Physics lesson in grade 9

1. Take out tables.
On a separate sheet:
Make a list of every equation we’ve not
yet used in this class.

2. Here is your choice:
a. I toss a bullet at you.
b. I shoot a bullet at you from a gun.
Which is more dangerous to you?
Why?

3. Linear Momentum
&
Impulse

4. Linear Momentum = mass in motion
A measure of how hard it is to stop an
object.
It is like a quantity of motion.
How is it different from inertia?

5. Momentum (p) depends on:
mass & velocity of object.
p = mv m in kg
v in m/s
Units are … kg m no name.
s

6. Momentum is a
Vector Quantity
Same direction as velocity
All Energy KE too is a scalar

7. Ex 1. A 2250 kg pickup truck has v =
25 m/s east. What is the truck’s
momentum?
p = mv = (2250 kg)(25 m/s)
= 5.6 x 104 kg m
s

8. Change in momentum - accl
occurs any time an object changes
velocity (speed or direction).

9. Momentum Change &
Newton’s 2nd Law
• F = ma
• F = m(Dv/Dt)
• FDt =mDv m (vf - vi) for const mass.
• FDt = Dp Impulse.
 Dp = Change in momentum

10. Stand up
• Try to hit a home run.
• Try to drive a golf ball really far.

11. Equations of Momentum Change
• J =FDt = Dp Impulse = change momentum.
• pf – pi.
 Dp = mvf – mvi
• for velocity change with constant mass can
factor out mass you can write,
• m (vf - vi) or mDv.

12. Force is required to change velocity or
momentum of a body in motion.
Force must be in contact for some time.

13. Increased force & contact time on
object give greatest impulse Dp = mDv.

14. Hit a homerun needs large impulse. The
more contact time, the less force needed to
give same impulse D p.

15. Impulse (J) is the momentum change.
It has the same units.
kg m or Ns
s
It is like force but includes a contact
time component!

16. Ex 2. How long does it take an
upward 100N force acting on
a 50 kg rocket to increase its
speed from 100 to 150 m/s?

17. F = 100 N
Dv = 50 m/s
m = 50 kg
Ft = mDv
t = mDv
F
50 kg(50 m/s)
100 kg m/s2 = 25 s.

18. Concept: A pitcher throws a fastball to a
catcher. Who exerts a larger force on the
ball? Explain.

19. Concept: Explain, in terms of impulse and
momentum, how airbags help avoid injury
in a car crash.

20. Examples of Impulse/
Change in Momentum
• Baseball batter swinging through ball.
• Applying brakes of car over time to stop.

21. Ex 3. How long does it take a
250 N force to increase to
speed of a 100 kg rocket
from 10 m/s to 200 m/s?

22. Ft = mDv t = mDv
F
F = 250 N
m= 100 kg
Dv =190 m/s
t = 100kg(190m/s)
250 kg m/s2. = 76 s.

23. Ex 4. The speed of a 1200 kg car
increases from 5 to 29 m/s in 12 s.
What force accelerated the car?
2400 - N

24. Ex 5: A 0.4 kg ball is thrown against a
wall with a velocity of 15 m/s. If it
rebounds with a velocity of 12 m/s:
a) what was its Dv?
b) What was its Dp?

25. Dv = vf – vi.
-12 m/s – (15 m/s) = - 27 m/s.
Dp = mDv
= 0.4kg(27m/s)
=10.8 kg m/s

26. How many water balloons does it
take to stop a bullet? 3:30
• http://www.unwindly.com/i/772-How-
Many-Water-Balloons-Does-It-Take-To-
Stop-A-Bullet

27. • Running with momentum. 15 min.
• https://www.youtube.com/watch?v=jLIyDf
kQcsk
• Relaxing with impulse.13 minutes.
• https://www.youtube.com/watch?v=0nOHL
Thv2mw

28. Understanding Car Crashes 22 min
start 8:53
• Hewitt Momentum 4:20
• https://www.youtube.com/watch?v=2Fwhj
UuzUDg
http://www.youtube.com/watch?v=yUpiV2I_IRI

29. Hwk read text 208 – 211
do pg 214 #1- 4 concepts
do p 211 #1 - 4. Impulse prbs.
Also worksheet
“Impulse Momentum”

30. Which are units of Impulse?
Nm
N/s
Ns
N/m
A ball mass 0.10 kg is dropped from 12-m. Its momentum just as
it strikes the ground is:
1.5 kgm/s
1.8 kgm/s
2.4 kgm/s
4.8 kgm/s

31. A 0.060-kg tennis ball, initially moving at 12 m/s, is
struck by a racquet causing it to move in the opposite
direction at a speed of 18 m/s. What is the impulse
exerted by the racquet on the ball?
0.36 kgm/s
0.72 kgm/s
1.1 kgm/s
1.8 kgm/s

32. Graphs

33. Constant force f - t graph:
Dp /Impulse is area under curve
FDt.
Force
N

34. Non-Constant Force
Force vs. time graph. The area under the curve =
impulse or Dp change in momentum.
What is the impulse during the 9 seconds of contact?
225 Ns

35. Consv Momentum Demos.

36. Conservation of Momentum
If no external force acts on a closed
system, the total momentum
remains unchanged even if objects
interact.

