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} = {m}{\frac{d\vec{v}}{dt}} }[/math] where p is the momentum of the system and F is the net force, m is the mass, and v is velocity. 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

How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript

Examples

Be sure to show all steps in your solution and include diagrams whenever possible

Simple

Middling

Difficult

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 airbag provides an opposing force over an interval of time. The inflated airbag reduces the speed of 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 impulsive force decreases, ultimately creating a safer impact for all passengers.

History

There is no specific record as to who discovered the Impulse-Momentum Theorem. However, it is derived from and logically correlates to Newton's Second Law, which states that the net force of an object is directly related to the rate of change of its linear momentum: [math]\displaystyle{ {\frac{d\vec{p}}{dt}} = \vec{F}_{net} }[/math].

Impulse Momentum

Contents