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Momentum and Impulse
Physics 11, Unit 3
This section: see pages 195 to
205 in text
Momentum and Impulse

http://www.youtube.com/watch?v=yUpi
V2I_IRI

Why are buses safer than other
vehicles???

Up to 13 minutes (we will watch the
rest later!)
What is momentum?



Sports: A team that has the
momentum is on the move and is
going to take some effort to stop.
Physics: It refers to the quantity of
motion that an object has. If an object
is in motion then it has momentum.
The amount of force over a given time.
Momentum - Summary

Momentum (p): The quantity of motion that
an object has.



Formula


If an object is in motion then it has momentum.
Vector (direction of velocity)
p = mv
Units

kg m/s
(don’t use P! P=Power!)
An example to think about…

Think of two cars of equal mass. If one car
is moving faster, it will take more force to
stop the faster car in the same time interval.

If you have a car and a truck, the truck has
more mass so has more momentum – it will
take longer for it to stop than the car.
Example



A cement truck full of cement has a
mass of 42000kg. It travels north at 18
m/s.
A) Calculate the truck's momentum.
B) How fast must a 750 kg Honda
Civic travel in order to have the same
momentum?
Example

A cyclist is
travelling at 32km/h
and the bike and
rider have a mass
of 85kg. What is
their momentum?


p  mv

p  85kg(8.89m / s )

p  760kgm / s
Try this:

Page 197, question 29
Relating this to Force



According to Newton's first law, if no net
force acts on an object, its velocity is
constant. Its mass will not change.
Therefore, if no force acts on an object,
momentum is constant. Momentum is
conserved.
Newton's second law describes how the
velocity of a body changes if a net force acts
on it. (Acceleration occurs if a net force acts
on it).
We have looked at motion and
forces already…However…


When an object is accelerated, typically the
force will only be applied for a given time
This holds true for things like:




Explosions
Collisions
Recoil
So instead of considering Newton’s Second
Law (F = ma) as we have previously
discussed, we will rearrange the equation so
we can look at momentum and impulse
Momentum – derivation of
formula


Momentum can also be
defined starting from
Newton’s Second Law
The rate of change of
momentum can also be
used to determine the
force


F  ma

 mv
F
t


 mv f  mvi
F
t


p  mv
Impluse - Derivation


Using the definition
of acceleration
(change in velocity
divided by change in
time) we can rewrite
Newton’s Second
Law
Rearranging gives
impulse


F  ma

 mv
F
t


j  Ft  mv
Impulse - Summary

Impulse (j): Force applied over a
given time


Also known as change in momentum
Vector (same direction as the force)
Formula: j = F∆t
 Units: Ns
***(but Ns = same unit as kg m/s)

How are impulse and
momentum related? (Copy)



Same units
Impulse is like momentum except we use
it for sudden changes in momentum, like
for collisions, explosions, and recoil
Impulse is the change in momentum (not
just the momentum) so you need vi and vf
Example

A tennis ball is
struck by a racquet
with a force of
750N; if the time of
contact was
0.023s, what
impulse was
delivered to the
ball?


j  Ft  mv
j  750 N (0.023s)
j  17 Ns
Try these…

Page 200, questions 30, 31, 32
How does impulse/momentum
affect sports?

Why does your coach tell you to “follow
through” when you shoot a puck in hockey
or hit a ball in baseball?

http://www.youtube.com/watch?v=OrLcZNG
0N0I (first part is “mathy” but second part is
about the follow through so keep watching
)
Impulse-Momentum
Connection


Collisions and explosions happen so
quickly that it is often impossible to
calculate anything more than an
average force. This is because the
force changes so quickly.
By examining the momentum before
and after the interaction between 2
objects, we can determine impulse.
Impulse-Momentum Theorem
(copy)

Impulse is the difference between the
final momentum and initial momentum
of an object involved in an interaction.
Problem

A baseball of mass 0.145kg is pitched
toward a batter with an initial velocity of
35m/s. If the batter hits the ball in the
opposite direction at 45m/s, determine the
force that is applied by the bat on the ball if
the contact time was 0.013s.

HINT: Remember that impulse is equal to
the change in momentum…

Did you get an answer of
890 N [away from the batter]
More Practice



http://www.physicsclassroom.com/class/mo
mentum/u4l2e.cfm (for you to check out if
needed)
Think of a dump truck and a car. If they are
stopped in the same time interval, it will take
______ (more or less) force to stop the truck
than the car. Why?
Think of two cars of equal mass. If one car
is moving faster, it will take _____ (more or
less) force to stop the faster car in the same
time interval.

A golf club strikes a golf ball. The club
and ball remain in contact for 0.60 ms.
The 45 g ball leaves the club with a
speed of 70. m/s. Calculate the
average force of the club on the ball.

Answer: 5250
= 5300 N [away from club]

Try These

Page 203

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33-35
Page 209
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37-46