# Math - Algebra

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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?

• Math - Algebra -

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

• Math - Algebra -

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

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