# Worksheet: Relativistic Mass

In this worksheet, we will practice calculating the increase in the mass of an object as it moves at greater speeds relative to an observer.

**Q1: **

Person A is sitting on a train that is moving at 80 km/h. Person B is standing next to the train tracks. The following formula can be used to calculate how much extra mass person A appears to have, as perceived by person B: .

If person A has a rest mass, , of 80 kg, how much extra mass are they perceived to have by person B? Give your answer to 3 significant figures (the answer will be very small, but not zero).

- A kg
- B kg
- C69.3 kg
- D kg
- E80.0 kg

**Q2: **

The graph shows relativistic mass, , against rest mass, , for objects moving at speed relative to an observer. What is the value of ? Give your answer as a multiple of .

- A
- B
- C
- D
- E

**Q3: **

What is the mass, as measured by an observer, of a metal sphere that has a rest mass of 2.00 kg and is moving at relative to the observer? Give your answer, in kilograms, to 3 significant figures.

**Q4: **

A space probe has a mass of 700.00 kg in its rest frame. The space probe is moving away from Earth at a speed of . What is the mass of the space probe in the rest frame of Earth? Give your answer to 5 significant figures.

**Q5: **

A spaceship moving away from Earth at a speed of has a mass of 250,000 kg in the rest frame of Earth. What is the mass of the spaceship in its rest frame?

**Q6: **

At how many meters per second slower than the speed of light would an object have to move in order to have a relativistic mass 10,000 times greater than its rest mass? Give your answer to 3 significant figures.

**Q7: **

What would the mass of an object that has a rest mass of 4 kg be if it were moving at the speed of light?

- A40 kg
- BInfinite
- C4 kg
- D0 kg
- E4,000,000 kg

**Q8: **

How fast must an object be traveling in a given reference frame for its mass in that reference frame to be three times its rest mass? Give your answer as a multiple of the speed of light to three significant figures.

- A
- B
- C
- D
- E

**Q9: **

A kaon in a particle accelerator is observed to have a mass of . The kaon moves at along the accelerator. What is the rest mass of the kaon? Give your answer in mega-electron volts per speed of light squared () to 3 significant figures.

**Q10: **

A muon produced in a cosmic-ray shower has a speed of relative to a particle detector on Earth. A muon has a mass of in its rest frame. What is the mass of the muon in the rest frame of the particle detector? Give your answer in mega-electron volts per speed of light squared () to 3 significant figures.

- A
- B
- C
- D
- E