# Worksheet: Total Relativistic Energy

In this worksheet, we will practice calculating the total relativistic energy of massive objects moving relative to an observer.

**Q1: **

A metal cube with a rest mass of 2 kg moves at a speed of in frame . What is its total relativistic energy in frame ? Give your answer to 3 significant figures.

- A J
- B J
- C J
- D J
- E J

**Q2: **

A spaceship moves at a speed in frame . Its mass in frame is measured to be 20,000 metric tons. What is its total relativistic energy?

- A joules
- B joules
- C joules
- D joules
- E joules

**Q3: **

The graph shows the total relativistic energy, , of an object against its speed, . The speed of light, , is defined to be 1. What is the rest mass of the object?

**Q4: **

An electron moves at a speed along a linear particle accelerator.
Its mass in the rest frame of the particle accelerator is measured to be
1,560 keV/c^{2}.
What is its total relativistic energy in the rest frame of the particle accelerator?

**Q5: **

The graph shows the total relativistic energy, , of an object against its speed, . The speed of light, , is defined to be 1. If the object is moving at a speed of in frame , what is its mass in frame ?

**Q6: **

A proton has a rest mass of . In frame , a proton is moving at a speed of . What is the total relativistic energy of the proton in frame ? Give your answer to three significant figures.

**Q7: **

A metal cube is moving at a speed of in frame . Its total relativistic energy as measured in frame is . What is the rest mass of the cube? Give your answer to the nearest kilogram.

**Q8: **

A proton has a rest mass of . At what speed would a proton have to move in order to have a total relativistic energy four times its rest mass energy? Give your answer as a multiple of the speed of light, , and to three significant figures.

- A
- B
- C
- D
- E

**Q9: **

A photon with an energy of 1,500 keV produces an electron-positron pair. What is the mass of the electron in the center-of-mass frame of the electron and the positron?

**Q10: **

An electron and a positron are collided in a particle accelerator. They annihilate and produce a photon with an energy of 1,043 keV. In the rest frame of the particle accelerator, the electron and the positron moved toward each other with equal speeds of . What is the rest mass of an electron? Give your answer to 3 significant figures in .

**Q11: **

In frame , a spaceship has a total relativistic energy of J. What is the mass of the spaceship as measured in frame ?

- A kg
- B kg
- C kg
- D kg
- E kg

**Q12: **

A spaceship with a rest mass of 40,000 metric tons has a total relativistic energy of J in frame . How fast is the spaceship moving in frame ? Give your answer to three significant figures.

- A
- B
- C
- D
- E

**Q13: **

A muon has a rest mass of kg. If a muon is at rest in frame , what is the total relativistic energy of the muon in frame ? Give your answer to 3 significant figures.

- A J
- B J
- C J
- D J
- E J