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: extramass=𝑚𝑚=(𝛾1)𝑚.

If person A has a rest mass, 𝑚, 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).

  • A3.29×10 kg
  • B2.19×10 kg
  • C69.3 kg
  • D6.91×10 kg
  • E80.0 kg

Q2:

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

  • A0.1𝑐
  • B0.9𝑐
  • C0.8𝑐
  • D0.5𝑐
  • E0.6𝑐

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 0.999𝑐 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 0.05𝑐. 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 0.6𝑐 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.

  • A0.992𝑐
  • B0.326𝑐
  • C0.943𝑐
  • D0.741𝑐
  • E0.889𝑐

Q9:

A kaon in a particle accelerator is observed to have a mass of 823/𝑐MeV. The kaon moves at 0.8𝑐 along the accelerator. What is the rest mass of the kaon? Give your answer in mega-electron volts per speed of light squared (MeV/𝑐) to 3 significant figures.

Q10:

A muon produced in a cosmic-ray shower has a speed of 0.2𝑐 relative to a particle detector on Earth. A muon has a mass of 106/𝑐MeV 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 (MeV/𝑐) to 3 significant figures.

  • A102/𝑐MeV
  • B103/𝑐MeV
  • C108/𝑐MeV
  • D116/𝑐MeV
  • E106/𝑐MeV

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