Question 1

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 correct answer is A.The kinetic energy of the electron is:$$K = \frac{1}{2}mv^2 = \frac{1}{2}(9.11 	imes 10^{-31} 	ext{ kg})(0.643 	imes 3.00 	imes 10^8 	ext{ m/s})^2 = 1.60 	imes 10^{-14} 	ext{ J}$$The potential difference through which the electron must be accelerated is:$$V = \frac{K}{e} = \frac{1.60 	imes 10^{-14} 	ext{ J}}{1.60 	imes 10^{-19} 	ext{ C}} = 160 	ext{ kV}$$

Question 2

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?

Accepted Answer

The answer of Two spaceships are approaching one another,each at...

Question 3

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

P = mv
The momentum of the 1.30-kg object, relative to the lab, is:
P = (1.30 kg)(0.515c) = 0.6695 kg•c
To find the velocity of the 0.272-kg object that has the same momentum, we can set its momentum equal to the momentum of the 1.30-kg object:
P = mv
0.6695 kg•c = (0.272 kg)(v)
v = 2.464 c
Therefore, the velocity of the 0.272-kg object relative to the lab is 2.464c. However, we want the velocity relative to the lab, so we need to use the relativistic velocity addition formula:
v_lab = (v + v_moving)/(1 + vv_moving/c^2)
where v is the velocity of the 0.272-kg object relative to the lab, and v_moving is the velocity of the 1.30-kg object relative to the lab (0.515c).
Plugging in the numbers:
v_lab = (2.464c + 0.515c)/(1 + (2.464c)(0.515c)/c^2) = 0.944c
Therefore, the velocity of the 0.272-kg object relative to the lab that has the same momentum as the 1.30-kg object moving at 0.515c relative to the lab is 0.944c.

Question 4

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_proton = 1.67 × 10^-27 kg)

Accepted Answer

The answer of In the lab,a relativistic proton has a...

Question 5

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)

Accepted Answer

The answer of How many joules of energy are required...

Question 6

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?

Accepted Answer

The answer of Three spaceships A,B,and C are in motion,as...

Question 7

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?

Accepted Answer

The answer of A spaceship is moving away from the...

Question 8

How much work must be done to accelerate a particle of mass  from a speed of  to a speed of

Accepted Answer

The answer of How much work must be done to...

Question 9

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?

Accepted Answer

The answer of The captain of spaceship A observes enemy...

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)

Accepted Answer

Explanation:The time it takes for the spaceship to travel from one station to the other, as measured by an observer in the spaceship, is given by:$$t = \frac{d}{v}$$where:* d is the distance between the two stations (6.0 × 10^7 m)* v is the speed of the spaceship relative to the stations (0.90c)Substituting these values into the equation, we get:$$t = \frac{6.0 	imes 10^7 	ext{ m}}{0.90 	imes 3.00 	imes 10^8 	ext{ m/s}} = 0.097 	ext{ s} = 97 	ext{ ms}$$Therefore, the correct answer is A) 97 ms.

Question 11

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  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?

Accepted Answer

The answer of In an "atom smasher," two particles collide...

Question 12

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)

Accepted Answer

The answer of An electron is accelerated from rest through...

Question 13

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?

Accepted Answer

The answer of Three spaceships A,B,and C are in motion...

Question 14

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).

Accepted Answer

The correct expression for momentum at relativistic speeds is given by p = mv/√(1-v^2/c^2), which is different from the Newtonian expression p = mv. Using the given velocity of 0.75c, we can calculate that the correct momentum is 1.5 times the Newtonian momentum. Therefore, the percentage error is (1.5-1)/1.5 *100 = 33.3%, which is closest to option A (34%).

Question 15

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)

Accepted Answer

The answer of A spacecraft is measured by an observer...

Question 16

System  has a velocity u = +0.56c relative to system S,as shown in the figure.The clocks of S and  are synchronized at t =  = 0 when the origins O and  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  of the event,measured by an observer in  ?

Accepted Answer

The answer of System  has a velocity u =...

Question 17

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?

Accepted Answer

The answer of Consider three galaxies,Alpha,Beta and Gamma.An observer in...

Question 18

System  has a velocity u = +0.45c relative to system S,as shown in the figure.The clocks of S and  are synchronized at t =  = 0 when the origins O and  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  -coordinate of the event,measured by an observer in  ?

Accepted Answer

The answer of System  has a velocity u =...

Question 19

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 formula for relativistic velocity addition: $v = \frac{v_1 + v_2}{1 + \frac{v_1 \cdot v_2}{c^2}}$, 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 $v = \frac{0.60c + 0.40c}{1 + \frac{0.60c \cdot 0.40c}{c^2}} = \frac{1.0c}{1 + 0.24} = \frac{1.0c}{1.24} = 0.81c$.

Question 20

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 special relativity, the total energy $E$ is related to the rest mass energy $E_0$ and the kinetic energy $K$ by $E = E_0 + K$. If $K = E_0$, then $E = 2E_0$. The relativistic total energy is also given by $E = \gamma E_0$, where $\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}$. Setting $E = 2E_0$, we get $\gamma = 2$, which implies $\frac{1}{\sqrt{1 - v^2/c^2}} = 2$. Solving for $v/c$, we find $v/c = \sqrt{1 - (1/2)^2} = \sqrt{3}/2 \approx 0.87$, hence the speed of the proton is approximately $0.87c$.

Quiz 36: Relativity

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)

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?

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?

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_proton = 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)

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?

How much work must be done to accelerate a particle of mass from a speed of to a speed of

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?

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)

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) .

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?

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?

Quiz 36: Relativity

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)

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?

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?

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)

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)

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?

How much work must be done to accelerate a particle of mass from a speed of to a speed of

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?

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)

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) .

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?

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?

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_proton = 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)

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)