1. Momentum-1
nfl football momentum

2. Momentum is a commonly used term in sports
Momentum is a commonly used term in sports. A team that has the momentum is on the move (to state!) and is going to take some effort to stop.

3. Momentum as a physics term; refers to the quantity of motion that an object has. A sports team which is "on the move" has the momentum. If an object is in motion (on the move) then it has momentum.

4. An object’s momentum will change if its mass and/or velocity changes.
Most common… a change in velocity.
What is a change in velocity called?
Acceleration a = Vf -Vo t
According to Newton’s laws,
a net force causes an object to accelerate,
or change its velocity.

6. IMPULSE
Impulse J is a force F acting for a small time interval Dt. F Dt
Impulse:
J = F Dt

7. The unit for impulse is the Newton-second (N·s)
Example 1: The face of a golf club exerts an average force of 4000 N for s. What is the impulse imparted to the ball? Dt F
J = F Dt
Impulse:
J = (4000 N)(0.002 s)
J = 8.00 Ns
The unit for impulse is the Newton-second (N·s)

8. Impulse from a Varying Force
Normally, a force acting for a short interval is not constant. It may be large initially and then play off to zero as shown in the graph. F
time, t
In the absence of calculus, we use the average force Favg.
Unless told otherwise, treat forces as average forces

9. Impulse Changes Velocity
Consider a mallet hitting a ball: F
Impulse = Change in “mv”

10. Momentum Defined v = 16 m/s p = mv
Momentum ρ is defined as the product of mass and velocity, mv. Units: kg m/s
p = mv
m = 1000 kg
v = 16 m/s
ρ = (1000 kg)(16 m/s)
ρ = 16,000 kg m/s

11. Impulse = Change in momentum
Impulse & Momentum
Impulse = Change in momentum
F Dt = mvf - mvo Dt F
A force F acting on a ball for a time Dt increases its momentum mv. mv

12. Choose right as positive.
Example 2: A 50-g golf ball leaves the face of the club at 20 m/s. If the club is in contact for s, what average force acted on the ball?
Given: m = 0.05 kg; vo = 0;
Dt = s; vf = 20 m/s Dt F mv +
Choose right as positive.
F Dt = mvf - mvo
F (0.002 s) = (0.05 kg)(20 m/s)
F = 500 N
Average Force:

13. 12/16
Monday you worked on Momentum WS I. I will only accept late work if you were absent yesterday.
Get your Momentum notes out. Answer example 3 now.
Today we will look at ranking exercises and conservation of momentum.
Example 3: A 500-g baseball moves to the left at 20 m/s striking a bat. The bat is in contact with the ball for s, and it leaves in the opposite direction at 40 m/s. What was average force on ball?

14. What’s ahead . . . Tonight – problems 9-10, 12-14
Wednesday & Thursday – complete the notes for the Momentum Unit
The test is Thursday after the holidays.
You should be working on your video

16. D>A=B>C The time interval is the same for all four cases, so the magnitudes of the momentum changes, which are equal to the impulse applied to the boxes, will be proportional to the net forces acting.

17. A 1000 kg car moving at 30 m/s (p = 30,000 kg m/s) can be stopped by
30,000 N of force acting for 1.0 s (a crash!) or
by 3000 N of force acting for 10.0 s (normal stop)

19. Another applications of impulse
Contact time is reduced if arm's deceleration is kept as small as possible.
This is done by using "follow-through", which means to continue to push during the contact period.

20. So to summarize…
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.
BUT the change in momentum is the SAME either way!

21. Vector Nature of Momentum
Consider the change in momentum of a ball that is dropped onto a rigid plate: + vo vf
A 2-kg ball strikes the plate with a speed of 20 m/s and rebounds with a speed of 15 m/s. What is the change in momentum?
Dp = mvf - mvo = (2 kg)(15 m/s) - (2 kg)(-20 m/s)
Dp = 30 kg m/s + 40 kg m/s
Dp = 70 kg m/s

22. + + - Dt F 40 m/s 20 m/s m = 0.5 kg F Dt = mvf - mvo
Example 3: A 500-g baseball moves to the left at 20 m/s striking a bat. The bat is in contact with the ball for s, and it leaves in the opposite direction at 40 m/s. What was average force on ball? + Dt F
40 m/s
20 m/s
m = 0.5 kg + -
F Dt = mvf - mvo
vo = -20 m/s; vf = 40 m/s
F(0.002 s) = (0.5 kg)(40 m/s) - (0.5 kg)(-20 m/s)
Continued . . .

