How many joules of energy are required to accelerate a $1.0 - \mathrm { kg }$ rock from rest to a speed of $0.866 c$ ? ( $c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s }$ )
A) $9.0 \times 10 ^ { 16 } \mathrm {~J}$
B) $3.0 \times 10 ^ { 3 } \mathrm {~J}$
C) $3.3 \times 10 ^ { 16 } \mathrm {~J}$
D) $1.8 \times 1017 \mathrm {~J}$

Question

Quizplus · Accepted Answer

To find the energy required to accelerate the rock, we use the relativistic energy formula: $E = \gamma mc^2 - mc^2$, where $\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}$. For $v = 0.866c$, $\gamma$ calculates to 2. Therefore, $E = (2 - 1)mc^2 = mc^2 = (1.0 \, \text{kg}) \times (3.0 \times 10^8 \, \text{m/s})^2 = 9.0 \times 10^{16} \, \text{J}$.

How Many Joules of Energy Are Required to Accelerate A 1.0