Download A Second Look at Newton`s Law

Unit 4: Momentum, Work and Energy
Momentum and Impulse
Physics 11
Back to bad humour…
Momentum:
A car at rest possesses:
Inertia
Amount identified by:
mass (m)
A moving car possesses:
Inertia
and

velocity (v)
A moving car also possesses:

momentum ( p )


p  mv
Momentum:
• Symbol: p
p=mv
• Product of the objects mass (kg) and
velocity (m/s)
• Is a vector
• Units = kg·m
s
Example #1:
• Determine the momentum of a 1.78 kg
soccer ball travelling at 4.55 m/s [S]
across a soccer field.
p = mv
= (1.78)(4.55)
= 8.10 kg·m [S]
s
Car at rest has mass
velocity = 0


p  mv

p0
Moving car has
mass and velocity


p  mv


p  mv
What happens when the car starts from
rest and achieves some velocity?
The car’s momentum:
Increases
What happens when the car moving
at some velocity comes to rest?
The car’s momentum:
Decreases
What causes the increase or
decrease in momentum?
Force
Let’s re-examine Newton’s 2nd Law:


Already F  ma
Know:


Combine:
v
F m
t

 v
Already a 
t
Know:
And re-arrange:


Ft  mv
Let’s re-examine Newton’s 2nd Law:


Ft  mv
Then:

Ft

Impulse (I)

mv
Change in
? momentum
Impulse:
• Symbol: J
J = F Δt
• Product of force (N) and time interval (s)
• Is a vector
• Units = N·s
Example #2:
• A halfback experienced a force of 800. N for
0.90 seconds to the west, what is the impulse?
J =Ft
= (800)(0.90)
= 720 N·s [W]
Momentum and Impulse
Connection:
• To stop such an object, it is necessary to apply a
force against its motion for a given period of time
J=mv
Momentum and Impulse
Connection:
• Impulse and
momentum can be
related in order to
solve dynamics
problems in one step
as opposed to two or
more
Impulse


Ft  mv



Ft  mv f  mvi



Ft  p f  pi


Ft  p
Change in
momentum


Ft  (mv )
What causes a change in momentum?
Force
How are force and time related?
If  t

Then
F
If
t
Then

F
hard to stop, small mass
m
v
hard to stop, small velocity
Mv
MV
Think about it!
A Mack truck has more mass than
a roller skate.
Will it always have more
momentum than the roller skate?
No
A Mack truck at rest will have no
momentum.
Think about it!
Could a Mack truck and a
roller skate have the same nonzero momentum.
Yes
Mack truck moving very slow and
roller skate moving very fast.
Example #3:
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.
Givens: m=0.145kg, Vi= 35m/s, Vf= -45m/s,
t= 0.013s
F=?
FΔt = m Δ v
F = m (Vf – Vi)
Δt
= (0.145)(-45-35)
0.013
= - 890 N
Summary
• The impulse experienced by an object is the
force x time
• The momentum change of an object is the
mass x velocity change
• The impulse equals the momentum change
Try it :
•
•
•
•
Page 197 # 29
Page 200 # 30, 31, 32
Page 203 #33, 34, 35
Page 209 # 37-46