23. + - Example Continued: m = 0.5 kg F 40 m/s 20 m/s Dt F Dt = mvf - mvo
F(0.002 s) = (0.5 kg)(40 m/s) - (0.5 kg)(-20 m/s)
F(0.002 s) = (20 kg m/s) + (10 kg m/s)
F = 15,000 N
F(0.002 s) = 30 kg m/s

24. Problems
The Big Mo’ Worksheet # and due tomorrow!

25. Impulse = Change in momentum
Summary of Formulas:
Impulse
J = FavgDt
Momentum
ρ = mv
Impulse = Change in momentum
F Dt = mvf - mvo

26. Collisions
Momentum-2

27. Conservation of Momentum
According to the law of conservation of linear momentum, when the vector sum of the external forces that act on a system of bodies equals zero, the total linear momentum of the system remains constant no matter what momentum changes occur within the system

28. For two objects interacting with one another, the conservation of momentum can be expressed as:
 v1 and v2 are initial velocities, and are final velocities

30. The order should have been A=C>D=E>B=F
The change in momentum is equal to m(Δv) and Δv is vf - vi .

31. Which of the following statements are true about momentum?
a. Momentum is a vector quantity.
b. The standard unit on momentum is the Joule.
c. An object with mass will have momentum.
d. An object which is moving at a constant speed has momentum.
e. An object can be traveling eastward and slowing down; its momentum is westward.
f. Momentum is a conserved quantity; the momentum of an object is never changed.
g. The momentum of an object varies directly with the speed of the object.
h. Two objects of different mass are moving at the same speed; the more massive object will have the greatest momentum.
i. A less massive object can never have more momentum than a more massive object.
j. Two identical objects are moving in opposite directions at the same speed. The forward moving object will have the greatest momentum.
k. An object with a changing speed will have a changing momentum.

32. Which of the following statements are true about momentum?
a. Momentum is a vector quantity.
b. The standard unit on momentum is the Joule.
c. An object with mass will have momentum.
d. An object which is moving at a constant speed has momentum.
e. An object can be traveling eastward and slowing down; its momentum is westward.
f. Momentum is a conserved quantity; the momentum of an object is never changed.
g. The momentum of an object varies directly with the speed of the object.
h. Two objects of different mass are moving at the same speed; the more massive object will have the greatest momentum.
i. A less massive object can never have more momentum than a more massive object.
j. Two identical objects are moving in opposite directions at the same speed. The forward moving object will have the greatest momentum.
k. An object with a changing speed will have a changing momentum.
Answer: ADGHK

33. ELASTIC AND INELASTIC COLLISIONS
Elastic Collision: A collision in which objects collide and bounce apart with no energy loss.
Inelastic Collision: A collision in which objects collide and some mechanical energy is transformed into heat energy.

34. The animation below portrays the inelastic collision between a 1000-kg car and a 3000-kg truck. The before- and after-collision velocities and momentum are shown in the data tables.

35. The animation below portrays the elastic collision between a 3000-kg truck and a 1000-kg car.
The before- and after-collision velocities and momentum are shown in the data tables.

36. Before the collision, the momentum of the truck is 60 000 Ns and the momentum of the car is 0 Ns;
the total system momentum is Ns.
After the collision, the momentum of the truck is Ns and the momentum of the car is Ns; the total system momentum is
Ns.

37. The animation below portrays the inelastic collision between a very massive diesel and a less massive flatcar. The diesel has four times the mass of the freight car. After the collision, both the diesel and the flatcar move together with the same velocity.

