The Moon has a mass of 7.36 1022 kg and a radius of 1.74 106 m.
(a) What is the acceleration due to gravity on the Moon
b) How much would a 4.03 kg person weigh on this planet
i take constant G is mass of the moon divided by radius square it by 2
then the weight is the mass of the person is g, g is given by the answer of part a ????????????????
G is the universal constant of gravity. Use it together with M and R to calculate g' using the formula i gave you.
If you are unfamiliar with G, read
http://en.wikipedia.org/wiki/Gravitational_constant
a) Well, the Moon may not have the same kind of gravity as Earth, but it still knows how to pull its weight! The acceleration due to gravity on the Moon can be calculated using Newton's law of universal gravitation. So, the acceleration due to gravity on the Moon is approximately 1.62 m/s².
b) Ah, gravity on the Moon is a bit kinder to our bodies than good old Earth. So, if you were a 4.03 kg person on the Moon, you would weigh approximately 6.5 newtons. That's like getting an interstellar weight loss plan for free! Just be careful not to float away when you jump.
To find the acceleration due to gravity on the Moon, we can use the formula:
acceleration due to gravity (g) = G * (mass of the Moon) / (radius of the Moon)^2
where G is the gravitational constant.
(a) Substitute the given values into the formula to find the acceleration due to gravity on the Moon:
g = (6.67 × 10^-11 N*m^2/kg^2) * (7.36 × 10^22 kg) / (1.74 × 10^6 m)^2
Simplifying the equation:
g = (6.67 × 10^-11 N*m^2/kg^2) * (7.36 × 10^22 kg) / (3.03 × 10^12 m^2)
g ≈ 1.62 m/s^2
Therefore, the acceleration due to gravity on the Moon is approximately 1.62 m/s^2.
(b) To determine how much a 4.03 kg person would weigh on the Moon, we can use the formula:
weight = mass * acceleration due to gravity
Substitute the mass of the person and the acceleration due to gravity on the Moon into the formula:
weight = 4.03 kg * 1.62 m/s^2
weight ≈ 6.52 N
Therefore, a 4.03 kg person would weigh approximately 6.52 Newtons on the Moon.
(a) g' = GM/R^2 is the value on the Moon. You will need the value of the universal gravity constant G.
It should be about 1.6 m/s^2
(b) Weight (on Moon) = M g' (in Newtons)