Question

A space vehicle with a rest mass of 150,000 kg travels past the International Space Station at a constant speed of (2.6 X 10^8m/s) with respect to the I.S.S. When an observer on the I.S.S. measures the moving vehicle, her measurement of the space vehicle length is 25.0 m. Determine the relativistic mass of the space vehicle.

A) (1.5 X 10^5kg)
B) (1.8 X 10^5kg)
C) (2.1 X 10^5kg)
D) (2.4 X 10^5kg)

Answer 1

The relativistic mass of the space vehicle is approximately 150,012 kg.

Step-by-step explanation:

To determine the relativistic mass of the space vehicle, we will use the equation for relativistic length contraction. The formula for relativistic length contraction is given by:

L′=L√(1−(v^2/c^2))

Where L is the rest length, L' is the measured length, v is the relative velocity, and c is the speed of light. Plugging in the values, we have:

L′=25.0m√(1−((2.6×10^8)^2/(3×10^8)^2))

L′≈24.998m

So, the measured length of the space vehicle is 24.998 m. Comparing this to the rest length, we can calculate the relativistic factor γ as:

γ=L/L′

γ=25.0m/24.998m

γ≈1.00008

The relativistic mass can then be calculated as:

m_rel=γm_rest

m_rel=1.00008(150,000kg)

m_rel≈150,012kg

Therefore, the relativistic mass of the space vehicle is approximately 150,012 kg.