1. Define momentum

An object’s tendency to resist changes in motion.

Variable Formula Vector or Scalar SI Unit

p

p mv

vectorm

kgs

2. What is the main cause of grief and loss of points in this chapter ?

• Momentum is a Vector

• Make sure you show velocity as negative and positive

3. How was Newton’s 2nd law of motion originally expressed ?

F = ∆p Or F = mvf –mv0

∆t ∆t

or F = m(vf -v0) or F = ma

∆t

4. How does this differ from what you learned for Newton’s second law ? Explain the difference.

Expressed in terms of where the second law is in terms of

p

a

5. What happens to momentum if there is no ∑F ?

• No change in momentum

• Object stays at rest or constant motion

6. State the law of conservation of momentum

• In an isolated system, the momentum before a collision equals the momentum after the collision.

p p

7. Define a “system” then define “isolated system” in terms of momentum

• System – set of objects

• Isolated system – only significant forces are between those in the system

no external forces change the system

8. Explain the following situations using the conservation of momentum

9. Define Impulse

• Force acting through a time interval

Variable Formula Vector or Scalar SI Unit

J

J F t vector N s

9.

10. How does Impulse relate to momentum ? Give several examples

J p

0fJ mv mv

11. Give the impulse-momentum theorem

and

J F t

J p

0fF t mv mv

Then,

If,

12. So a change in momentum requires what ?

• A change is velocity• You must have a Net Force

• No Net Force– 1st law (no acceleration)– No change in momentum

• Net Force– 2nd law (acceleration)– change in momentum

13. How is the force required effected by a change

in momentum over a long period of time ?

• If the stopping time is increased then,

the F that is decreased.

F t p p

Ft

Inversely Proportional

14.Use the graph to answer the following questions.

Pushing the wagon

0

2

4

6

8

0 2 4 6 8

Time (s)

Fo

rce

(N

)

Describe a scenario for the graph

What impulse is given to the wagon from t = 0 s to t= 7 s ?

What is the change in the wagon’s momentum from t = 0 s to t = 7 s ?

How fast was the wagon going after 7 seconds if its mass = 5000 kg and it started from rest ?

15. Do the units for impulse then equal the units for momentum ?

mN s kg

s

2

m mkg s kgs s

16. What is an elastic collision ?

• When two objects collide and continue to move separately after the collision

Elastic collision

• What kinds of object undergo elastic collisions ?– Rigid objects, don’t deform a lot

• What happens to momentum in an elastic collisions ?– Momentum is conserved

• What happens to energy in an elastic collision– Kinetic Energy is conserved

17. What is an inelastic collision ?

• Objects collide and stick together

Inelastic collision

• What kinds of object undergo inelastic collisions ?- Objects that deform

• What happens to momentum in an inelastic collisions ?– Momentum is conserved

• What happens to energy in an inelastic collision– Kinetic Energy is NOT conserved

18. Elastic collision examples:

1 1 2 2 1 1 2 2m v m v m v m v

1 1 2 2 1 1 2 2M v m v M v m v

19. Examples of inelastic collisions

1 1 2 2 1 2

1 1 2 2 1 2

( )

( ) ( )

m v m v m m v

m v m v m m v

1 1 1 2 2( )m v m m v

21

2mv mgh

20. Show collisions in two dimensions and write equations for them

• Break vectors into components and write

conservation of momentum equations in the “x” and “y”

2

1&2

1

• “x”

• “y”

2 2 1 2( ) ym v m m v

1 1 1 2( ) xm v m m v

x yv v v

• A) The two balls shown in the figure collide and bounce off each other as shown. What is the final velocity of the 500g ball if the 800g ball has a speed of 15cm/s after the collision. B) Is the collision perfectly elastic ?

• A) .26m/s @ 280 • B) It is not perfectly elastic

300

θ

mb= 800gvb = 30 cm/s

mo= 500gvo = 50 cm/s

Billiard ball A moving with speed vaa = 3.0 m/sin the +x direction strikes an equal-mass ball B initially at rest. The two balls are observed to move off at 450 to the x axis, ball A above the x axis and ball B below. What are the speeds of the two balls after colliding ?

• 2.1 m/s

A 90 kg fullback moving east with a speed of 5.0 m/s is tackled by a 95 kg opponent running north at 3.0 m/s. If the collision is perfectly inelastic, calculate a) the velocity of the players just after the tackle b) the kinetic energy lost

• A) 2.9 m/s• B) 780 J

21. To this point how have we viewed mass and its distribution in an object?

• The mass of the object has been uniform in all directions. So, we put a dot in the center and assumed all mass was located at this place.

22. What is the center of mass ?

• One particle that would move if subjected to a net force.

23. Find the center of mass for several

situations given

24.What is the center of gravity of an object ?

• Point at which gravity acts. For our purposes center of mass and center of gravity are the same.

25. How can the center of gravity be found for an irregularly shaped object ?

• Hang the object from at least two points and find where their plumb lines cross.

26. Explain how a trapeze walker uses center of mass/gravity to his/her advantage.

Center of mass does not have to be on the

Object !