Question

Physics HELP!!!!! On the surface of the Moon an astronaut has a weight of Fg = 140 N. The radius of the Moon is Rm = 1.74 x 106 m, the gravitational constant is G = 6.67 x 10-11 N m2kg2 and the mass of the Moon is Mm = 7.35 x 1022 kg. Solve numerically for the mass of the astronaut ma in kg.

Answer 1

Mass of the astronaut is 86.45 kg

Step-by-step explanation:

It is given that,

Weight on the surface of astronaut,
`F_g=140\ N`

The radius of the moon is,
`R_m=1.74* 10^6\ m`

The gravitational constant is,
`G=6.67* 10^(-11)\ Nm^2/kg^2`

Mass of the moon,
`m_1=7.35* 10^(22)\ kg`

We need to find the mass of the astronaut. It can be calculated using the formula as :

`F=G(m_1m_2)/(R^2)`

m₂ = mass of the astronaut

`m_2=(FR^2)/(Gm_1)`

`m_2=(140\ N* (1.74* 10^6\ m)^2)/(6.67* 10^(-11)\ Nm^2/kg^2* 7.35* 10^(22)\ kg)`

m₂ = 86.45 kg

So, the mass of the astronaut is 86.45 kg. Hence, this is the required solution.