Compute the weight of a 75 kg space ranger (a) on Earth, (b) on Mars, where$\mathbf{g}\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{7}\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$, and (c) in interplanetary space, where$\mathit{g}\mathit{=}\mathit{0}$. (d) What is the ranger’s mass at each location?

1. $m=75\mathrm{kg}$,
2. $g_{\mathit{M}}\mathit{=}3.7\mathrm{m}/{\mathrm{s}}^2$,
3. Interplanetary space g=0.

Weight of an object is equal to the product of the mass and gravitational acceleration. Weight is the form of force and the formula is derived from Newton’s second law.

Use gravitational acceleration to find weight of the ranger; using mass and value of g of the respective planet we can find weight.

Formulae:

$\mathbf{W}\mathbf{=}\mathbf{mg}$

(a) We know,$g_{\mathrm{e}}=9.8\mathrm{m}/{\mathrm{s}}^2$

Therefore, weight of the ranger on Earth is,

$$\begin{gathered} W_e=m{g}_e \\ =75\mathrm{kg}\times 9.8\mathrm{m}/{\mathrm{s}}^2 \\ =7.4\times {10}^2\mathrm{N} \end{gathered}$$

(b) To calculate the weight of the ranger on Mars, multiply the mass of the ranger with the gravitational acceleration on the mars.

$$\begin{gathered} W_M=m{g}_M \\ =75\mathrm{kg}\times 3.7\mathrm{m}/{\mathrm{s}}^2 \\ =2.8\times {10}^2\mathrm{N} \end{gathered}$$

(c) As the g=0, the weight of the ranger is zero.

(d) The mass is an intrinsic property. Therefore, the mass of the ranger doesn’t affect the location, mass will remain the same in every location.