A proton's rest mass is 1.67 × 10−27 kg. Calculate its total energy when it is accelerated to a speed of 0.80c.
A)1.5 × 10−10 J
B)1.0 × 10−10 J
C)2.5 × 10−10 J
D)2.0 × 10−10 J
E)7.5 × 10−10 J

Question

Quizplus · Accepted Answer

We can use the relativistic equation for energy: $E = \gamma mc^2$, where $\gamma$ is the relativistic factor given by $\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$.

Plugging in the values given, we get:

$v = 0.80c$
$m = 1.67 	imes 10^{-27} 	ext{ kg}$

First, we can calculate $\gamma$:

$$\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} = \frac{1}{\sqrt{1-0.8^2}} = 1.67$$

Then, we can calculate the total energy:

$$E = \gamma mc^2 = 1.67 	imes 1.67 	imes 1.99 	imes 10^{-8} 	ext{ J} = 4.13 	imes 10^{-8} 	ext{ J} \approx 2.5 	imes 10^{-10} 	ext{ J}$$

Therefore, the best answer choice is C) 2.5 × 10−10 J.

A Proton's Rest Mass Is 1