Question 1

A proton in a certain particle accelerator has a kinetic energy that is equal to its rest energy. What is the TOTAL energy of the proton as measured by a physicist working with the accelerator? (c = 3.00 × 10⁸ m/s, mproton = 1.67 × 10^-27 kg) A) 5.69 × 10^-11 J B) 1.50 × 10^-10J C) 2.07 × 10^-10 J D) 3.01 × 10^-10 J E) 8.77 × 10^-10 J

Accepted Answer

The total energy of the proton is given by:
E = K + rest energy
where K is the kinetic energy.
Since the kinetic energy is equal to the rest energy, we have:
E = 2(rest energy)
The rest energy of the proton is given by:
E0 = mc^2
where m is the mass of the proton.
Substituting the given values, we get:
E0 = (1.67 × 10^-27 kg)(3.00 × 10^8 m/s)^2
E0 = 1.51 × 10^-10 J
Therefore, the total energy of the proton is:
E = 2E0
E = 3.01 × 10^-10 J
Thus, the best choice is D.

Question 2

During a nuclear reaction, the particles involved lose 4.8 × 10^-28 kg of mass. How many joules of energy are released by this reaction? (c = 3.00 × 10⁸ m/s) A) 4.3 × 10^-11 J B) 1.4 × 10^-19 J C) 1.6 × 10^-36 J D) 2.1 × 10^-40 J E) 5.3 × 10^-45 J

Accepted Answer

The energy released can be calculated using Einstein's equation E=mc². Substituting the given values, E = (4.8 × 10⁻²⁸ kg) × (3.00 × 10⁸ m/s)² = 4.32 × 10⁻¹¹ J, which is approximately 4.3 × 10⁻¹¹ J.

Question 3

An electron is accelerated from rest through a potential difference of 50.0 kV. What is the TOTAL energy of the electron? (c = 3.00 × 10⁸ m/s, e = 1.60 × 10^-19 C, mel = 9.11 × 10^-31 kg) A) 8.00 × 10^-15 J B) 16.2 × 10^-15 J C) 8.20 × 10^-14 J D) 9.00 × 10^-14 J E) 16.2 × 10^-14J

Accepted Answer

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

Question 4

A relativistic proton has a momentum of 1.0 × 10^-17 kg ∙ m/s and a rest energy of 0.15 nJ. What is the kinetic energy of this proton? (c = 3.00 × 10⁸ m/s, mproton = 1.67 × 10^-27 kg) A) 1.3 pJ B) 1.6 pJ C) 3.0 pJ D) 2.2 pJ E) 2.5 pJ

Accepted Answer

The answer of A relativistic proton has a momentum of...

Question 5

As a spaceship is moving toward Earth, an Earthling measures its length to be 325 m, while the captain on board radios that her spaceship's length is 1150 m. (c = 3.00 × 10⁸ m/s) (a) How fast is the rocket moving relative to Earth? (b) What is the TOTAL energy of a 75.0-kg crewman as measured by (i) the captain in the rocket and (ii) the Earthling?

Accepted Answer

The answer of As a spaceship is moving toward Earth,...

Question 6

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)

Accepted Answer

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

Question 7

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) 1.8 × 10¹⁷ J B) 9.0 × 10¹⁶J C) 2.7 × 10¹² J D) 4.5 × 10⁹ J E) 3.0 × 10³ J

Accepted Answer

The relativistic kinetic energy is calculated using the formula $ KE = (\gamma - 1)mc^2 $, where $\gamma = \frac{1}{\sqrt{1 - v^2/c^2}} $. For $ v = 0.866c $, $\gamma = 2$. Thus, $ KE = (2 - 1)(1 \, \text{kg})(3.00 \times 10^8 \, \text{m/s})^2 = 9.0 \times 10^{16} \, \text{J} $.

Question 8

Assume that a certain city consumes electrical energy at an average rate of 2.0 × 10⁹ W. What would be the mass change in producing enough energy to keep this city running for 21 weeks? (c = 3.00 × 10⁸ m/s) A) 0.28 kg B) 0.32 kg C) 0.40 kg D) 0.48 kg

Accepted Answer

Using E=mc², calculate the energy consumed in 21 weeks, then solve for mass change: m = E/c².

