Question 1

A proton with mass 1.67*10^-²⁷ kg moves in an accelerator with a speed of 0.600c. What is its total energy? (c = 3.00 * 10⁸ m/s)

Accepted Answer

The answer of A proton with mass 1.67*10^-²⁷ kg moves...

Question 2

What is the total energy of a proton moving at a speed of 2.10 * 10⁸ m/s? (proton mass is 1.67 * 10 ^- ²⁷kg and c = 3.00 * 10⁸ m/s)

Accepted Answer

The answer of What is the total energy of a...

Question 3

As measured from the Earth, a spacecraft is moving at speed c/2 toward a second spacecraft that is not moving. The first spacecraft emits a laser pulse toward the second spacecraft. What is the speed of the laser pulse measured by the second spacecraft as it passes by?

Accepted Answer

The answer of As measured from the Earth, a spacecraft...

Question 4

What is the relativistic kinetic energy of an electron moving at a speed of 2.00 * 10⁸m/s? (electron mass is 9.11 *10^-³¹ kg and c = 3.00 * 10⁸m/s)

Accepted Answer

The correct answer is A because the relativistic kinetic energy of an electron moving at a speed of 2.00 x 10^8 m/s is 2.80 x 10^-14 J.

Question 5

The total energy of a particle:

Accepted Answer

The total energy of a particle increases with increasing relativistic momentum because, in relativity, the total energy includes both rest energy and kinetic energy, which increases with momentum.

Question 6

A particle of mass m is moving at speed  . What is its momentum?

Accepted Answer

The answer of A particle of mass m is moving...

Question 7

An object moves by an observer at 0.600c. The total energy of the object will be what factor times that of the rest energy?

Accepted Answer

According to Einstein's theory of relativity, the total energy of an object moving at a velocity close to the speed of light can be calculated using the equation E = γmc^2, where E is the total energy, m is the rest mass of the object, c is the speed of light, and γ is the Lorentz factor given by γ = 1/√(1 - v^2/c^2), where v is the velocity of the object.

Plugging in the given values, we get:
γ = 1/√(1 - (0.600c)^2/c^2) = 1.25
E = γmc^2 = 1.25m*c^2

This means that the total energy of the object is 1.25 times that of the rest energy. Therefore, the best choice is A: 1.25.

Question 8

An electron of mass 9.11 *10^-³¹ kg moves with a speed of 0.800c. What is its momentum? (c = 3.00 * 10⁸ m/s)

Accepted Answer

The relativistic momentum is given by p = γmv, where γ = 1/√(1-v²/c²). For v = 0.800c, γ ≈ 1.667. Thus, p = 1.667 * 9.11 x 10^-31 kg * 0.800 * 3.00 x 10^8 m/s ≈ 3.64 x 10^-22 kg·m/s.

Question 9

A proton with mass 1.67 *10^-²⁷ kg moves with a speed of 0.800c in an accelerator. What is its kinetic energy? (c = 3.00*10⁸ m/s)

Accepted Answer

The answer of A proton with mass 1.67 *10^-²⁷ kg...

Question 10

Two spaceships are approaching one another, one with speed  and the other with speed  . Neither speed is 0. Their speed of approach, according to Newtonian mechanics, is  . Special relativity tells us that the speed of approach

Accepted Answer

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

Question 11

When one compares the relativistic kinetic energy to the classically calculated kinetic energy for a moving object, at which of the speeds listed below does the classical calculation give a greater value than the relativistic calculation?

Accepted Answer

The classical kinetic energy is always less than the relativistic kinetic energy for any non-zero speed. The classical calculation never gives a greater value than the relativistic calculation.

Question 12

Including relativistic effects, doubling the speed of a object:

Accepted Answer

Relativistically, momentum is given by p = γmv, where γ is the Lorentz factor. As speed increases, γ increases, so doubling speed more than doubles momentum.

Question 13

At what speed is the momentum of an object triple that found classically?

Accepted Answer

The answer of At what speed is the momentum of...

Question 14

A proton with mass 1.67 * 10^-²⁷kg moves with a speed of 0.800c in an accelerator. What is its relativistic momentum? (c = 3.00*10⁸ m/s)

Accepted Answer

The relativistic momentum is calculated using the formula p = γmv, where γ = 1/√(1-v²/c²). For v = 0.800c, γ ≈ 1.667. Thus, p = 1.667 * 1.67 x 10^-27 kg * 0.800 * 3.00 x 10^8 m/s ≈ 6.68 x 10^-19 kg·m/s.

