Question

A lion with a mass of 190 kg is chasing a gazelle with a mass of 15 kg. The distance between the lion and the gazelle is 2 meters.
a. How much gravitational force does the lion exert on the gazelle?
b. How much gravitational force does the gazelle exert on the lion?

Answer 1

(a) $4.7\cdot 10^{-8} N$

The gravitational force between two objects is given by:

$F=G\frac{m_1 m_2}{r^2}$

where

$G=6.67\cdot 10^{-11} m^3 kg^{-1} s^{-2}$ is the gravitational constant

m1 and m2 are the two masses

r is the separation between the objects

In this problem, we have:

$m_1 = 190 kg$ is the mass of the lion

$m_2 = 15 kg$ is the mass of the gazelle

r = 2 m is their separation

Substituting into the equation, we find the gravitational force exerted by the lion on the gazelle:

$F=(6.67\cdot 10^{-11})\frac{(190)(15)}{2^2}=4.7\cdot 10^{-8} N$

(b) $4.7\cdot 10^{-8} N$

According to Newton's third law of motion:

"When an object A exerts a force (action) on an object B, object B exerts an equal and opposite force (reaction) on object A".

In this problem, we can identify:

- The lion as object A

- The gazelle as object B

This means that according to the abovementioned law, the gravitational force exerted by the lion on the gazelle is equal to the gravitational force exerted by the gazelle on the lion. Therefore, the answer is again

$4.7\cdot 10^{-8} N$