1. Section 9-3: Collisions & Impulse

2. Impulse received is J = p = Fct
Lets Briefly consider the details of a collision
Assume that the collision lasts a very small time t
During the collision, the net force on the object is, from Newton’s 2nd Law: ∑F = p/t
Or: p = (∑F)/t (the momentum change of the object considered) Definiton
The Impulse  p  J that the collision gives the object (The impulse received is the change in momentum for the object!)
We usually replace the net force by the average collision force: ∑F= Fc so that the
Impulse received is J = p = Fct

3. This integral is defined as the Impulse J:
Equivalently, during a collision, objects can be deformed due to the large forces involved.
Since we write
Integrating gives
Figure 9-8. Caption: Tennis racket striking a ball. Both the ball and the racket strings are deformed due to the large force each exerts on the other.
This integral is defined as the Impulse J:
The impulse one mass receives from the other in a collision is equal to the change in momentum of that mass:

4. Favg is equivalent to replacing the area under
Since the time of the collision is often very short, we often can use the a average force, Favg, which would produce the same impulse over the a same time interval.
∆t is often very small & F is time dependent.
The impulse in the collision is the area
under the F vs. t curve. Replacing F with
Favg is equivalent to replacing the area under
the curve with the area of the rectangle.
The maximum
F is usually
very large!
The collision
time ∆t is
usually very
small!
Figure 9-9. Caption: Force as a function of time during a typical collision: F can become very large; Δt is typically milliseconds for macroscopic collisions.
Figure Caption: The average force acting over a very brief time interval gives the same impulse (FavgΔt) as the actual force.