# Worksheet: Relativistic Energy

In this worksheet, we will practice calculating the kinetic energy of objects moving at speeds large enough such that relativistic effects need to be taken into account.

**Q1: **

A Van de Graaff accelerator utilizes a 50.0 MV potential difference to accelerate charged particles such as protons. The kinetic energy provided by such a large potential difference is sufficiently great that relativistic effects need to be taken into account when finding the velocity of accelerated particles.

What is the velocity of a proton accelerated by such a potential?

- A
- B
- C
- D
- E

What is the velocity of an electron accelerated by such a potential?

- A
- B
- C
- D
- E

**Q7: **

K mesons have an average lifetime in their rest frame of s. Plans for an accelerator that produces a secondary beam of K mesons to scatter from nuclei, for the purpose of studying the strong force, call for them to have a kinetic energy of 500 MeV.

What would the relativistic quantity be for these particles?

What would be the average lifetime of these particles, as measured by a laboratory based observer?

- A s
- B s
- C s
- D s
- E s

How far would these particles travel during their average lifetime, as measured by a laboratory based observer?

**Q10: **

A neutral kaon is a particle that decays into two -mesons. The kaon has a rest mass energy of 497.6 MeV and muons have a rest mass energy of 105.7 MeV. Suppose the kaon is at rest and all the missing mass goes into the muons’ kinetic energy. Assuming energy is shared equally between the two muons, how fast will the muon move?

- A
- B
- C
- D
- E

**Q11: **

A positron is an antimatter version of the electron, having the same mass. When a positron and an electron meet, they annihilate converting all their mass into energy.

Find the energy released, assuming negligible kinetic energy before the annihilation.

If the annihilation energy released is given to a proton in the form of kinetic energy, what is the proton’s velocity?

- A
- B
- C
- D
- E

If the annihilation energy released is given to an electron in the form of kinetic energy, what is the electron’s velocity?

- A
- B
- C
- D
- E

**Q15: **

When an electron and a positron collide in a linear accelerator, they each have a kinetic energy of 48.5 GeV. What is the total collision energy available? Assume that the energy produced from the annihilation of the two particles is negligible.

- A 146 GeV
- B 48.5 GeV
- C 24.3 GeV
- D 20.6 GeV
- E 97.0 GeV

**Q16: **

An electron’s rest energy can be measured in either joules or electron volts.

Find the rest energy of an electron in joules, precise to three significant figures.

- A J
- B J
- C J
- D J
- E J

Find the rest energy of an electron in mega-electron volts, precise to three significant figures.

- A MeV
- B MeV
- C MeV
- D MeV
- E MeV

**Q19: **

The energy released from the fission of uranium by a Hiroshima-sized bomb containing 1.00 kg of uranium is J.

Calculate the mass converted to energy by the fission reaction.

- A kg
- B kg
- C kg
- D kg
- E kg

What is the ratio of mass of the uranium destroyed by the fission reaction to the original mass of the uranium in the bomb?

- A
- B
- C
- D
- E