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Momentum
Webster’s:
A property of a moving body that determines
the length of time required to bring it to rest
when under the action of a constant force or
moment.
“Moving Inertia”
What Quantities determine how
hard it is to stop an object?
• Mass
• Velocity
Which of the following has the most
momentum?
a) A person jogging down the street.
b) A Volkswagen Bug traveling down the
road.
c) A Hummer parked at the mall.
d) A freight train at the station.
p = mv
m = mass (kg)
v = velocity (m/s)
p = momentum ( kg•m/s = Ns)
momentum is a vector quantity, it has
magnitude and direction. Pay attention to
directions!!!!!!
Rewriting Newton’s 2nd Law
v
 F  ma
a
t
 v f  vo  mv f  mvo p f  po p
 
 F  m


t
t
t
 t 
p
F 
t
An impulse is a change in
momentum, which is caused by
applying a force for a period of
time.
picture
impulse  J  p  Ft
Graphically: The area of a force vs. t graph
is equal to the impulse or the p.
F(N)
impulse
p
t(s)
The same p can be produced by
applying a large force for a short
time or a small force for a long time
F
p = t
p =
F
t
Example 1:
A net force of 8N acts on a 200g object for a period
of 5s.
(a) What is the change in momentum?
(b) Assuming the object starts from rest what is its
final velocity after 5 seconds?
a)
 Ft  p
8 N 5s   p
40 Ns  p
b)
p  mv f  mvo
kgm
 m
40
 .200kg v f  .200kg  0 
s
 s
m
v f  200
s
Example 2:
A 300g ball strikes a wall horizontally with a
speed of 25m/s and bounces straight back with a
speed of 15m/s. The ball is in contact with the
wall for 5x10-3s. What average force does the
wall apply to the ball?
25m/s
15m/s
 Ft  p
Ft  mv f  mvo
  .3 15  .325

F 5 10   12
F 5 10
3
3
F  2400 N
Example 3:
The following graph represents the net force
applied to a 5kg object vs. the time the force is
applied. Find the final velocity of the object if the
original velocity was 12m/s.
100Ns
50Ns
50Ns
area = impulse = p
200 Ns  p  mv f  mvo
 m
200 Ns  5kg v f  5kg 12 
 s
260 Ns  5kg v f
m
v f  52
s