Question 1

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, m_el = 9.11 × 10^-31 kg)

Accepted Answer

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

Question 2

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

Accepted Answer

The energy released can be calculated using Einstein's equation, E=mc^2, where m is the mass lost (4.8 × 10^-28 kg) and c is the speed of light (3.00 × 10^8 m/s). Plugging in the values, E = (4.8 × 10^-28 kg)(3.00 × 10^8 m/s)^2 = 4.32 × 10^-11 J, which rounds to 4.3 × 10^-11 J.

Question 3

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

Accepted Answer

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

Question 4

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, m_proton = 1.67 × 10^-27 kg)

Accepted Answer

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

Question 5

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

Accepted Answer

The total energy of a particle can be given by the equation E^2 = (pc)^2 + (mc^2)^2, where p is the momentum, m is the mass, and c is the speed of light. Since we want the kinetic energy to be 80% of the total energy, we can set K = 0.8E and solve for the momentum.

K = (pc)^2 / (2m)
0.8E = (pc)^2 / (2m)
0.8[(pc)^2 + (mc^2)^2] = (pc)^2
0.8(pc)^2 + 0.8(mc^2)^2 = (pc)^2
0.8(mc^2)^2 = 0.2(pc)^2
(mc^2)^2 = 0.25(pc)^2
(mc^2)^2 + (pc)^2 = E^2
(5/4)(pc)^2 = E^2

Now we can solve for p:

(mc^2)^2 + (pc)^2 = E^2
(mc^2)^2 + (5/4)(pc)^2 = (5/4)E^2
(pc)^2 = (4/5)[(5/4)E^2 - (mc^2)^2]
p = [(4/5)[(5/4)E^2 - (mc^2)^2]]^(1/2) / c

Substituting the mass and solving for p, we get:

p = [(4/5)[(5/4)(mpc^2)^2 - (mpc^2)^2]]^(1/2) / c = (3/5)mpc

So the speed of the proton can be found by dividing by its relativistic mass:

v = p / (gamma*m)
v = [(3/5)mpc] / [(1 - (v/c)^2)^(1/2)*mp]
v = 0.98c

Therefore, the answer is D) 0.98c.

Question 6

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 7

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, m_proton = 1.67 × 10^-27 kg)

Accepted Answer

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

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)

Accepted Answer

The energy consumed is E = power × time = (2.0 × 10^9 W) × (21 weeks × 7 days/week × 24 hours/day × 3600 seconds/hour). Using E = mc^2, the mass change m = E/c^2. Calculating gives approximately 0.28 kg.

Question 9

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)

Accepted Answer

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

Quiz 36: Relativity

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)

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 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 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)