1.
MOMENTUM
1. Define momentum as mass times velocity .
2. Recognise that momentum is a vector quantity, and that its direction must
always be stated or shown.
3. Describe experiments that show that momentum is conserved during
collisions
4. Distinguish between external and internal forces in a collision
5. Introduce Force - time graphs in the context of a collision and use this to
relate the change in momentum to the force impulse
6. Explain the difference between elastic and inelastic
collisions.
Reading p121 to 130
2.
BUILDING A DEFINITION
Example 1
Why would this ship be difficult
to slow down?
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Example 2
What makes the Ferrari difficult to slow down
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The harder an object is too stop, the greater momentum it has.
3.
BUILDING A DEFINITION
Example 1
Why would this ship be difficult
to slow down?
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Example 2
What makes the Ferrari difficult to slow down
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The harder an object is too stop, the greater momentum it has.
4.
BUILDING A DEFINITION
Example 1
Why would this ship be difficult
to slow down?
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Example 2
What makes the Ferrari difficult to slow down
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The harder an object is too stop, the greater momentum it has.
5.
MOMENTUM IS A QUANTITY OF MOTION
Clikview: “Collisions” > Conservation of momentum
It is the product of an object’s mass and velocity.
Momentum = Mass x velocity
p = the object’s momentum (kgms-1)
p = mv m = the object’s mass (kg)
~ ~
v = the object’s velocity (ms-1)
Note
Momentum is a vector quantity since it depends on velocity which is a vector
quantity.
Change in Momentum
The change in momentum of an object equals the final momentum minus the
initial momentum.
p = pf - pi
~ ~ ~
6.
EXAMPLES
1. Calculate the momentum of a car that has a mass of 1200 kg and is travelling at
30 ms-1
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2. Calculate the mass of a cricket ball that is bowled at 36 ms-1 and has a momentum
of 7.2 kgms-1
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3. Calculate the velocity of a person that has a mass of 140 kg and has a momentum
of 1400 kgms-1
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Complete Q.1 - “Momentum & Impulse”
7.
INTERNAL & EXTERNAL FORCES
Example
Consider that two masses (A and B) initially stationery, push away from each other.
v=0 F F v=?
2 ms-1 0.5 ms -1
A B A B A B
0.1 kg 0.1 kg 0.1 kg 0.1 kg
BEFORE DURING AFTER
In this situation there are no external forces. The forces necessary for the separation
are internal.
A exerts a force on B and B exerts a force on A as shown in the diagram (below).
These forces are equal and opposite and are called an action - reaction couple.
Examples of external forces: Friction, a push on one of the objects as it collides with
the other object.
In this example it is possible to calculate v using the law of conservation of
momentum ......
8.
THE LAW OF CONSERVATION OF MOMENTUM
In all collisions and explosions, provided there is no external force then the
momentum of the system is conserved.
Total momentum before = Total momentum after
Note that momentum is a vector and therefore direction needs to be shown. In a
problem where objects travel in a straight line, use + and - to indicate direction.
Examples
1. A toy railway carriage of mass 5 kg travelling a 2 ms-1 collides with a stationery
carriage which has a mass of 3 kg. After the collision the two carriages stick
together and move as one. Calculate the speed of the carriages after the collision.
- +
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9.
2. The carriages, in a second collision, collide head on as shown in the diagram below.
Calculate the velocity of the 3 kg carriage after the collision.
- +
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Complete Q.1 to 3 - “Collisions & Explosions”
10.
CHANGE IN MOMENTUM & IMPULSE
[Examples: 1.Airbags 2. Jumping from a burning building onto a matress]
• Impulse is a term that means “The change in momentum of an object”
• Impulse = the final momentum - the initial momentum of the object.
p = the object’s Impulse
p = pf - pi
~ ~ ~ pf = the object’s final momentum
pi = the object’s initial momentum
Note:
• Momentum is a vector and therefore direction needs to be shown. In a problem
where objects travel in a straight line, use + and - to indicate direction.
