Question

You have landed on Mars, and observe that it takes a stone 1.8 sec to fall 6 m.

Answer 1

Answer:

$3.7\ \text{m/s}^2$

$7.4\ \text{N}$

4 m

$3397678.06\ \text{m}$

$1.55\times 10^{14}\ \text{N}$

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

$s=ut+\dfrac{1}{2}at^2\\\Rightarrow 6=0t+\dfrac{1}{2}\times a\times1.8^2\\\Rightarrow a=\dfrac{6\times2}{1.8^2}\\\Rightarrow a=3.7\ \text{m/s}^2$

The acceleration due to gravity (g) on Mars is $3.7\ \text{m/s}^2$

Weight is given by

$w=mg\\\Rightarrow w=2\times 3.7\\\Rightarrow w=7.4\ \text{N}$

Weight of the stone on Mars is $7.4\ \text{N}$

On Earth

$v^2-u^2=2as\\\Rightarrow u=\sqrt{v^2-2as}\\\Rightarrow u=\sqrt{0-2\times-9.81\times1.5}\\\Rightarrow u=5.42\ \text{m/s}$

On Mars

$v^2-u^2=2as\\\Rightarrow s=\dfrac{v^2-u^2}{2a}\\\Rightarrow s=\dfrac{0-(5.42)^2}{2\times -3.7}\\\Rightarrow s=4\ \text{m}$

A person could jump 4 m on Mars.

Acceleration due to gravity on planet is given by

$g=\dfrac{GM}{R^2}\\\Rightarrow R=\sqrt{\dfrac{GM}{g}}\\\Rightarrow R=\sqrt{\dfrac{6.674\times 10^{-11}\times 6.4\times 10^{23}}{3.7}}\\\Rightarrow R=3397678.06\ \text{m}$

Radius of Mars is $3397678.06\ \text{m}$

Gravitational force is given by

$F=\dfrac{GMm}{r^2}\\\Rightarrow F=\dfrac{GM(M\times 3\times 10^{-9})}{r^2}\\\Rightarrow F=\dfrac{6.674\times 10^{-11}\times (6.4\times 10^{23})^2\times 3\times 10^{-9}}{(2.3\times 10^7)^2}\\\Rightarrow F=1.55\times 10^{14}\ \text{N}$

The force of gravity between Mars and Deimos is $1.55\times 10^{14}\ \text{N}$