1. IMPULSE AND MOMENTUM When ever things collide, I’ve heard,
Momentum is the chosen word.
And if the crash is quick,
You’ll see –
It’s Impulse! (that’s dp/dt)

2. LINEAR MOMENTUM
For an individual mass we define the linear momentum to be:
From the 2nd law we have:

3. Momentum MOMENTUM IS: SYMBOLIZED BY p MEASURED IN UNITS OF kg m/s
MASS x VELOCITY
CONSERVED (FOR A CLOSED, ISOLATED SYSTEM)
A VECTOR
THE DIRECTION OF AN OBJECT’S MOMENTUM IS THE SAME AS THE VELOCITY

4. Momentum There are two general types of momentum problems: Explosions
Guns, objects connected by springs, nuclear decay, etc
Total momentum is always zero (both objects initially at rest)
Collisions
Elastic (both p and K are conserved)
Inelastic (p conserved, TOTAL ENERGY is conserved)
Totally inelastic (p conserved, TOTAL ENERGY is conserved)

5. IMPULSE
For a constant force, the impulse is defined as the force multiplied by the time over which it acts
If the force is not constant, the impulse is defined by an integral:

6. IMPULSE Impulse is defined as the change in momentum: J = Dp
According to Newton’s second law (F = ma), a force is required to change velocity (a = dv/dt). Since this force acts during some finite time interval (F = m dv/dt). Impulse is equal to the product of the force and the time period, Fdt = m dv Therefore: Fdt = dp
The units of impulse are the same as the units of momentum and may be expressed as: kgm/s or Ns

7. IMPULSE
The area under the curves in the diagram represents the impulse on an object.
Impulse may also be calculated by determining the change in momentum before and after a collision

8. EXAMPLE PROBLEM
A 5kg mass moving at 10m/s in the +x direction is acted upon by a force in the –x direction with a magnitude given as a function of time by the graph. Determine the velocity of the mass after the force has stopped acting
Force (x 103N) 8 6 4 2
Time (x 10-3 s)

9. solution The initial momentum of the object is: 50 kgm/s
The area under the curve is:
- 80 N s.
The final momentum is:
-30 kgm/s
The final velocity is:
-6m/s

10. CONSERVATION OF LINEAR MOMENTUM
If no net external force acts on a system of particles, the total linear momentum of the system cannot change. (CH. 9 #40)
Valid for objects moving or initially at rest
Momentum is a vector (CH 9 #22)
In two, or three, dimensions, if the net external force on a closed system is zero along an axis, then the component of the linear momentum along that axis cannot change. (CH. 9 #20)

11. Elastic Collisions in One Dimension
BOTH OBJECTS MOVING
Momentum is conserved

12. Elastic Collisions in One Dimension
So is kinetic energy!
Ko = Kf

13. Elastic Collisions in One Dimension
THE RESULT OF THIS?
WHICH LEADS TO:
WHICH BECOMES:
The relative velocity changes direction but keeps same magnitude.

14. EXAMLE ONE
A baseball with a speed of -40m/s is hit by a bat with a speed of 18m/s. If the ball leaves the bat with a speed of 75m/s, what is the speed of the bat just after the collision? (assume the collision is completely elastic)

15. YOU MUST BE ABLE TO DERIVE EQUATIONS (9-67),
ALGEBRA ALERT!
YOU MUST BE ABLE TO DERIVE EQUATIONS (9-67),
(9-68), (9-75),
AND (9-76)

16. Inelastic Collisions
When objects collide and stick together – momentum and total energy is conserved but kinetic energy is not.
Some of the kinetic energy is transferred into _______
EXAMPLE: The ballistic pendulum

17. THANK YOU FOR YOUR INTEREST IN PHYSICS!