Question

Suppose the mass of a fully loaded module in which astronauts take off from the Moon is 10,000 , {kg}. The thrust of its engines is 30,000 , {N}. (a) Calculate the magnitude of acceleration in a vertical takeoff from the Moon. (b) Could it lift off from Earth? If not, why not? If it could, calculate the magnitude of its acceleration.

The magnitude of acceleration during takeoff from the Moon is approximately:
a) 1.00 , {m/s}²
b) 2.00 , {m/s}²
c) 3.00 , {m/s}²
d) 4.00 , {m/s}²

Answer 1

The magnitude of acceleration of the module during a vertical takeoff from the Moon is 3.00 m/s², which corresponds to option c). The module could not lift off from Earth as the thrust is insufficient to overcome Earth's stronger gravity.

Step-by-step explanation:

To determine the magnitude of acceleration of the module during a vertical takeoff from the Moon, we use Newton's second law of motion, which states that force equals mass times acceleration (F = ma). Given that the mass (m) of the module is 10,000 kg and the thrust (F) provided by its engines is 30,000 N, we can rearrange the equation to solve for acceleration (a) as follows: a = F / m.

By substituting the given values, the acceleration will be a = 30,000 N / 10,000 kg = 3 m/s2. Therefore, the correct option is c) 3.00 m/s2.

Regarding the possibility of the module lifting off from Earth, it's important to compare the thrust of the engines to the weight of the module on Earth. The gravitational force on Earth is stronger than on the Moon, and Earth's gravity (g) is approximately 9.81 m/s2. The weight of the module on Earth would be W = m * g = 10,000 kg * 9.81 m/s2 = 98,100 N, which is greater than the thrust of the engines. Hence, the module could not lift off from Earth because the thrust is insufficient to overcome the gravitational pull of Earth.