According to the theory of relativity, as an object approaches the speed of light, its mass appears to increase from the perspective of an observer at rest relative to the object. This effect is known as relativistic mass.
The formula to calculate relativistic mass is given by:
m' = m / sqrt(1 - (v^2/c^2))
Where: m' is the relativistic mass, m is the rest mass (mass at rest), v is the velocity of the object, and c is the speed of light.
In this case, let's consider a 1-kilogram object with a velocity of 0.999c (99.9% of the speed of light):
v = 0.999c m = 1 kg c = speed of light
Plugging these values into the formula, we can calculate the relativistic mass:
m' = 1 kg / sqrt(1 - (0.999c)^2/c^2)
Simplifying the equation:
m' = 1 kg / sqrt(1 - 0.998^2)
m' = 1 kg / sqrt(1 - 0.996004)
m' = 1 kg / sqrt(0.003996)
m' = 1 kg / 0.063227
m' ≈ 15.8 kg
Therefore, at 99.9% of the speed of light, the relativistic mass of a 1-kilogram object would be approximately 15.8 kilograms. It's important to note that relativistic mass is a concept used within the framework of relativity, and it is different from the rest mass (mass at rest) which remains constant regardless of the object's velocity.