Question 15

A nuclear reaction, which gives off a total of 2.0 * 10¹⁶ J of energy, expends how much mass in the process? (c = 3.00 * 10⁸ m/s)

Accepted Answer

The energy-mass equivalence principle is given by E=mc². Solving for mass (m), we have m=E/c². Substituting the given values, m = (2.0 x 10¹⁶ J) / (3.00 x 10⁸ m/s)² = 0.22 kg.

Question 16

Doubling the momentum of a particle:

Accepted Answer

The answer of Doubling the momentum of a particle:
...

Question 17

If a proton with mass 1.67 *10^-²⁷ kg moves in an accelerator such that its total energy is two times its rest energy, what is its speed? (c = 3.00 * 10⁸ m/s)

Accepted Answer

The total energy being twice the rest energy implies that the kinetic energy is equal to the rest energy. Using the relativistic energy-momentum relation, the speed can be calculated as v = c√(1 - (1/2)²) = 2.60 × 10⁸ m/s.

Question 18

As the speed of an object increases, its relativistic momentum:

Accepted Answer

Relativistic momentum increases more than classical momentum because it accounts for the effects of special relativity, where momentum is given by p = γmv, with γ (gamma) being the Lorentz factor, which increases with speed.

Question 19

As measured from the Earth, a spacecraft is moving at speed 0.80c when it releases a probe at speed 0.60c relative to the spacecraft in a forward direction. What would be the speed of the probe as measured from the Earth?

Accepted Answer

First, we need to use the velocity addition formula to find the velocity of the probe relative to Earth:
v_probe_earth = (v_probe_spacecraft + v_spacecraft_earth) / (1 + (v_probe_spacecraft * v_spacecraft_earth) / c^2)
where v_probe_spacecraft = 0.60c and v_spacecraft_earth = 0.80c.

v_probe_earth = (0.60c + 0.80c) / (1 + (0.60c * 0.80c) / c^2)
v_probe_earth = 1.40c / (1 + 0.48)
v_probe_earth = 1.40c / 1.48
v_probe_earth = 0.95c

Therefore, the speed of the probe as measured from the Earth would be 0.95c, which is option D.

Question 20

An unknown particle in an accelerator moving at a speed of 2.00 * 10⁸ m/s has a measured total energy of 1.22*10^-⁹ J. What is its mass? (c = 3.00 * 10⁸ m/s)

Accepted Answer

The answer of An unknown particle in an accelerator moving...

Quiz 27: Relativity

A proton with mass 1.6710^-²⁷ kg moves in an accelerator with a speed of 0.600c. What is its total energy? (c = 3.00 10⁸ m/s)

What is the total energy of a proton moving at a speed of 2.10 * 10⁸ m/s? (proton mass is 1.67 * 10 ^- ²⁷kg and c = 3.00 * 10⁸ m/s)

As measured from the Earth, a spacecraft is moving at speed c/2 toward a second spacecraft that is not moving. The first spacecraft emits a laser pulse toward the second spacecraft. What is the speed of the laser pulse measured by the second spacecraft as it passes by?

What is the relativistic kinetic energy of an electron moving at a speed of 2.00 * 10⁸m/s? (electron mass is 9.11 10^-³¹ kg and c = 3.00 10⁸m/s)

The total energy of a particle:

A particle of mass m is moving at speed . What is its momentum?

An object moves by an observer at 0.600c. The total energy of the object will be what factor times that of the rest energy?

An electron of mass 9.11 10^-³¹ kg moves with a speed of 0.800c. What is its momentum? (c = 3.00 10⁸ m/s)

A proton with mass 1.67 10^-²⁷ kg moves with a speed of 0.800c in an accelerator. What is its kinetic energy? (c = 3.0010⁸ m/s)

Two spaceships are approaching one another, one with speed and the other with speed . Neither speed is 0. Their speed of approach, according to Newtonian mechanics, is . Special relativity tells us that the speed of approach

When one compares the relativistic kinetic energy to the classically calculated kinetic energy for a moving object, at which of the speeds listed below does the classical calculation give a greater value than the relativistic calculation?

Including relativistic effects, doubling the speed of a object:

At what speed is the momentum of an object triple that found classically?

A proton with mass 1.67 * 10^-²⁷kg moves with a speed of 0.800c in an accelerator. What is its relativistic momentum? (c = 3.00*10⁸ m/s)

A nuclear reaction, which gives off a total of 2.0 * 10¹⁶ J of energy, expends how much mass in the process? (c = 3.00 * 10⁸ m/s)

Doubling the momentum of a particle:

If a proton with mass 1.67 10^-²⁷ kg moves in an accelerator such that its total energy is two times its rest energy, what is its speed? (c = 3.00 10⁸ m/s)

As the speed of an object increases, its relativistic momentum:

As measured from the Earth, a spacecraft is moving at speed 0.80c when it releases a probe at speed 0.60c relative to the spacecraft in a forward direction. What would be the speed of the probe as measured from the Earth?

