Question 1

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 2

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 3

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 4

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?

Accepted Answer

The answer of Two space stations are at rest relative...

Question 5

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, ,m_el = 9.11 × 10^-31 kg)

Accepted Answer

The answer of An electron has a speed of 0.643c.Through...

Question 6

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 7

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,

Accepted Answer

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

Question 8

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?

Accepted Answer

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

Question 9

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 Newtonian momentum is given by p = mv, while the relativistic momentum is p = γmv, where γ = 1/√(1-v²/c²). For v = 0.75c, γ ≈ 1.511. The percentage error is [(γmv - mv) / (γmv)] * 100% ≈ 34%.

Question 10

A navigational beacon in deep space broadcasts at a radio frequency of 50 MHz.A spaceship approaches the beacon with a relative velocity of 0.40c.The spaceship passes the beacon and departs from it with a DIFFERENT relative velocity.The beacon signal is now detected at a frequency of 40 MHz.What is the new velocity of the spaceship relative to the beacon?

Accepted Answer

The frequency detected by the spaceship can be calculated using the formula:

f' = f(1 - v/c)

where f is the frequency of the beacon signal, v is the velocity of the spaceship relative to the beacon, c is the speed of light, and f' is the frequency detected by the spaceship.

Initially, the frequency of the beacon signal was 50 MHz. When the spaceship approaches the beacon with a relative velocity of 0.40c, the frequency detected by the spaceship is:

f' = 50 MHz (1 - 0.40c/c) = 30 MHz

When the spaceship departs from the beacon with a different relative velocity, the frequency detected by the spaceship is 40 MHz. We can use the same formula to find the new velocity of the spaceship relative to the beacon:

40 MHz = 50 MHz (1 - v/c)

1 - v/c = 0.8

v/c = 0.2

v = 0.2c

Therefore, the new velocity of the spaceship relative to the beacon is 0.2c or 0.22 times the speed of light. The best choice is B).

Question 11

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 12

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 13

A navigational beacon in deep space broadcasts at a radio frequency of 50 MHz.A spaceship approaches the beacon with a relative velocity of 0.40c.What is the frequency of the beacon radio signal that is detected on the ship?

Accepted Answer

The answer of A navigational beacon in deep space broadcasts...

Question 14

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 15

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 16

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 17

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 18

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 kinetic energy gained by the electron is equal to the work done on it by the electric field, which is eV. Using the equation for kinetic energy (1/2)mv² = eV, we can solve for v: v = sqrt(2eV/m). Substituting the given values, v = sqrt(2 * 1.60 × 10^-19 C * 50,000 V / 9.11 × 10^-31 kg) ≈ 1.24 × 10^8 m/s.

Question 19

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 20

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...

Quiz 37: Relativity

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?

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?

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, ,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,

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) .

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?

A navigational beacon in deep space broadcasts at a radio frequency of 50 MHz.A spaceship approaches the beacon with a relative velocity of 0.40c.What is the frequency of the beacon radio signal that is detected on the ship?

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?

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)

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?

Quiz 37: Relativity

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?

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?

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, ,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,

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) .

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?

A navigational beacon in deep space broadcasts at a radio frequency of 50 MHz.A spaceship approaches the beacon with a relative velocity of 0.40c.What is the frequency of the beacon radio signal that is detected on the ship?

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?

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)

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?

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, ,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,

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)