Momentum in the real life scenario
1. A player struck by the ball during a table tennis game is not injured severely, whereas a fast-moving cricket ball can cause injury to a spectator.
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The above scenario shows the effect of momentum. But, which one do you think will have a higher momentum and which one the lower?
Imagine the table tennis ball and cricket ball of mass \(0.1\ kg\) and \(0.8\ kg\), respectively, are thrown at the velocity of \(5\ m\ s^{ –1}\).
Momentum (p)= Mass(m)×Velocity(v)
The momentum of table tennis ball:
\(p\) \(=\) 0.1 ·5 \(=\) 1 \(kg\ m\ s^{ –1}\)
The momentum of cricket ball:
\(p\) \(=\) 0.8 ·5 \(=\) 4 \(kg\ m\ s^{ –1}\)
The momentum of the cricket ball is higher than the table tennis ball. It is not only due to the velocity but also the mass of the ball.
In the same scenario, if a fast bowler hits a batsman with the cricket ball, it may cause severe injury. But, if a slow bowler bowls the same ball, it does not cause any injury to the batsman.
Here, the mass of the cricket ball is the same, but only the velocity of it varies. If the velocity is more, then the momentum will be higher and vice-versa.
2. A vehicle when parked along the side of the lane, it does not need any attention. However, even at speed as low as \(5\ m\ s^{ –1}\), a moving truck or a vehicle can kill anyone who is caught in its way.
3. A bullet with a small mass can kill a person when shot from a gun.
All these results indicate that the object's mass and velocity influence the impact produced by them.
Newton's second law of motion
The rate of change of momentum (acceleration) of an object is directly proportional to the applied unbalanced force in the same direction of force and inversely proportional to the mass of the object.
The elephant with a higher mass has a small acceleration due to the lesser force applied for the movement. On the other hand, a football having a smaller mass than the elephant moves with a larger acceleration.
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The word "Directly proportional" means that an increase in one quantity increases the other quantity. For example, as the acceleration increases, the force also increases.
The word "Inversely proportional" means that an increase in one quantity decreases the other. For example, as the acceleration increases, the mass decreases.