Question

Suppose 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 10^8 m/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) 149,000 kg
b) 150,000 kg
c) 151,000 kg
d) 152,000 kg

Answer 1

The relativistic mass of the space vehicle is approximately 259,800 kg.

Step-by-step explanation:

To determine the relativistic mass of the space vehicle, we can use the formula for relativistic mass:

m = γ * m0

Where m is the relativistic mass, γ is the Lorentz factor, and m0 is the rest mass. The Lorentz factor can be calculated using the formula:

γ = 1 / sqrt(1 - (v^2 / c^2))

Where v is the speed of the space vehicle and c is the speed of light. Plugging in the given values, we get:

v = 2.6 x 10^8 m/s

c = 3 x 10^8 m/s

m0 = 150,000 kg

Calculating γ:

γ = 1 / sqrt(1 - ((2.6 x 10^8)^2 / (3 x 10^8)^2))

γ ≈ 1.732

Now, calculating the relativistic mass:

m = γ * m0

m ≈ 1.732 * 150,000 kg ≈ 259,800 kg

Therefore, the relativistic mass of the space vehicle is approximately 259,800 kg.