Impulse Momentum

This topic focuses on the simple relation between momentum and impulse.

Impulse Momentum Theorem

The Impulse Momentum Theorem relates the momentum of a body or system to the force acting on the body. Impulse(J) is also the change in momentum. As a force on a body is applied for a longer amount of time, the impulse also changes. If there is a changing force over the same time interval, the impulse also changes. The impulse is the product of the average force and the time interval over which it acts. Like linear momentum, impulse is a vector quantity and has the same direction as the average force. Its units are given in Newton-seconds (Ns).

A large impulse will cause a large change in an object's momentum, just as a small impulse will cause a smaller change in an object's momentum. When looking at the equation [math]\displaystyle{ {J} = {d\vec{p}} }[/math], one can replace J with the product of the average force and the time interval. Rearranging that equation results in [math]\displaystyle{ {F} = {\frac{d\vec{p}}{dt}} }[/math], which shows that whenever momentum changes with time, there is some force acting on the body.

To clarify, impulse is the effect of a net force acting on a body over a period of time, while momentum is the force within a body or system due to its total velocity.

A Mathematical Model

Impulse can mathematically be defined as the force on a body multiplied by the duration of that force. [math]\displaystyle{ {\frac{d\vec{p}}{dt}} = \vec{F}_{net} }[/math] where p is the momentum of the system and F is the net force. This can be rearranged to represent impulse, J as a relationship between the net force and time of the collision: [math]\displaystyle{ {J} = {d\vec{p}} = \vec{F}_{net}{dt} }[/math]

A Computational Model

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Examples

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Connectedness

One way to think of the importance of measuring impulse and its relationship to force is by imagining a car collision. When a car hits, for example, a wall or another car, a certain amount of force from the impact will cause the airbags in the car, ultimately leading to fewer deaths and injuries among drivers and passengers than if there had not been an air bag. When you think about it, due to the relationship between impulse, force, and time duration, the force of a collision where the momentum is changing is indirectly proportional to the time interval over which the force acts. To decrease the force, the time before the final impact must be increased. An air bag fulfills that necessity by inflating and thus creating a barrier between the human inside of the car and the other car or object with which it collides. The inflated airbag slows down the human and increases the time before the person in the car comes to a full stop because of the collision. As a result, the magnitude of the force decreases, ultimately creating a safer impact for all passengers.

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Impulse Momentum

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