• Change in momentum is also a vector quantity and will therefore be positive or
negative
• An object experiences a change in momentum or impulse when it experiences a
force over a period of time:
Where F = the force acting on the object
∆p = F∆t
~ ~
and t = the time for which that force acts
11.
Change in momentum & force EXAMPLES
1. An apple of mass 250 g falls of a branch and lands on the ground. It is travelling at
3 ms-1 just before it hits the ground and stops. Calculate its change in momentum.
2. A 0.2 kg tennis ball collides with a solid wall as shown:
20 ms-1 20 ms-1
Determine the change in momentum of the ball.
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Describe the force responsible for this change in momentum.
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If the collision time is 0.1 s, calculate the size of this force.
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Complete Q.2 - “Momentum & Impulse - Exercises”
12.
THE FORCE - TIME GRAPH
An object receives an impulse when we change its momentum by applying a force
to the object over a period of time.
∆p = F∆t ....... a rearrangement of F = ∆p
~ ~ ~
∆t
Impulse Force applied
Consider...
Taking a fall and hitting your head on the pavement wearing a helmet compared to
having the equivalent fall without the helmet.
F
Without helmet
With helmet => LESS force over a LONGER period
of time.
SAME AREA under the graph.
Impulse = Area under the
Force - time
graph
t
Complete Q.3, 4, 7 & 8 - “Impulse & Momentum - Exercises”
13.
ELASTIC & INELASTIC COLLISIONS
Momentum is always conserved in a collision (provided there are no external forces)
Kinetic energy is not always conserved:
• During elastic collisions, Kinetic energy is conserved.
Ek before the collision = Ek after the collision
• During inelastic collisions, Kinetic energy is not conserved.
Some of the Ek is converted into other forms during the collision - commonly heat
and sound
Examples
A trolley of mass 3 kg and speed 4 ms-1 collides head on with a stationery trolley of
mass 1 kg. They stick together and move off with a speed of 3 ms-1. Momentum can
be shown to be conserved in this collision.
(a) Show that kinetic energy is not conserved in the collision.
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(b) Where has the lost energy gone?
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14.
Example
A ballistic pendulum is used to measure the speed of a bullet. It is a large soft mass which
has been suspended from the ceiling. When a bullet with speed v1 embeds itself into the
mass the mass swings and rises a distance h as shown:
1 2 3
v1 v2
M
m h
v= 0
M +m
The masses and the height are measured and recorded as follows:
M = 998 g
m=2g
h = 10 cm
Calculate the speed of the bullet v1 (in ms-1)
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15.
MOMENTUM SUMMARY
Momentum is the product of an object’s mass and velocity.
Momentum = Mass x velocity
p = the object’s momentum (kgms-1)
p = mv m = the object’s mass (kg)
~ ~
v = the object’s velocity (ms-1)
Internal forces A exerts a force on B and B exerts an equal and
in collisions opposite force on A
A B
and explosions
Provided there are no external forces (forces acting from outside the system like
friction)
Momentum is always conserved:
Momentum before the event = Momentum after the event
16.
Direction
Momentum is a vector quantity. In 2D (motion along a straight line), one direction
can be shown using a positive sign and the opposite direction can be shown using a
negative sign.
Example - Two utes collide
14 ms-1 10 ms-1 12 ms-1 v
1000 kg 1200 kg
AFTER
BEFORE
Momentum after collision = Momentum before collision (since there
are no external forces)
(1000 x 12) + (1200.v) = (1000 x 14) + (1200 x 10)
Solving this equation for v gives: v = 11.7 ms-1
17.
Change in Momentum, ∆p (or Impulse)
~
∆p = pf - pi = F∆t Example - Crash helmets allow the same
~ ~ ~ ~ change in momentum to be achieved but with a
smaller force over a larger collision time.
∆p = F ∆t
Constant
Conservation of kinetic energy occurs only in an elastic collision. This law is
summarised as follows:
For an elastic collision: Ek before the collision = Ek after the collision
For an inelastic collision: Ek before the collision ≠ Ek after the collision
In an inelastic collision some of the kinetic energy of the moving object/s is converted
to other forms.