Question

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?

Short answer

(a) Weight of the ranger on earth is $7.4\times {10}^2\mathrm{N}$.

(b) Weight of the ranger on Mars $2.8\times {10}^2\mathrm{N}$.

(c) Weight at interplanetary space is 0N.

(d) Mass of the ranger at each location will remain the same.

Step-by-step solution

Given information

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

Understanding the concept

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:

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

Calculate the weight of ranger on Earth

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

Therefore, weight of the ranger on Earth is,

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

(a) Calculate the weight of ranger on Mars

(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) Calculate the weight of ranger in interplanetary space

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

(d) Calculate the mass of ranger at each location

(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.