# True mass, different weights, and the force of gravity

1. Oct 17, 2011

### sdoi

1. The problem statement, all variables and given/known data
An astronaut enters a rocket ship and gets blasted to another planet. The mass of the planet is 2.5 times as large as the mass of Earth, and the radius is 1.2 times as large as Earth's. If the astronauts scale at home says "60.0kg", what will it say on the new planet? In which case does the scale display his true mass and why?

2. Relevant equations
F=mg/r^2

3. The attempt at a solution
i was able to find the weight of the astronaut on the new planet without any problems:
m(planet)= m(earth) x 2.5
m(planet)= 1.48x10^25 kg

r(planet)= r(earth) x 1.2
r(planet)= 7.65x10^6m

find mass of astronaut:
F=Gm/r^2
g=Gm/r^2
= (6.67x10^-11)(5.97x10^24)/ (6.38x10^6)^2
=9.8N/kg
m= 60.0kg/ 9.8N/kg
m=6.12N

g= Gm/r^2
= (6.67x10^-11)(1.49x10^25)/ (7.65x10^6)^2
= 16.9 N/kg

W=mg
= (6.12N)(16.9 N/kg)
Therefore the atronaut would read 103.4kg on the scale while on the new planet.

For the second part of the question i'm just a little confussed. It asks which scale displays his true mass, but a scale doesn't display mass, it displays weight. Is this part a trick question?

2. Oct 18, 2011

### susskind_leon

I would say the scale shows the true mass on earth. In fact, it measures weight, but from the measured weight, it calculated the mass and shows it. But it works only on earth.