Question

1. an astronaut with a mass of 110.0 kg visits the moon (which has a different gravitational force than earth). the astronaut climbs 5.0 m up the ladder into his spacecraft and gains 880.0 j in gpe. what is the strength of gravity on the moon?

Explanation:

Step1: Recall GPE formula

The formula for gravitational potential energy (GPE) is \( GPE = mgh \), where \( m \) is mass, \( g \) is the acceleration due to gravity (strength of gravity), and \( h \) is height. We need to solve for \( g \), so rearrange the formula: \( g=\frac{GPE}{mh} \).

Step2: Identify given values

We know \( m = 110.0\space kg \), \( h = 5.0\space m \), and \( GPE = 880.0\space J \).

Step3: Substitute values into formula

Substitute the values into \( g=\frac{GPE}{mh} \): \( g=\frac{880.0}{110.0\times5.0} \).

Step4: Calculate the result

First, calculate the denominator: \( 110.0\times5.0 = 550.0 \). Then, divide: \( g=\frac{880.0}{550.0}=1.6\space m/s^2 \).

Answer:

The strength of gravity on the moon is \( 1.6\space m/s^2 \).