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 0.1𝑐 in frame 𝑆. What is its total relativistic energy in frame 𝑆? Give your answer to 3 significant figures.

  • A6.70×10 J
  • B9.05×10 J
  • C9.49×10 J
  • D1.90×10 J
  • E1.81×10 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?

  • A6.0×10 joules
  • B6.0×10 joules
  • C1.8×10 joules
  • D1.8×10 joules
  • E2.3×10 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 0.8𝑐 in frame 𝑆, what is its mass in frame 𝑆?

Q6:

A proton has a rest mass of 938/𝑐MeV. In frame 𝑆, a proton is moving at a speed of 0.6𝑐. 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 0.8𝑐 in frame 𝑆. Its total relativistic energy as measured in frame 𝑆 is 7.5×10J. What is the rest mass of the cube? Give your answer to the nearest kilogram.

Q8:

A proton has a rest mass of 938/𝑐MeV. 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.

  • A0.938𝑐
  • B0.974𝑐
  • C0.912𝑐
  • D0.999𝑐
  • E0.968𝑐

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 0.2𝑐. What is the rest mass of an electron? Give your answer to 3 significant figures in keV/𝑐.

Q11:

In frame 𝑆, a spaceship has a total relativistic energy of 4.5×10 J. What is the mass of the spaceship as measured in frame 𝑆?

  • A3.0×10 kg
  • B6.0×10 kg
  • C1.5×10 kg
  • D10×10 kg
  • E5.0×10 kg

Q12:

A spaceship with a rest mass of 40,000 metric tons has a total relativistic energy of 3.6045×10 J in frame 𝑠. How fast is the spaceship moving in frame 𝑠? Give your answer to three significant figures.

  • A0.0500𝑐
  • B0.00250𝑐
  • C0.0186𝑐
  • D0.0353𝑐
  • E0.0266𝑐

Q13:

A muon has a rest mass of 1.89×10 kg. If a muon is at rest in frame 𝑆, what is the total relativistic energy of the muon in frame 𝑆? Give your answer to 3 significant figures.

  • A5.67×10 J
  • B1.89×10 J
  • C1.70×10 J
  • D2.12×10 J
  • E3.40×10 J

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