 0.944c

Therefore, the answer is A) 0.944c.

Question 10

Two space stations are at rest relative to each other and are 6.0 × 10⁷ m apart,as measured by observers on the stations.A spaceship traveling from one station to the other at 0.90c relative to the stations passes both of them,one after the other.As measured by an observer in the spaceship,how long does it take to travel from one station to the other? (c = 3.00 × 10⁸ m/s)

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Question 11

A particle is moving at 0.75c relative to a lab on Earth.By what percentage is the Newtonian expression for its momentum in error? (The percentage error is the difference between the erroneous and correct values,divided by the correct one).

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Question 12

System S' has a velocity u = +0.56c relative to system S,as shown in the figure.The clocks of S and S'are synchronized at t = t' = 0 when the origins O and O' coincide.An event is observed in both systems.The event takes place at x = 800 m and at time t = 3.0 μs as measured by an observer in S.What is the time t' of the event,measured by an observer in S'?

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Question 13

A spaceship is moving away from the earth with a constant speed of 0.80c. The spaceship fires a 28-kg missile with a speed of 0.50c relative to the spaceship.What is the speed of the missile measured by observers on the earth if the missile is fired
(a)away from the earth?
(b)toward the earth?

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Question 14

System S' has a velocity u = +0.45c relative to system S,as shown in the figure.The clocks of S and S'are synchronized at t = t' = 0 when the origins O and O' coincide.An event is observed in both systems.The event takes place at x = 600 m and at time t = 1.9 μs,as measured by an observer in S.What is the x'-coordinate of the event,measured by an observer in S'?

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Question 15

An electron is accelerated from rest through a potential difference of 50.0 kV.What is the speed of the electron? (c = 3.00 × 10⁸ m/s,e = 1.60 × 10^-19 C,m_el = 9.11 × 10^-31 kg)

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Question 16

An electron has a speed of 0.643c.Through what potential difference would the electron need to be accelerated (starting from rest)in order to reach this speed? (c = 3.00 × 10⁸ m/s,e = 1.60 × 10^-19 C, M_el = 9.11 × 10^-31 kg)

Accepted Answer

The kinetic energy of the electron can be calculated using the formula:
KE = (1/2) * m * v^2
where m is the mass of the electron and v is its velocity.

Substituting the given values, we get:
KE = (1/2) * (9.11 × 10^-31 kg) * (0.643c)^2
KE = 3.01 × 10^-14 J

The potential difference can be calculated using the formula:
Potential difference = KE / e
where e is the charge of the electron.

Substituting the given values, we get:
Potential difference = (3.01 × 10^-14 J) / (1.60 × 10^-19 C)
Potential difference = 188.2 × 10^3 V
Potential difference = 188.2 kV

Therefore, the closest answer is option A) 160 kV.

Question 17

In the lab,a relativistic proton has a momentum of 1.00 × 10^-19 kg ∙ m/s and a rest energy of 0.150 nJ.What is the speed of the proton in the lab? (c = 3.00 × 10⁸ m/s,m_p_roton = 1.67 × 10^-27 kg)

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Question 18

Two spaceships are approaching one another,each at a speed of 0.28c relative to a stationary observer on Earth.What speed does an observer on one spaceship record for the other approaching spaceship?

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Question 19

Three spaceships A,B,and C are in motion as shown in the figure.The commander on ship B observes ship C approaching with a relative velocity of 0.83c.The commander also observes ship A,advancing in the rear,with a relative velocity of 0.48c.As measured by commander on ship B,at what speed is ship A approaching ship C?

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Question 20

How many joules of energy are required to accelerate a 1.0-kg mass from rest to a speed of 86.6% the speed of light? (c = 3.00 × 10⁸ m/s)

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Quiz 14: Special Relativity

The captain of spaceship A observes enemy spaceship E escaping with a relative velocity of 0.48c,as shown in the figure.A missile M is fired from ship A,with a velocity of 0.72c relative to ship A.What is the relative velocity of approach of missile M,observed by the crew on ship E?

A spaceship approaching an asteroid at a speed of 0.60c launches a rocket forward with a speed of 0.40c relative to the spaceship.At what speed is the rocket approaching the asteroid as measured by an astronaut on the asteroid?

In a certain particle accelerator,a proton has a kinetic energy that is equal to its rest energy.What is the speed of the proton relative to the accelerator?

Consider three galaxies,Alpha,Beta and Gamma.An observer in Beta sees the other two galaxies each moving away from him in opposite directions at speed 0.70c.At what speed would an observer in Alpha see the galaxy Beta moving?

How much work must be done to accelerate a particle of mass 2.1 × 10^-14kg from a speed of 1.5 × 10⁸m/s to a speed of 2.5 × 10⁸m/s? (c = 3.00 × 10⁸ m/s)

At what speed relative to the lab will a 0.272-kg object have the same momentum as a 1.30-kg object that is moving at 0.515c relative to the lab?

A particle is moving at 0.75c relative to a lab on Earth.By what percentage is the Newtonian expression for its momentum in error? (The percentage error is the difference between the erroneous and correct values,divided by the correct one) .

