Question

An astronaut with a mass of 91 kg is 0.30 m above the moons surface. The astronauts potential energy is 46 J. Calculate the free-fall acceleration on the moon?

Answer 1

The free-fall acceleration on the moon can be found using the formula for gravitational potential energy and the given values. It is approximately 1.685 m/s², which aligns with the known value of moon's gravity being about 1/6 of Earth's.

Step-by-step explanation:

To calculate the free-fall acceleration on the moon, we can use the formula for gravitational potential energy (PE), which is PE = mgh, where m is the mass of the astronaut, g is the acceleration due to gravity, and h is the height above the moon's surface. We know the astronaut's mass m is 91 kg, the potential energy PE is 46 J, and the height h is 0.30 m. The formula can be rearranged to solve for g: g = PE / (m*h).

Plugging in the known values, we get g = 46 J / (91 kg * 0.30 m) which yields an acceleration due to gravity g of approximately 1.685 m/s². This is about 1/6 of the gravity on Earth, which is expected, as the Moon has a much smaller mass than Earth does.

Answer 2

the free-fall acceleration on the moon is 1.68 m/s^2

Step-by-step explanation:

recall the formula for the gravitational potential energy (under acceleration of gravity "g"):

PE = m * g * h

replacing with our values for the problem:

46 J = 91 * g * 0.3

solve for the "g" on the Moon:

g = 46 / (91 * 0.3)

g = 1.68 m/s^2