# 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?

Nov 8, 2017

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

$W = m \times g$

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 $\frac{1}{6}$ of the value of $g$ on Earth (which is $9.8 \frac{m}{s} ^ 2$, the weight on the Moon is

$W = \left(\frac{1}{6}\right) \left(9.8\right) \left(7.86\right) = 12.84 N$

and on Jupiter

$W = \left(2.64\right) \left(7.86\right) \left(9.8\right) = 203.35 N$

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 $m \text{/} {s}^{2}$), which ties in nicely with the question here.

Nov 8, 2017

${W}_{m} = m {g}_{m} = 7.86 \cdot 1.635 \approx 12.85 N$
${W}_{j} = m {g}_{j} = 7.86 \cdot 25.8984 \approx 203.56 N$

#### Explanation:

The equation for weight is $W = m g$, where:

• $W$ = Weight ($N$)
• $m$ = mass ($k g$)
• $g$ = acceleration due to gravity ($m {s}^{- 2}$)

On Earth, $g = 9.81 m {s}^{- 2}$

For the Moon, ${g}_{m} = \frac{g}{6} = 1.635 m {s}^{- 2}$

For Jupiter, ${g}_{j} = 2.64 g = 25.8984 m {s}^{- 2}$

${W}_{m} = m {g}_{m} = 7.86 \cdot 1.635 \approx 12.85 N$
${W}_{j} = m {g}_{j} = 7.86 \cdot 25.8984 \approx 203.56 N$