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: extra mass = 𝑚 𝑚 = ( 𝛾 1 ) 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).

  • A 3 . 2 9 × 1 0 kg
  • B 2 . 1 9 × 1 0 kg
  • C 6 . 9 1 × 1 0 kg
  • D 80.0 kg
  • E 69.3 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 .

  • A 0 . 9 𝑐
  • B 0 . 8 𝑐
  • C 0 . 5 𝑐
  • D 0 . 1 𝑐
  • E 0 . 6 𝑐

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 . 9 9 9 𝑐 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 . 0 5 𝑐 . 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 . 6 𝑐 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?

  • AInfinite
  • B 40 kg
  • C 0 kg
  • D 4 kg
  • E 4,000,000 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 0 . 7 4 1 𝑐
  • B 0 . 3 2 6 𝑐
  • C 0 . 8 8 9 𝑐
  • D 0 . 9 9 2 𝑐
  • E 0 . 9 4 3 𝑐

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