Question

An astronaut's pack weighs 13.5 when she is on earth but only 3.97 when she is at the surface of an asteroid. What is the acceleration due to gravity on this asteroid? What is the mass of the pack on the asteroid?

Answer 1

[I'm assuming the weights are in Newtons]

Given:
F = Force of gravity
m = mass
a = acceleration
g = acceleration due to gravity = 9.81m/s^2

Newton's second law:
\[\large F=ma=>F_{gravity}=mg=\text{'weight'}\]
Plug in the values given for Earth to calculate the mass:\[\large 13.5N = m(9.81m/s^2)\]\[\large m=\text{~}1.38kg\]
**The mass of the backpack will be exactly the same on the asteroid.**

The difference in forces (13.5N versus 3.97N) is related to the differences in the acceleration due to gravity for each object. If you want to calculate the acceleration due to gravity on the asteroid you can simply plug in the mass to get:\[\large a_{asteroid}=\frac{F}{m}=\frac{3.97N}{1.38kg}=2.88m/s^2\]