38. In elastic collisions no permanent deformation occurs; objects elastically rebound from each other. In head-on elastic collisions between equal masses,
velocities are exchanged.

39. p before = p after m1V1 + m2V2 = m1Vf1 + m2V2f V2f = - 2 m/s
Example 4: A 0.50-kg ball traveling at 6.0 m/s collides head-on with a 1.00-kg ball moving in the opposite direction at a velocity of m/s. The 0.50-kg ball moves away at -14 m/s after the collision. Find the velocity of the second ball.
M1 = 0.50 kg M2 = 1.00 kg
V1 = 6.0 m/s V2 = m/s Vf1 = -14 m/s
p before = p after
m1V1 + m2V2 = m1Vf1 + m2V2f
(.5kg)(6m/s) + (1kg)(-12m/s) = (.5kg)(-14m/s) + (1kg)(V2f)
V2f = - 2 m/s

40. Inelastic collisions are characterized by objects sticking together and permanent deformation.

41. p before = p after m1V1 + m2V2 = (m1+ m2 )V V = 1.25 km/hr, right
Example 5: A 3000-kg truck moving rightward with a speed of 5 km/hr collides head-on with a 1000-kg car moving leftward with a speed of 10 km/hr. The two vehicles stick together and move with the same velocity after the collision. Determine the post-collision velocity of the car and truck.
p before = p after
m1V1 + m2V2 = (m1+ m2 )V
M1 = 3000 kg
V1 = 5.0 km/hr
M2 = 1000 kg
V2 = -10 km/hr
(3000kg)(5km/hr) + (1000kg)(-10km/hr)
(3000kg kg)
V = km/hr, right

42. Review Elastic Collisions: Bounce, No deformation, Energy is conserved
Inelastic Collisions: Stick, permanent deformation, Energy is “lost” to friction/heat

43. Mom WS I Answers Check your work
2000 kg m/s kg
1.2 kg m/s or Ns
16.8 m/s
30 s
340 m/s
-250 N
-5 m/s
-2.5 m/s
kg m/s

44. Which of the following statements are true about momentum?
a. Momentum is a vector quantity.
b. The standard unit on momentum is the Joule.
c. An object with mass will have momentum.
d. An object which is moving at a constant speed has momentum.
e. An object can be traveling eastward and slowing down; its momentum is westward.
f. Momentum is a conserved quantity; the momentum of an object is never changed.
g. The momentum of an object varies directly with the speed of the object.
h. Two objects of different mass are moving at the same speed; the more massive object will have the greatest momentum.
i. A less massive object can never have more momentum than a more massive object.
j. Two identical objects are moving in opposite directions at the same speed. The forward moving object will have the greatest momentum.
k. An object with a changing speed will have a changing momentum.

45. Which of the following statements are true about momentum?
a. Momentum is a vector quantity.
b. The standard unit on momentum is the Joule. Kg m/s
c. An object with mass will have momentum. Inertia
d. An object which is moving at a constant speed has momentum.
e. An object can be traveling eastward and slowing down; its momentum is westward. Momentum in direction of motion. The change in momentum is negative because it is losing momentum.
f. Momentum is a conserved quantity; the momentum of an object is never changed. Individual momentum can change, system momentum constant
g. The momentum of an object varies directly with the speed of the object.
h. Two objects of different mass are moving at the same speed; the more massive object will have the greatest momentum.
i. A less massive object can never have more momentum than a more massive object. Depends on the mass and the velocity
j. Two identical objects are moving in opposite directions at the same speed. The forward moving object will have the greatest momentum. They have the same momentum, just different directions
k. An object with a changing speed will have a changing momentum.
Answer: ADGHK

46. 12/18 Solve now Ex 7 in notes
You should be able to solve all problems through 19
Do not worry about center of mass problems
We will go through 2D collisions at angles today, then I will help you with questions on the HW and will do this Friday as well
#10 on Mom WS I: Consider only vertical velocity because the horizontal doesn’t change, therefore no change in momentum
#12 on HW the answer is 84kg. Remember to distribute
Review set at your discretion
Test is Tuesday 1/6
e. An object can be traveling eastward and slowing down; its momentum is westward. FALSE: Momentum in direction of motion. The change in momentum is negative because it is losing momentum.

