Impulse (physics)
In classical mechanics, an impulse is defined as the integral of a force with respect to time:
- [math]\displaystyle{ \mathbf{I} = \int \mathbf{F}\, dt }[/math]
where
- I is impulse (sometimes marked J),
- F is the force, and
- dt shows it is with respect to time.
Impulse is also described as the change in momentum. If the force and the mass of the object do not change, impulse can be simply expressed as:
- [math]\displaystyle{ \mathbf{I} = \mathbf{F}\,\Delta t = m \,\Delta \mathbf{v} = \Delta\mathbf{p} }[/math]
where
- F is the constant total net force applied,
- Δt is the time over which the force is applied,
- m is the constant mass of the object,
- Δv is the change in velocity produced by the force in the time that passed, and
- Δp is the change in linear momentum.
Impulse (physics) Media
The impulse delivered by the "sad" ball is mv0, where v0 is the speed upon impact. To the extent that it bounces back with speed v0, the "happy" ball delivers an impulse of mΔv = 2mv0.
