Transcript Impulse

Impulse
Storm Damage

A house takes damage from the force of a 60 mph
gale-force wind. If the house is subject to a hurricane
at 120 mph the force on the house is
•
•
•
•
A) Equal.
B) Two times stronger.
C) Four times stronger.
D) Eight times stronger.
Linear Momentum

Momentum is the measure of inertia in motion.
• Momentum equals mass times velocity
• Momentum is symbolized by p

Like velocity, momentum is a vector.
• Momentum is parallel to velocity


p  mv
p
m
v
Applying Force
Newton’s law uses mass and
acceleration.


F  ma

Acceleration is the time rate
of change of velocity.


v
F m
t

If the mass is constant the
force depends on
momentum.

  (mv ) p
F

t
t
Change in Momentum


A force acting during a time
changes momentum.
The change in momentum is
called the impulse (J).
 p
F
t



 
Ft  p f  pi  p  J
Storm Force

At 60 mph the momentum of
the air is due to the mass (m)
and velocity (v).
 (mv )
F
t
p = mv

At 120 mph the speed is
double.
• Half as much time to get the
same amount of mass

F


m
(mv )
(2v )  4
(t / 2)
t
p = m(2v)
Nonzero Force

When momentum changes in a system, an external
force has acted.
• Constant force like gravity
• Position-dependent force like the elastic force
• Time-dependent force during brief contact
pi
pf
F(t)
before
after
Force of Collision

Collisions seem
instantaneous.

They actually take place
during a short time span.

The force (an elastic force)
greatly increases during the
contact, then decreases.
Impulsive Force

A karate strike to a board
can break it.
• Mass of the hand: 0.70 kg
• Weight of the hand: 6.9 N
• Velocity of the hand: 5.0 m/s
pi = (0.7 kg)(5.0 m/s)
= 3.5 kg m/s
• Stopping distance: 6.0 mm
pf = 0
J = pf  pi = 3.5 kg m/s
directed upwards on the hand
Average Force

The average force is the
constant force that gives the
same impulse in the same
time.


J
Fav 
t

Impulse = area under force
vs. time curve





J   Ft  p f  pi  p
Brief Time


Breaking an object benefits
from a short time interval.
The average force is
hundreds of times larger
than the weight.
t = y / vav = y / (v/2)
= (0.006 m) / (2.5 m/s)
= 2.4 ms
Fav = J / t
= (3.5 kg m/s)/(0.0024 s)
= 1.5 kN
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