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.
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
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 .
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.
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.
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?
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.
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
- C4 kg
- D0 kg
- E4,000,000 kg
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 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.
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.