# Momentum

We have seen that when a force is applied to an object it is accelerated. The acceleration produced is related to the force applied by Newtonâ€™s second law of motion

F = ma

That is, if the velocity of the object changes from v_{1} m/s to v_{2} m/s in t seconds,

F = =

The quantity mv_{1} or mv_{2} that appears in the above equation is called the momentum of the object.

The momentum of an object is the product of its mass and velocity and is denoted by p.

p = mv

The second law of motion can therefore, be also written as

F =

That is, force on a body is the change of momentum per unit time. Since the momentum of a body is the product of its mass and its velocity, the momentum of a truck moving at 10 km/h is more than the momentum of a small marble moving with the same speed. If both are brought to rest, the change in the momentum of the truck would be much more than that of the marble. It is not surprising, therefore, that it requires more force to stop a truck than to stop a marble moving with the same speed.

In our daily life we come across many examples, which are related to the second law of motion. For example, a fielder in the game of cricket lowers his hands gradually while catching a fast moving ball. Here he increases the time during which the velocity of the ball is brought to zero. Therefore the acceleration is reduced and so the impact of catching the fast moving ball is also reduced. Had the ball been stopped suddenly, in a very short time its velocity would have decreased to zero. The rate of change of momentum would be very large and a large force would have to be applied to hold the ball. This could hurt the palms of the fielder.

In high jump, the athlete is made to fall on a cushioned bed or a sand bed. This is to increase the time of the fall to stop. This decreases the force with which he lands on the bed.

Similarly, a karate player is able to break a pile of tiles or ice slabs with a single blow of his hand. He strikes the pile with his hand very fast. Thus the entire momentum of the fast moving hand is reduced to zero in a very short time. This enables him to exert a very large force on the pile of tiles and break them.

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