Question 9

A proton in a certain particle accelerator has a kinetic energy that is equal to its rest energy. What is the momentum of the proton as measured by a physicist working with the accelerator? (c = 3.00 × 10⁸ m/s, mproton = 1.67 × 10^-27kg) A) 2.51 × 10^-19 kg ∙ m/s B) 2.89 × 10^-19kg ∙ m/s C) 4.34 × 10^-19 kg ∙ m/s D) 5.01 × 10^-19 kg ∙ m/s E) 8.68 × 10^-19 kg ∙ m/s

Accepted Answer

The answer of A proton in a certain particle accelerator...

Question 10

How fast must a proton move so that its kinetic energy is 80% of its total energy?
A) 0.020c
B) 0.87c
C) 0.92c
D) 0.98c
E) 0.80c

Accepted Answer

The total energy of a proton is given by:

E = mc^2 / sqrt(1 - v^2/c^2)

where m is the rest mass of the proton, v is its velocity, and c is the speed of light.

The kinetic energy of the proton is given by:

K = E - mc^2

We want to find the velocity v when K is 80% of E. That is, we want:

K = 0.8 E

Substituting the expressions for K and E above, we get:

(mc^2 / sqrt(1 - v^2/c^2)) - mc^2 = 0.8 (mc^2 / sqrt(1 - v^2/c^2))

Simplifying this equation, we get:

sqrt(1 - v^2/c^2) = 0.6

Squaring both sides, we get:

1 - v^2/c^2 = 0.36

Solving for v/c, we get:

v/c = sqrt(0.64) = 0.8

Therefore, the answer is D) 0.98c.

Question 11

During a nuclear reaction, 1.7 × 10^-4 J of energy is released. What is the resulting change in mass of the particles involved? (c = 3.00 × 10⁸ m/s) A) 5.1 × 10^-4 kg B) 4.3 × 10^-11 kg C) 1.5 × 10^-13 kg D) 4.8 × 10^-18 kg E) 1.9 × 10^-21kg

Accepted Answer

The answer of During a nuclear reaction, 1.7 × 10^-4...

Quiz 36: Relativity

A proton in a certain particle accelerator has a kinetic energy that is equal to its rest energy. What is the TOTAL energy of the proton as measured by a physicist working with the accelerator? (c = 3.00 × 108 m/s, mproton = 1.67 × 10-27 kg)

During a nuclear reaction, the particles involved lose 4.8 × 10-28 kg of mass. How many joules of energy are released by this reaction? (c = 3.00 × 108 m/s)

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

A relativistic proton has a momentum of 1.0 × 10-17 kg ∙ m/s and a rest energy of 0.15 nJ. What is the kinetic energy of this proton? (c = 3.00 × 108 m/s, mproton = 1.67 × 10-27 kg)

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)

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)

Assume that a certain city consumes electrical energy at an average rate of 2.0 × 109 W. What would be the mass change in producing enough energy to keep this city running for 21 weeks? (c = 3.00 × 108 m/s)

A proton in a certain particle accelerator has a kinetic energy that is equal to its rest energy. What is the momentum of the proton as measured by a physicist working with the accelerator? (c = 3.00 × 108 m/s, mproton = 1.67 × 10-27 kg)

How fast must a proton move so that its kinetic energy is 80% of its total energy?

During a nuclear reaction, 1.7 × 10-4 J of energy is released. What is the resulting change in mass of the particles involved? (c = 3.00 × 108 m/s)

A proton in a certain particle accelerator has a kinetic energy that is equal to its rest energy. What is the TOTAL energy of the proton as measured by a physicist working with the accelerator? (c = 3.00 × 10⁸ m/s, mproton = 1.67 × 10^-27 kg)

During a nuclear reaction, the particles involved lose 4.8 × 10^-28 kg of mass. How many joules of energy are released by this reaction? (c = 3.00 × 10⁸ m/s)

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

A relativistic proton has a momentum of 1.0 × 10^-17 kg ∙ m/s and a rest energy of 0.15 nJ. What is the kinetic energy of this proton? (c = 3.00 × 10⁸ m/s, mproton = 1.67 × 10^-27 kg)

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)

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)

Assume that a certain city consumes electrical energy at an average rate of 2.0 × 10⁹ W. What would be the mass change in producing enough energy to keep this city running for 21 weeks? (c = 3.00 × 10⁸ m/s)

A proton in a certain particle accelerator has a kinetic energy that is equal to its rest energy. What is the momentum of the proton as measured by a physicist working with the accelerator? (c = 3.00 × 10⁸ m/s, mproton = 1.67 × 10^-27kg)

During a nuclear reaction, 1.7 × 10^-4 J of energy is released. What is the resulting change in mass of the particles involved? (c = 3.00 × 10⁸ m/s)