Download Momentum - HRSBSTAFF Home Page

Momentum and Impulse
Physics 11, Unit 3
This section: see pages 195 to
205 in text
Think about…

What do you already know about the
following. Think about them as we study
this unit…






Work
Energy
Power
Efficiency
Momentum
Impulse
Think about…






Why is energy important?
Where does energy come from?
Where does energy go?
How do we capture energy?
Why is this an important part of our
everyday lives???
How does energy impact kinematics
(motion) and dynamics (forces)?
First …

What is momentum?


What is the formula for momentum?


The product of mass and velocity.
p = mv
(don’t use P!!! Power!)
What are the units for momentum?

kg m/s
An example to think about…

Give an example involving momentum.



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.
Is momentum a vector or scalar?

Vector (same direction as the motion or
velocity).
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?
Momentum


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
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 these:

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, in this situation, 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.
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 it, we will rearrange the equation
so we can look at momentum and impulse
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





Force applied over a given time
It is a VECTOR and the direction is the
same direction as the force
Its symbol is j
Formula: j = F∆t
Units: Ns
But what is impulse?

http://www.youtube.com/watch?v=yUpi
V2I_IRI

Why are buses safer than other
vehicles???

Up to 13 minutes (rest is next
unit…types of energy)
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
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.

Did you get an answer of
890 N [away from the batter]
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

Impulse is the difference of the final
momentum and initial momentum of an
object involved in an interaction.
Impulse-Momentum Theorem

Impulse and
momentum can be
related in order to
solve dynamics
problems in one step
as opposed to two or
more


Ft  mv



Ft  mv f  mvi



Ft  p f  pi


Ft  p
More Practice



http://www.physicsclassroom.com/class/mo
mentum/u4l2e.cfm
Think of a dump truck and a car. If they are
stopped in the same time interval, it will take
a ______ (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 cement truck full of cement has a
mass of 42000 kg. It travels north at
18 m/s. Calculate the truck's
momentum. How fast must a 750 kg
Honda Civic travel in order to have the
same momentum?

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.
Example from before…

A baseball of mass .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.
Example


Ft  p

 mv
F
t
 .145kg(45m / s  (35m / s )
F
.013s

F  890 N
Try These

Page 203


33-35
Page 209

37-46