# How much would a 2000 N car weigh on the Moon?

Jul 19, 2018

$300 N$

#### Explanation:

A car that weighs $2000 N$ on the Earth must weigh:

$F = m a$

$\frac{2000 N}{9.8 \frac{m}{s} ^ 2} = 204.08 k g$

So it's weight on moon would be:
$\left(204.08 k g\right) \left(1.6 \frac{m}{s} ^ 2\right) \approx 300 N$ reported with 1 sig fig

$331.2946 \setminus N$

#### Explanation:

The weight $W$ of any body of mass $m$ (universally constant) under the acceleration due to gravity $g$ is given as

$W = m g$

Now, given that weight of car on the Earth ($g = 9.81 \setminus \setminus {\textrm{\frac{m}{s}}}^{2}$) is $2000 \setminus N$ hence we have

$2000 = m \left(9.81\right) \setminus \ldots \ldots \ldots \left(1\right)$

Now, let $W '$ be the weight of car on the Moon ($g = 1.625 \setminus \setminus {\textrm{\frac{m}{s}}}^{2}$) will be given as

$W ' = m \left(1.625\right) \setminus \ldots \ldots \ldots \left(2\right)$

Now, dividing (2) by (1) as follows

$\setminus \frac{W '}{2000} = \setminus \frac{m \left(1.625\right)}{m \left(9.81\right)}$

$W ' = \setminus \frac{2000 \setminus \times 1.625}{9.81}$

$= 331.2946$

Hence the weight of car on the Moon will be $331.2946 \setminus N$