Question

Hew much eneray is required to accelerate a spaceship with a rest mass of 122 metric tons to a speed of 0.439 c? Hints: In the acceleration process the energy we have is converted to the kinetic energ

Answer 1

To determine the energy required to accelerate the spaceship, we can use the formula for kinetic energy and calculate the rest mass energy using Einstein's equation. By plugging in the values, we can find the energy needed to achieve the desired speed.

Step-by-step explanation:

To calculate the energy required to accelerate the spaceship, we need to use the formula:

Kinetic Energy (KE) = (γ - 1) × Rest Mass Energy (E0)

Given that the rest mass of the spaceship is 122 metric tons and the speed is 0.439 c, we can calculate the Lorentz factor (γ) using the formula:

γ = 1 / √(1 - (v/c)2)

Plugging in the values, we find γ ≈ 1.153.

Next, we can calculate the rest mass energy E0 using Einstein's famous equation:

E0 = m × c2

where m is the rest mass in kg and c is the speed of light (3 × 108 m/s).

Converting the rest mass of the spaceship to kg (1 metric ton = 1000 kg), we find m = 122 × 1000 kg.

Calculating E0, we get E0 ≈ (122 × 103 kg) × (3 × 108 m/s)2.

Finally, plugging in the values into the kinetic energy formula, we have:

KE = (1.153 - 1) × (122 × 103 kg) × (3 × 108 m/s)2

Calculating the expression gives us the energy required to accelerate the spaceship.