1. Chapter 9 – Momentum and its Conservation

2. 9.1 Impulse and Momentum

3. 9.1 Impulse and Momentum
When a bat strikes a ball the magnitude of the force exerted on the ball is not constant.
The magnitude rises to a maximum value and then returns to zero when the ball leaves the bat.

4. 9.1 Impulse and Momentum
Even though the contact time may be quite short, the maximum force can be quite large
Since the time of the collision is very short, we consider the average force.

5. 9.1 Impulse and Momentum
If a ball is to be hit well, both the size of the force and the time of contact are important
We bring together the average force and the time of contact, calling the product impulse

6. Impulse = FΔt Definition of Impulse:
9.1 Impulse and Momentum
Definition of Impulse:
The impulse of a force is the product of the average force, F, and the time interval, Δt, during which the force acts:
Impulse = FΔt
Impulse is a vector quantity and has the same direction as the average force.
SI Unit of Impulse: Newton · second (N · s)

7. 9.1 Impulse and Momentum
Vi = 0
A large impulse produces a large response, that is, the ball leaves the bat with a large velocity
However a more massive the ball has more inertia, so it resists acceleration and has less velocity after leaving the bat
Both mass and velocity play a role in how an object responds to a given impulse

8. p = mv Definition of Linear Momentum:
9.1 Impulse and Momentum
Definition of Linear Momentum:
The linear momentum, p, of an object is the product of the object’s mass, m, and velocity, v:
p = mv
Linear momentum is a vector quantity that points in the same direction as the velocity.
SI Unit of Momentum: kilogram · meter/second (kg · m/s)

9. 9.1 Impulse and Momentum
“But our team, we've been building momentum and building momentum. And, if you're going to have a chance to win, you're going to have to play great defense and we certainly did."
To stop an object with momentum it is necessary to apply a force against its motion for a given period of time

10. ( ) 9.1 Impulse and Momentum
When the velocity of an object changes from vi to vf during a time interval Δt, the average acceleration is given by: a =
vf - vi Δt
But, by Newton’s second law:
F = ma
Substituting for a:
F = m (
vf - vi Δt )
equals
F =
mvf - mvi Δt
The numerator on the right side is the change in momentum

11. FΔt = mvf - mvi or: FΔt = mΔv
9.1 Impulse and Momentum
Impulse-Momentum Theorem:
When a net force, F, acts on an object, the impulse of the net force is equal to the change in the momentum of the object:
FΔt = mvf mvi
final momentum
initial momentum
impulse
Impulse = Change in momentum
or: FΔt = mΔv

12. 9.1 Impulse and Momentum
FΔt = mvf mvi
to minimize the effect of the force on an object involved in a collision, the time must be increased
to maximize the effect of the force on an object involved in a collision, the time must be decreased

13. 9.1 Impulse and Momentum
Air bags in a car extend the time required to stop the momentum of the driver and passenger.

14. 9.1 Impulse and Momentum
Padding a potential impact area can be observed in gymnasiums (underneath the basketball hoops)

15. Catching a foul ball at a baseball game
9.1 Impulse and Momentum
Catching a foul ball at a baseball game
Egg toss

16. Rebounding requires a large impulse
9.1 Impulse and Momentum
Rebounding requires a large impulse
Thus, a hailstone of the same mass as a raindrop can dent a car because its change in velocity is much greater
(Also, because a liquid changes shape, the time of impact is increased, further reducing the force.)

17. 9.1 Impulse and Momentum
A kg vehicle traveling at 94 km/h (26 m/s) can be stopped in 21 s by gently applying the brakes. It can be stopped in 3.8 s if the driver slams on the brakes, or in 0.22 s if it hits a concrete wall. What average force is exerted on the vehicle in each of these stops?