If a man wewighs 41 newtons (N) on the surface of the earth while he weighs 81.5N on the surface of the moon, approximately how much lighter is he on the moon? What would be his weight on the surface of the earth if he weighs 90 N on the surface of the moon?

Are you sure it's 81.5 N on the surface of the moon?

#1. Anyway, what we'll do is first get the mass of the man. Note that mass is constant, and in physics, it is different from the term 'weight' (though in other cases, they are interchangeable, like in chemistry).
W = mg
where
W = weight (in Newton)
m = mass (in kg)
g = acceleration due to gravity (on Earth) = 9.8 m/s^2

On Earth,
41 = m * 9.8
m = 4.18 kg

On Moon, we'll solve for acceleration due to gravity of moon:
81.5 = 4.18 * g,moon
g,moon = 19.5 m/s^2
How much lighter is he on the moon? If it means the mass, then his mass is constant and he is neither heavier nor lighter on the moon.

#2. Given his weight on the moon, solve for the mass using the g,moon.
90 = m * 19.5
m = 4.62 kg
Thus, his weight on the earth is
W = 4.62 * 9.8
W = 45.3 N

Hope this helps :3

Thank you so much Jai. You explained it very well:)

To calculate how much lighter the man is on the moon compared to the Earth, we need to find the difference between his weight on each surface.

First, find the difference in weight between the man on the moon and the man on Earth:
Weight on the moon = 81.5 N
Weight on Earth = 41 N

Difference = Weight on the moon - Weight on Earth
Difference = 81.5 N - 41 N
Difference = 40.5 N

Therefore, the man is approximately 40.5 Newtons lighter on the moon than on Earth.

To find the man's weight on Earth if he weighs 90 N on the moon, we need to determine the relationship between the weight on Earth and the weight on the moon. We can use the concept of gravity.

The acceleration due to gravity on the moon is approximately 1/6th that of Earth's gravity. So, we can use this ratio to convert the weight on the moon to the weight on Earth.

Weight on the moon = 90 N
Weight on Earth = ?

The weight on the moon is 1/6th that on Earth, so we can express it as a ratio:
Weight on the moon / Weight on Earth = 1/6

Substituting the values:
90 N / Weight on Earth = 1/6

To find the weight on Earth, we can cross-multiply and solve for Weight on Earth:
Weight on Earth = (90 N * 6) / 1
Weight on Earth = 540 N

Therefore, the man would weigh 540 Newtons on the surface of the Earth if he weighs 90 N on the surface of the moon.