Question

A bag of sugar has a mass of 7.86 kg. a. What is its weight in newtons on the moon, where the acceleration due to gravity is one-sixth that on earth? b. What is its weight on Jupiter, where the acceleration due to gravity is 2.64 times that on earth?

Answer 1

The bag weighs 77.0 N on Earth, 12.84 N on the Moon and 203.35 N on Jupiter.

Explanation:

Whenever we are asked to determine the weight of an object based on its mass, the relation is

`W=mxxg`

where `W` is the weight and `g` is the acceleration due to gravity in the location where the mass `m` is found.

So, if `g` on the moon is `1/6` of the value of `g` on Earth (which is `9.8m/s^2`, the weight on the Moon is

`W= (1/6)(9.8)(7.86) = 12.84 N`

and on Jupiter

`W= (2.64)(7.86)(9.8) = 203.35 N`

By the way, it is also common to call `g` the strength of the gravitational field in a location. Its units are N/kg (notice how this ultimately simplifies to `m"/"s^2`), which ties in nicely with the question here.

Answer 2

`W_m=mg_m=7.86*1.635~~12.85N`
`W_j=mg_j=7.86*25.8984~~203.56N`

Explanation:

The equation for weight is `W=mg`, where:

• `W` = Weight (`N`)
• `m` = mass (`kg`)
• `g` = acceleration due to gravity (`ms^(-2)`)

On Earth, `g=9.81ms^(-2)`

For the Moon, `g_m=g/6=1.635ms^(-2)`

For Jupiter, `g_j=2.64g=25.8984ms^(-2)`

`W_m=mg_m=7.86*1.635~~12.85N`
`W_j=mg_j=7.86*25.8984~~203.56N`