Question

the gravitational force of a lunar rover is 1,607.2 newtons on earth. what will the rover’s gravitational force be on the moon?

on earth, g = 9.8m/s².
on the moon, g = 1.62 m/s².

(1 point)

○ 265.7 n

○ 992.1 n

○ 164 n

○ 2,603.7 n

Explanation:

Step1: Recall the formula for gravitational force

The formula for gravitational force is \( F = mg \), where \( F \) is the force, \( m \) is the mass, and \( g \) is the acceleration due to gravity. First, we need to find the mass of the lunar rover using the information on Earth.
Given \( F_{Earth} = 1607.2 \, N \) and \( g_{Earth} = 9.8 \, m/s^2 \), we can solve for mass \( m \) using \( m=\frac{F_{Earth}}{g_{Earth}} \).
So, \( m = \frac{1607.2}{9.8} \).
Calculating that: \( \frac{1607.2}{9.8}=164 \, kg \).

Step2: Calculate the gravitational force on the Moon

Now that we have the mass \( m = 164 \, kg \), we can find the gravitational force on the Moon using \( F_{Moon}=m\times g_{Moon} \).
Given \( g_{Moon} = 1.62 \, m/s^2 \), so \( F_{Moon}=164\times1.62 \).
Calculating that: \( 164\times1.62 = 265.68\approx265.7 \, N \).

Answer:

265.7 N