Question

How many joules of energy are required to accelerate one kilogram of mass from rest to a velocity of 0.866c?

Answer 1

Answer:

the amount of energy needed is 1.8 x 10¹⁷ J.

Explanation:

Given;

mass of the object, m₀ = 1 kg

velocity of the object, v = 0.866 c

By physics convection, c is the speed of light = 3 x 10⁸ m/s

The energy needed is calculated as follows;

E = Mc²

As the object approaches the speed of light, the change in the mass of the object is given by Einstein's relativity formula;

$M = \frac{M_0}{\sqrt{1- \frac{v^2}{c^2} } } \\\\ M = \frac{1}{\sqrt{1- \frac{(0.866c)^2}{c^2} } }\\\\ M = \frac{1}{\sqrt{1- \frac{0.74996c^2}{c^2} } }\\\\ M = \frac{1}{\sqrt{0.25} } \\\\ M = 2 \ kg$

The energy required is calculated as;

E = 2 x (3 x 10⁸)²

E = 1.8 x 10¹⁷ J

Therefore, the amount of energy needed is 1.8 x 10¹⁷ J.