1. Chapter 7
Impulse and Momentum

2. Momentum
The linear momentum of an object of mass m moving with a velocity is defined as the product of the mass and the velocity
SI Units are kg m / s
Vector quantity, the direction of the momentum is the same as the velocity’s

3. Momentum components
Applies to two-dimensional motion

4. Impulse
In order to change the momentum of an object, a force must be applied
The time rate of change of momentum of an object is equal to the net force acting on it, e.g.
Gives an alternative statement of Newton’s second law

5. Impulse cont.
When a single, constant force acts on the object, there is an impulse delivered to the object
is defined as the impulse
Vector quantity, the direction is the same as the direction of the force
Unit N·s=kg·m/s

6. Impulse-Momentum Theorem
The theorem states that the impulse acting on the object is equal to the change in momentum of the object
Impulse=change in momentum (vector!)
If the force is not constant, use the average force applied

7. Impulse Applied to Auto Collisions
The most important factor is the collision time or the time it takes the person to come to a rest
This will reduce the chance of dying in a car crash
Ways to increase the time
Seat belts
Air bags

8. Air Bags The air bag increases the time of the collision
It will also absorb some of the energy from the body
It will spread out the area of contact
decreases the pressure
helps prevent penetration wounds

9. Example
0.05 kg ball moving at 2.0 m/s rebounds with the same speed. If the contact time with the wall is 0.01 s, what is average force of the wall on the ball?

10. Conservation of Momentum
Total momentum of a system equals to the vector sum of the momenta
When no resultant external force acts on a system, the total momentum of the system remains constant in magnitude and direction.
Components of Momentum

11. Conservation of Momentum
Momentum in an isolated system in which a collision occurs is conserved
A collision may be the result of physical contact between two objects
“Contact” may also arise from the electrostatic interactions of the electrons in the surface atoms of the bodies
An isolated system will have not external forces

12. Conservation of Momentum, cont
The principle of conservation of momentum states when no external forces act on a system consisting of two objects that collide with each other, the total momentum of the system remains constant in time
Specifically, the total momentum before the collision will equal the total momentum after the collision

13. Conservation of Momentum, cont.
Mathematically:
Momentum is conserved for the system of objects
The system includes all the objects interacting with each other
Assumes only internal forces are acting during the collision
Can be generalized to any number of objects

14. Example
Two skaters are initially at rest. Masses are 80kg and 50kg. If they push each other so that woman is given a velocity of 2.5 m/s. What is the velocity of the man?

15. Types of Collisions Momentum is conserved in any collision
Perfect elastic collision
both momentum and kinetic energy are conserved
Collision of billiard balls, steel balls

16. More Types of Collisions
Inelastic collisions
Kinetic energy is not conserved
Some of the kinetic energy is converted into other types of energy such as heat, sound, work to permanently deform an object
completely inelastic collisions occur when the objects stick together
Not all of the KE is necessarily lost
Actual collisions
Most collisions fall between elastic and completely inelastic collisions

17. More About Perfectly Inelastic Collisions
When two objects stick together after the collision, they have undergone a perfectly inelastic collision
Conservation of momentum becomes

18. Example
Railroad car (10,000kg) travels at 10m/s and strikes another railroad car (15,000kg) at rest. They couple after collision. Find the final velocity of the two cars. What is the energy loss in the collision?

19. Recoil System is released from rest
Momentum of the system is zero before and after

20. Example
4 kg rifle shoots a 50 grams bullet. If the velocity of the bullet is 280 m/s, what is the recoil velocity of the rifle?

21. Some General Notes About Collisions
Momentum is a vector quantity
Direction is important
Be sure to have the correct signs

22. More About Elastic Collisions
Both momentum and kinetic energy are conserved
Typically have two unknowns (1d)
Solve the equations simultaneously

23. A Simple Case, v2i=0
Head on elastic collision with object 2 at rest before collision.
One can show
Special cases

25. Ballistic Pendulum Measure speed of bullet
Momentum conservation of the collision
Energy conservation during the swing of the pendulum

26. Summary of Types of Collisions
In an elastic collision, both momentum and kinetic energy are conserved
In an inelastic collision, momentum is conserved but kinetic energy is not
In a perfectly inelastic collision, momentum is conserved, kinetic energy is not, and the two objects stick together after the collision, so their final velocities are the same

27. Example
7.31. Balls A and B collide head-on in a perfectly elastic collision. It is known that mA=2mB and that the initial velocities are +3 m/s for A and –2 m/s for B. Find their velocities after the collision.

28. Glancing Collisions
For a general collision of two objects in three-dimensional space, the conservation of momentum principle implies that the total momentum of the system in each direction is conserved

30. Example
Car, 1500 kg. SUV 2500 kg.
Find speed and direction after collision.

31. Example m1=0.15 kg, m2=0.26 kg, v1i=0.9 m/s at 50° to y-axis,
v2i=0.54 m/s, v2f=0.7 m/s at 35° below x-axis
Find v2f (magnitude and direction)