Question

An astronaut aboard the International Space Station, which is orbiting at an altitude of 4.00 x 105 m above the Earth's surface, has a gravitational potential energy of 2.94 x 106 J. What is the weight of the astronaut when he returns to the Earth's surface

Answer 1

The weight of the astronaut is 0.4802 N.

Step-by-step explanation:

Gravitational potential energy,
`U=2.94* 10^6\ J`

Distance above earth,
`d=4* 10^5\ m`

The gravitational potential energy is given by :

`U=(GMm)/(R)`

G is universal gravitational constant

M is the mass of Earth,
`M=5.97* 10^(24)\ kg`

m is mass of astronaut

R is the radius of earth, R = R + d

`R=6.37* 10^6\ m+4* 10^5\ m=6770000\ m`

`m=(U(R+d)^2)/(GM)`

`m=(2.94* 10^6\ J* (6770000\ m))/(6.67* 10^(-11)* 5.97* 10^(24)\ kg)`

m = 0.049 kg

The weight of the astronaut is given by :

W = mg

`W=0.049\ kg* 9.8\ m/s^2`

W = 0.4802 N

So, the weight of the astronaut when he returns to the earth surface is 0.4802 N. Hence, this is the required solution.