A spaceship is moving away from the earth with a constant speed of 0.80c. The spaceship fires a 28-kg missile with a speed of 0.50c relative to the spaceship.What is the speed of the missile measured by observers on the earth if the missile is fired (a)away from the earth? (b)toward the earth?

An electron is accelerated from rest through a potential difference of 50.0 kV.What is the speed of the electron? (c = 3.00 × 10⁸ m/s,e = 1.60 × 10^-19 C,m_el = 9.11 × 10^-31 kg)

An electron has a speed of 0.643c.Through what potential difference would the electron need to be accelerated (starting from rest) in order to reach this speed? (c = 3.00 × 10⁸ m/s,e = 1.60 × 10^-19 C, M_el = 9.11 × 10^-31 kg)

In the lab,a relativistic proton has a momentum of 1.00 × 10^-19 kg ∙ m/s and a rest energy of 0.150 nJ.What is the speed of the proton in the lab? (c = 3.00 × 10⁸ m/s,m_p_roton = 1.67 × 10^-27 kg)

Two spaceships are approaching one another,each at a speed of 0.28c relative to a stationary observer on Earth.What speed does an observer on one spaceship record for the other approaching spaceship?

How many joules of energy are required to accelerate a 1.0-kg mass from rest to a speed of 86.6% the speed of light? (c = 3.00 × 10⁸ m/s)

Quiz 14: Special Relativity

The captain of spaceship A observes enemy spaceship E escaping with a relative velocity of 0.48c,as shown in the figure.A missile M is fired from ship A,with a velocity of 0.72c relative to ship A.What is the relative velocity of approach of missile M,observed by the crew on ship E?

A spaceship approaching an asteroid at a speed of 0.60c launches a rocket forward with a speed of 0.40c relative to the spaceship.At what speed is the rocket approaching the asteroid as measured by an astronaut on the asteroid?

In a certain particle accelerator,a proton has a kinetic energy that is equal to its rest energy.What is the speed of the proton relative to the accelerator?

Consider three galaxies,Alpha,Beta and Gamma.An observer in Beta sees the other two galaxies each moving away from him in opposite directions at speed 0.70c.At what speed would an observer in Alpha see the galaxy Beta moving?

How much work must be done to accelerate a particle of mass 2.1 × 10-14 kg from a speed of 1.5 × 108 m/s to a speed of 2.5 × 108 m/s? (c = 3.00 × 108 m/s)

At what speed relative to the lab will a 0.272-kg object have the same momentum as a 1.30-kg object that is moving at 0.515c relative to the lab?

A particle is moving at 0.75c relative to a lab on Earth.By what percentage is the Newtonian expression for its momentum in error? (The percentage error is the difference between the erroneous and correct values,divided by the correct one) .

A spaceship is moving away from the earth with a constant speed of 0.80c. The spaceship fires a 28-kg missile with a speed of 0.50c relative to the spaceship.What is the speed of the missile measured by observers on the earth if the missile is fired (a)away from the earth? (b)toward the earth?

An electron is accelerated from rest through a potential difference of 50.0 kV.What is the speed of the electron? (c = 3.00 × 108 m/s,e = 1.60 × 10-19 C,mel = 9.11 × 10-31 kg)

An electron has a speed of 0.643c.Through what potential difference would the electron need to be accelerated (starting from rest) in order to reach this speed? (c = 3.00 × 108 m/s,e = 1.60 × 10-19 C, Mel = 9.11 × 10-31 kg)

In the lab,a relativistic proton has a momentum of 1.00 × 10-19 kg ∙ m/s and a rest energy of 0.150 nJ.What is the speed of the proton in the lab? (c = 3.00 × 108 m/s,mproton = 1.67 × 10-27 kg)

Two spaceships are approaching one another,each at a speed of 0.28c relative to a stationary observer on Earth.What speed does an observer on one spaceship record for the other approaching spaceship?

How many joules of energy are required to accelerate a 1.0-kg mass from rest to a speed of 86.6% the speed of light? (c = 3.00 × 108 m/s)

How much work must be done to accelerate a particle of mass 2.1 × 10^-14kg from a speed of 1.5 × 10⁸m/s to a speed of 2.5 × 10⁸m/s? (c = 3.00 × 10⁸ m/s)

An electron is accelerated from rest through a potential difference of 50.0 kV.What is the speed of the electron? (c = 3.00 × 10⁸ m/s,e = 1.60 × 10^-19 C,m_el = 9.11 × 10^-31 kg)

An electron has a speed of 0.643c.Through what potential difference would the electron need to be accelerated (starting from rest) in order to reach this speed? (c = 3.00 × 10⁸ m/s,e = 1.60 × 10^-19 C, M_el = 9.11 × 10^-31 kg)

In the lab,a relativistic proton has a momentum of 1.00 × 10^-19 kg ∙ m/s and a rest energy of 0.150 nJ.What is the speed of the proton in the lab? (c = 3.00 × 10⁸ m/s,m_p_roton = 1.67 × 10^-27 kg)

How many joules of energy are required to accelerate a 1.0-kg mass from rest to a speed of 86.6% the speed of light? (c = 3.00 × 10⁸ m/s)