An unknown particle in an accelerator moving at a speed of 2.00 * 10⁸ m/s has a measured total energy of 1.2210^-⁹ J. What is its mass? (c = 3.00 10⁸ m/s)

Quiz 27: Relativity

A proton with mass 1.67*10-27 kg moves in an accelerator with a speed of 0.600c. What is its total energy? (c = 3.00 * 108 m/s)

What is the total energy of a proton moving at a speed of 2.10 * 108 m/s? (proton mass is 1.67 * 10 - 27 kg and c = 3.00 * 108 m/s)

As measured from the Earth, a spacecraft is moving at speed c/2 toward a second spacecraft that is not moving. The first spacecraft emits a laser pulse toward the second spacecraft. What is the speed of the laser pulse measured by the second spacecraft as it passes by?

What is the relativistic kinetic energy of an electron moving at a speed of 2.00 * 108 m/s? (electron mass is 9.11 *10-31 kg and c = 3.00 * 108 m/s)

The total energy of a particle:

A particle of mass m is moving at speed . What is its momentum?

An object moves by an observer at 0.600c. The total energy of the object will be what factor times that of the rest energy?

An electron of mass 9.11 *10-31 kg moves with a speed of 0.800c. What is its momentum? (c = 3.00 * 108 m/s)

A proton with mass 1.67 *10-27 kg moves with a speed of 0.800c in an accelerator. What is its kinetic energy? (c = 3.00*108 m/s)

Two spaceships are approaching one another, one with speed and the other with speed . Neither speed is 0. Their speed of approach, according to Newtonian mechanics, is . Special relativity tells us that the speed of approach

When one compares the relativistic kinetic energy to the classically calculated kinetic energy for a moving object, at which of the speeds listed below does the classical calculation give a greater value than the relativistic calculation?

Including relativistic effects, doubling the speed of a object:

At what speed is the momentum of an object triple that found classically?

A proton with mass 1.67 * 10-27 kg moves with a speed of 0.800c in an accelerator. What is its relativistic momentum? (c = 3.00*108 m/s)

A nuclear reaction, which gives off a total of 2.0 * 1016 J of energy, expends how much mass in the process? (c = 3.00 * 108 m/s)

Doubling the momentum of a particle:

If a proton with mass 1.67 *10-27 kg moves in an accelerator such that its total energy is two times its rest energy, what is its speed? (c = 3.00 * 108 m/s)

As the speed of an object increases, its relativistic momentum:

As measured from the Earth, a spacecraft is moving at speed 0.80c when it releases a probe at speed 0.60c relative to the spacecraft in a forward direction. What would be the speed of the probe as measured from the Earth?

An unknown particle in an accelerator moving at a speed of 2.00 * 108 m/s has a measured total energy of 1.22*10-9 J. What is its mass? (c = 3.00 * 108 m/s)

A proton with mass 1.6710^-²⁷ kg moves in an accelerator with a speed of 0.600c. What is its total energy? (c = 3.00 10⁸ m/s)

What is the total energy of a proton moving at a speed of 2.10 * 10⁸ m/s? (proton mass is 1.67 * 10 ^- ²⁷kg and c = 3.00 * 10⁸ m/s)

What is the relativistic kinetic energy of an electron moving at a speed of 2.00 * 10⁸m/s? (electron mass is 9.11 10^-³¹ kg and c = 3.00 10⁸m/s)

An electron of mass 9.11 10^-³¹ kg moves with a speed of 0.800c. What is its momentum? (c = 3.00 10⁸ m/s)

A proton with mass 1.67 10^-²⁷ kg moves with a speed of 0.800c in an accelerator. What is its kinetic energy? (c = 3.0010⁸ m/s)

A proton with mass 1.67 * 10^-²⁷kg moves with a speed of 0.800c in an accelerator. What is its relativistic momentum? (c = 3.00*10⁸ m/s)

A nuclear reaction, which gives off a total of 2.0 * 10¹⁶ J of energy, expends how much mass in the process? (c = 3.00 * 10⁸ m/s)

If a proton with mass 1.67 10^-²⁷ kg moves in an accelerator such that its total energy is two times its rest energy, what is its speed? (c = 3.00 10⁸ m/s)

An unknown particle in an accelerator moving at a speed of 2.00 * 10⁸ m/s has a measured total energy of 1.2210^-⁹ J. What is its mass? (c = 3.00 10⁸ m/s)