Question

The mass of a spaceship is 1000 kg. It is to be launched from the Earth's surface out into free space. The value of 'g' and 'r' (radius of Earth) are 10 m/s² and 6400 km, respectively. The required energy for this work will be:

(a) 3.2 x 10¹¹ J
(b) 4.0 x 10¹¹ J
(c) 5.0 x 10¹¹ J
(d) 6.4 x 10¹¹ J

Answer 1

The required energy to launch the spaceship is (d) 6.4 x 10^10 J.

Step-by-step explanation:

To calculate the required energy to launch a spaceship into space, we can use the concept of work. The work done is equal to the change in potential energy.

The potential energy of the spaceship on the surface of the Earth can be calculated using the formula: PE = mgh, where m is the mass of the spaceship, g is the acceleration due to gravity, and h is the height above the surface of the Earth.

In this case, the height h is equal to the radius of the Earth, r. So the potential energy is given by: PE = mgh = mgr.

Substituting the values given, we have: PE = (1000 kg)(10 m/s²)(6.4 × 10⁶ m) = 6.4 × 10¹⁰ J.

Therefore, the required energy for this work is 6.4 × 10¹⁰ J, which is option (d).