37. What is a system?
Two or more objects that interact
in motion. One may transfer part
or all of its momentum to the
other(s).
Common examples: collisions,
explosions.

38. One Ball transfers all its momentum.

39. The astronaut transfers part of his
momentum to the second astronaut.

40. Conservation of Momentum
Calc’s
• Total momentum before = total after
interactions.
• Collisions.
• Explosions
• Pushing apart.

41. SPbefore = Spafter
m1v1 + m2v2 = m1fv1f + m2fv2f
v1 and v2 velocities for objects
one and two.
m1 and m2 masses of objects
To Calculate:

42. Recoil From Explosions

43. Recoil illustrates conservation
of momentum where initial and
final momentum = 0.
0 = p1 + p2.

44. 1. Two spring loaded lab carts A and B, explode apart
from rest. Cart A is twice the mass of cart B. The final
velocity of cart A is 2 m/s. What is the final
momentum of the system?
• 0

45. 2. The cannon is 100kg and the cannonball is 5 kg.
If the ball leaves the cannon with a speed of 100
m/s, find the recoil velocity of the cannon.
- 5 m/s = vcf

46. Before Firing After Firing
m1v1 + m2v2 = m1fv1f + m2fv2f
0 = (100kg)vcf + (5kg)(100m/s)
-500 kgm/s = (100 kg) vcf
- 5 m/s = vcf
recoil velocity of cannon

47. 3. A 63-kg astronaut is in spacewalk when the tether
breaks. The astronaut throws a 10-kg oxygen tank
directly away from the spaceship at 12 m/s.
Assuming the astronaut was initially at rest, what is
his final speed after throwing the tank?
• 1.9 m/s

48. • Hwk. Consv Momentum wksht

49. Collisions
• Sticky
• Bouncy

50. Let’s say a 4 kg fish swimming at 5 m/s,
eats a 1 kg fish. What is their final
velocity?
Stick em together problems

51. Bg fish sm.fish Bg fish sm.fish
m1v1 + m2v2 = m1fv1f + m2fv2f
(4kg)(5m/s)+(1 kg)0 =(4kg)v1+(1kg)v2
But the final velocities are equal so factor out
the vf:
20 kg m/s = vf (4+1kg)
vf = (20 kg m/s) / (5kg) = 4m/s

52. Find the final velocity of the cart and brick
together
4. A 2 kg brick not moving horizontally is
dropped on a 3 kg cart moving at 5.0 m/s.

53. cart brick cart brick
m1v1 + m2v2 = m1fv1f + m2fv2f
(3kg)(5.0m/s) + 0 = (3kg)v1 + (2kg)v2
150 kg m/s = v (3kg + 2 kg)
(150 kg m/s )/5 kg = 3.0 m/s

54. Elastic & Inelastic Collisions
Elastic: no KE lost at all
(to heat, light, sound etc.) Usu. Involves
objects that don’t make contact or bounce
off.
Inelastic: involves greatest loss of KE. Usu
damage done. Most extreme case – objects
stick together.

55. Which is totally elastic?
Inelastic?

56. Inelastic Collision
mc = 1000 kg mt = 3000 kg
vc = 20 m/s vt = 0
pc = pt =
6. A 1000 kg car moving east at 20 m/s rear
ends a stationary truck. The truck’s mass is
3000-kg. If the bumpers lock on impact, what is
the final velocity of truck/car wreck?

57. m1v1 + m2v2 = m1fv1f + m2fv2f
(1000kg)(20m/s) + 0 = (1000)v + (3000)v
(20000 kg m/s) = (1000kg + 3000kg)v
(20000 kg m/s) = (4000 kg)v
(20000 kg m/s) = v
4000 kg
v = 5 m/s

58. Elastic Collision
mc = 1000 kg mt = 3000 kg
vc = 20 m/s vt = 0
7. Find final velocity of the car if truck
has final velocity of 10 m/s.

59. m1v1 + m2v2 = m1fv1f + m2fv2f
(1000kg)(20m/s) + 0 =
(1000kg)vc+(3000kg)(10m/s)
20,000 kg m/s = (1000kg)vc+30000 kg m/s
20,000 kg m/s – 30,000 kg m/s = vc
(1000kg)
- 10 m/s = vc

60. Do Now: On July 4th my family likes to shoot off
fireworks. One rocket was shot straight up, climbed
to a height 18-m and exploded into hundreds of
pieces in all directions at its highest point.
Thinking about conservation laws, think about the
rocket at its highest point just before & just after it
explodes:
How does the rocket’s momentum compare before
& after the explosion?
How does its KE compare compare before & after
the explosion?

61. Inelastic Collisions
Stick em together
KE “lost” converted
Elastic Collisions – no KE lost.
Bounce off each other.

62. Hwk Read Rev Book pg 57 – 58
Do sheet 1-8

63. Film Understanding Car Crashes 23
min
http://www.youtube.com/watch?v=yUpiV2I_IRI
Hwk Prob’s in momentum sheet

64. Hewitt Cons Momentum 6:30
https://www.youtube.com/watch?v=1-s8NZ8xKW0
Fish lunch Hewitt 4:00
https://www.youtube.com/watch?v=
MK0B5hEU7OI