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 0 . 1 𝑐 in frame 𝑆 . What is its total relativistic energy in frame 𝑆 ? Give your answer to 3 significant figures.

  • A 6 . 7 0 × 1 0 J
  • B 1 . 8 1 × 1 0 J
  • C 9 . 4 9 × 1 0 J
  • D 1 . 9 0 × 1 0 J
  • E 9 . 0 5 × 1 0 J

Q2:

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

  • A 1 . 8 × 1 0 joules
  • B 2 . 3 × 1 0 joules
  • C 6 . 0 × 1 0 joules
  • D 6 . 0 × 1 0 joules
  • E 1 . 8 × 1 0 joules

Q3:

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

Q4:

An electron moves at a speed 𝑣 along a linear particle accelerator. Its mass in the rest frame of the particle accelerator is measured to be 1,560 keV/c2. What is its total relativistic energy in the rest frame of the particle accelerator?

Q5:

The graph shows the total relativistic energy, 𝐸 , of an object against its speed, 𝑣 . The speed of light, 𝑐 , is defined to be 1. If the object is moving at a speed of 0 . 8 𝑐 in frame 𝑆 , what is its mass in frame 𝑆 ?

Q6:

A proton has a rest mass of 938 MeV/ 𝑐 . In frame 𝑆 , a proton is moving at a speed of 0 . 6 𝑐 . What is the total relativistic energy of the proton in frame 𝑆 ? Give your answer to three significant figures.

Q7:

A metal cube is moving at a speed of 0 . 8 𝑐 in frame 𝑆 . Its total relativistic energy as measured in frame 𝑆 is 7 . 5 × 1 0 J . What is the rest mass of the cube? Give your answer to the nearest kilogram.

Q8:

A proton has a rest mass of 9 3 8 / 𝑐 M e V . 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, 𝑐 , and to three significant figures.

  • A 0 . 9 9 9 𝑐
  • B 0 . 9 6 8 𝑐
  • C 0 . 9 7 4 𝑐
  • D 0 . 9 1 2 𝑐
  • E 0 . 9 3 8 𝑐

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 0 . 2 𝑐 . What is the rest mass of an electron? Give your answer to 3 significant figures in k e V / 𝑐 .

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