Situation 27.1
A proton (rest energy = 938 MeV)has a speed of 0.80 c.
-In Situation 27.1,the ratio of the kinetic energy of the proton to its rest energy is closest to:
A)0.60
B)0.67
C)0.80
D)1.2
E)1.7

Question

Quizplus · Accepted Answer

The ratio of the kinetic energy of a particle to its rest energy can be calculated using the formula:

K/E₀ = (γ - 1)

where K is the kinetic energy, E₀ is the rest energy, and γ is the Lorentz factor:

γ = 1/√(1 - v²/c²)

In Situation 27.1, the proton has a speed of 0.80 c, so its Lorentz factor is:

γ = 1/√(1 - 0.80²) ≈ 1.67

Therefore, the ratio of the kinetic energy to the rest energy is:

K/E₀ ≈ (1.67 - 1) ≈ 0.67

Thus, the closest answer choice is B) 0.67.

Situation 27.1 a Proton (Rest Energy = 938 MeV)has a Speed of Speed