when on earth, an astronaut steps on a scale and notices their weight is 784N. when they step on the same scale on the moon, it tells them their weight is 130N. determine the gravitational field strength on the moon.
To determine the gravitational field strength on the moon, we need to use the formula:
Weight = mass × gravitational field strength
We have the weight on both Earth (784N) and the moon (130N), and we can assume that the astronaut's mass remains the same in both situations. Therefore, we can set up the following equation:
784N = mass × gravitational field strength on Earth
130N = mass × gravitational field strength on the moon
Dividing the second equation by the first equation, we can find the ratio of the gravitational field strengths:
130N / 784N = (mass × gravitational field strength on the moon) / (mass × gravitational field strength on Earth)
0.1656 = (gravitational field strength on the moon) / (gravitational field strength on Earth)
Rearranging the equation, we find:
gravitational field strength on the moon = 0.1656 × gravitational field strength on Earth
We can substitute the standard gravitational field strength on Earth, which is approximately 9.8 m/s², into the equation:
gravitational field strength on the moon = 0.1656 × 9.8 m/s² ≈ 1.61688 m/s²
Therefore, the gravitational field strength on the moon is approximately 1.62 m/s².