47. Explosions
When an object separates suddenly, as in an explosion, all forces are internal.
Momentum is therefore conserved in an explosion.
There is also an increase in kinetic energy in an explosion. This comes from a potential energy decrease due to chemical combustion.

48. a. increase the impact time b. decrease an occupant's impulse
 Cars are equipped with padded dashboards. In collisions, the padded dashboards would be safer than non-padded ones because they ____. List all that apply.
a. increase the impact time
b. decrease an occupant's impulse
c. decrease the impact force
d. none of the above
Both A and C are correct. Padded dashboard serve to increase the time over which the momentum of a passenger is reduced to zero. With this increase in time, there is a decrease in force (big T, little f).
The impulse acting upon the passenger is not changed. The passenger still must have his/her mass slowed down from the pre-impact velocity to zero velocity. This means the velocity change is the same whether the collision occurs with a padded dashboard, an air bag or a glass windshield. Since the velocity change is independent of the collision time, the momentum change and the required impulse are also independent of the collision time.

49. Recoil Guns and cannons “recoil” when fired.
This means the gun or cannon must move backward as it propels the projectile forward.
The recoil is the result of action-reaction force pairs, and is entirely due to internal forces. As the gases from the gunpowder explosion expand, they push the projectile forwards and the gun or cannon backwards.

50. Summary of Formulas: Impulse Momentum p = mv J = FavgDt
Impulse = Change in momentum
F Dt = mvf - mvo
Conservation of Momentum

51. Mo’ at an angle
Momentum-3

52. Do you remember solving for resultant using components?

53. Determine the components
Force Vector
X component
Cos H
Y component
Sin H
65 N at 60° N of E
32.5 N
56.3 N
111 N at 125°CCW to E
-63.7 N
90.9 N
185 N at 195°CCW to E
-179 N
-47.9 N
Total

54. 2D-Collisions Momentum in the x-direction is conserved.
SPx (before) = SPx (after)
Momentum in the y-direction is conserved.
SPy (before) = SPy (after)
Treat x and y coordinates independently.
Ignore x when calculating y
Ignore y when calculating x
Let’s look at a simulation:

55. 2D-Collisions: Other Hints
Set system up with known momentum on the X axis
Doing this makes the y value of the known momentum zero
Solve for x component using cos. Must account for direction
Solve for y component using sin. Must account for direction
Substitute to determine final velocities

56. Example 6 A 7500-kg truck traveling at 5 m/s east collides with a 1500-kg car moving at 20 m/s in a direction 210. After the collision, the two vehicles remain tangled together. With what speed and in what direction does the wreckage begin to move?
m1 = 7500 kg v1 = 5 m/s, 0º
m2 = 1500 kg v2 = 20 m/s, 210º
m1 v1+ m2 v2 =( m1 +m2)V

57. 1500kg (20m/s cos 210º) 1500 kg (20m/s sin 210º)
m1 v1+ m2 v2 =( m1 +m2)V
x-comp y-comp
7500 kg (5 m/s)
1500kg (20m/s cos 210º) kg (20m/s sin 210º)
Σx = 11,519 kg m/s Σy = - 15,000 kg m/s
Initial Momentum
= 18,912.7 kg m/s

58. initial momentum = final momentum
= (m1 + m2) V
= 2.1 m/s
= 52.5º S of E or
IV quadrant V (2.1 m/s, 307.5º)
307.5º = 360º º

59. Example 7: Suppose a 5.0-kg projectile launcher shoots a 209 gram projectile at 350 m/s. What is the recoil velocity of the projectile launcher?
Ans: m/s

60. Ex 8
3 m/s
2 kg
8 kg
0 m/s
Before
2 m/s v
After
50o x y

61. Ex 8 y x Calculate velocity of 8-kg ball after the collision. 3 m/s
Before
2 m/s v
After
50o x y

62. Example 9