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The first law of motion states that when an object is subjected to an unbalanced external force, the object accelerates due to a change in velocity.
Let us see the dependence of the acceleration of an object on the force applied to it.
We know that accelerating an object needs more force to attain a higher velocity.
Momentum is an essential quantity that combines the object's mass and velocity. It was Isaac Newton who first coined the term "momentum" to describe one of these properties.
Momentum
The product of mass, (\(m\)) and velocity, (\(v\)) gives the momentum, (\(p\)). That is,
\(p\) \(=\) \(m\ v\)
The SI unit is \(kilogram\ metre\ per\ second\) (\(kg\ m\ s^{ –1}\)).
Momentum is a vector quantity, which specifies both direction and magnitude. The direction of the momentum is the same as that of velocity (\(v\)).
Since the unbalanced force induces velocity change, it is clear that a force also produces a change in momentum.
Consider the following scenario:
A car with a dead battery is driven along a straight road at a speed of \(1\ m\ s^{ –1}\), which is adequate to start the engine. It hardly starts even if one or two people give it a sudden unbalanced push. However, pushing the car steadily for a while will gradually accelerate to this pace.
Inference:
The above scenario implies that the size of the impact and the time in which the force applied decides the change of the car's momentum.
Hence, the force that changes an object's momentum is proportional to the time at which the momentum changes.
Solved example:
Calculate the momentum of a person of mass \(30\ kg\) moving at \(8\ m\ s^{ –1}\).
Mass, \(m\) \(=\) \(30\ kg\)
Velocity, \(v\) \(=\) \(8\ m\ s^{ –1}\)
\(p\) \(=\) \(=\) 240 \(kg\ m\ s^{ –1}\)
Hence, the momentum of a person is 240 \(kg\ m\ s^{ –1}\).
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