Question

Just before it landed on the moon, the Apollo 12 lunar lander had a mass of 1.0×10⁴ kg. What rocket thrust was necessary to have the lander touchdown with zero acceleration?

Answer 1

The necessary rocket thrust for the Apollo 12 lunar lander to touchdown on the moon with zero acceleration is calculated using Newton's Second Law and the lunar gravity, resulting in a thrust of 16,000 N.

Step-by-step explanation:

The question asks what rocket thrust is necessary for the Apollo 12 lunar lander, with a mass of 1.0×10⁴ kg, to touchdown on the moon with zero acceleration. To find this, we need to use the concept of Newton's Second Law of Motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma).

Now, if the lunar lander is to touchdown with zero acceleration, the only force acting on it would be its weight due to the moon's gravity, which is the mass of the lander multiplied by the acceleration due to gravity on the moon. The acceleration due to gravity on the moon is about 1.6 m/s². So the necessary thrust (T) that the engines must provide to counteract this force is T = mass × gravity = 1.0×10⁴ kg × 1.6 m/s² = 1.6×10⁴ N. Hence, a thrust of 16,000 N is necessary for a zero acceleration touchdown.