Question

Calculate the momentum of the following:
A) Elephant of mass 2000 kg moving at 5 m/s
B) Bullet of mass 0.02 kg moving at 400 m/s

Answer 1

Hint: In order to solve this question, we have to define the quantity momentum. The direct application of the mathematical definition of the quantity momentum is enough to solve both of these questions. However, comparing the values of the momentums of the two cases, we see the direct significance of the quantity of momentum.

Complete step by step answer:
When a body is moving at a velocity, the effect that is produced by the body when it is stopped or when it interacts with another body is not just, defined by the magnitude of the velocity of the body, but also, the combined effect of the mass and velocity of the body, which is equal to another quantity called momentum.
The momentum is mathematically, defined as the product of the mass and velocity of the body.
$p = mv$
where m = mass and v = velocity.
It is a vector quantity whose direction is the same as that of the velocity.
The momentum represents the impact that is produced by the body by the virtue of its mass and its velocity, when the body collides with another body or the change of which, causes an effect known as the force, which is defined as the rate of change of momentum of the body.
We have two cases of an elephant and bullet moving at different speeds.
(A) Elephant:
Mass of the elephant, $m = 2000kg$
Velocity of the elephant, $v = 5m{s^{ - 1}}$
Momentum of the elephant, ${p_e} = mv = 2000 \times 5 = {10^4}kgm{s^{ - 1}}$

(B) Bullet:
Mass of the bullet, $m = 0.02kg$
Velocity of the elephant, $v = 400m{s^{ - 1}}$
Momentum of the elephant, ${p_b} = mv = 0.02 \times 400 = 8kgm{s^{ - 1}}$
From the calculations of the above momentum values, we can infer the significance of the quantity momentum as follows:
The bullet is moving at 8 times to that of the speed at which the elephant is moving. However, due to the lesser mass of the bullet, the net impact of the bullet caused is way too less than the elephant because the momentum is very low compared to the elephant.

Note: The momentum is originally defined in Newton's second law which states that the rate of change of momentum is equal to the force applied on the object. Based on the definition of the second law and the momentum, we obtain the famous expression of force applied on a body $F = ma$.