Transcript Impulse Momentum PowerPoint

From a Consumer Reports article on Crash
Tests of Cars…
…..The tests don’t say what happens when a small
car impacts a big car. Physics dictates that the
smaller car bears the brunt of the collision.
Why? What Physics?
p  mv
v
1. Momentum = mass x velocity
2. A vector quantity
3. Its direction is parallel to the velocity
4. Units are kg · m/s
p
Large Momentum Examples

Huge ship moving at a
small velocity
P = mv

High velocity bullet
P = mv
1. A 15 g bullet is moving with a speed of 300 m/s, what is
the magnitude of its momentum.
p = mv = (.015 kg) (300 m/s)
= 4.5 kgm/s
2. A 75 kg sprinter running with a speed of 10 m/s, what
is the magnitude of her momentum?
p = mv = (75 kg) (10 m/s)
= 750 kgm/s
Two identical objects move toward one another along the
same line as shown. Which is correct?
a.
b.
c.
d.
The magnitude of the total momentum before the impact is mv
The magnitude of the total momentum before the impact is 3mv
The magnitude of the total momentum after the impact is 2mv
The total kinetic energy before the impact is 3mv2/2
Equivalent Formulation of
Newton’s Second Law
p
 F=
t
*The
time rate of change
of momentum equals the
net force applied to it.*
Impulse
J  p
Change in
Momentum
MOVIE
The greater
the change in
momentum the
greater the
impulse!
Newton’s Second Law Derivation
The rate of change of momentum of a body is equal to
the net force applied to it.
Δp Δmv
mΔv
 F = Δt = Δt = Δt = ma
Δp = FΔt
Having a net force is not enough to cause a change in the motion of
an object. It must be present for some time. A huge force acting for
zero seconds accomplishes nothing. A small force acting for a long
time can be as effective as a huge force acting for a short time.
You can abruptly stop a car by stomping on the brakes or gradually by lightly
applying the brakes. In either case the car gets stopped. When we multiply the
average force by the time, we find that in all three cases above is the same. It’s
called the Impulse. The formula for it actually comes from a little manipulation of
Newton's Second Law shown below.
Two ways to calculate the Impulse
J  p
And since 
p = F t
J  F t
Louis
Newton’s Second Law & Momentum




If there is a net force the momentum changes.
 p = F t = Impulse = J
If there’s no net force the momentum is constant.
 p = F t = 0
Fore!
A golf ball of mass .05 kg is hit off the tee at 45 m/s.
The golf club was in contact with the ball for 5.0 x 10-3 s.
1. Find the force imparted to the golf ball by the club.
2. Find the impulse imparted to the ball.
J = Impulse = F t =  p = mvf – mvi
J = Impulse = m(vf – vi ) = 0.05kg · (45 – 0)m/s
J = Impulse = 2.25 kg·m/s = 2.25 N·s
2. Find the average force given to the golf ball by the club.
J= F t ( = 2.25 N· s )
J/ t = F
F = 2.25 N·s/5.0 x10-3 s
= 450 N
F
t
How can you maximize the Impulse?
Apply the force for a long time !!
Follow through on a golf swing
 Pushing a car


Hitting a baseball
How can you minimize the force?
Increasing




t
decreases F !!
Catching a ball
Bungee jumping
Air bags
Bending knees
Increasing the
time decreases the force!
t
F
When a boxer sees that he will be hit he relaxes his neck and allows
his head to move backwards upon impact, it’s called riding the
punch. A boxer does this to extend the time of impact of the glove
with their head. Why?
A 1500 kg car initially moving with a speed of 15 m/s collides head
on with a pole and is brought to rest in .3 seconds.
J  F t  p
a.
b.
c.
d.
e.
What is its initial momentum?
What is its final momentum?
What is the change in momentum of the car?
What impulse was imparted to the car?
What is the average force exerted on the car?
vi
vf
A .15 kg tennis ball traveling to the right at 30 m/s strikes the
racquet and rebounds at 30 m/s:
1. What impulse was delivered to the ball?
2. If the collision lasted .2 seconds what average force was given
to the ball?
3. What impulse was delivered to the racquet?
Estimate the Impulse imparted to the 100 kg passenger
J  mv f  mvi
Calculate: The impulse
given to the 300 kg car in
each case
A soccer player hits a ball (mass
m = 440 g) coming at him at 20 m/s.
After it was hit, the ball travels in
The opposite direction with a
velocity of 30 m/s.
(a) What impulse acts on the ball while
it is in contact with the foot?
(b) The impact time is 0.1s. What is the
force acting on the ball?
Force vs. Time

Area under the curve = Impulse
Force vs. Time




Area under the curve = Impulse
Area above the x-axis is positive Impulse
Area below the x-axis is negative Impulse
Total Impulse is the sum of all the individual areas
F
Force vs. Time
Jp= Positive impulse
Impulse = Area
I
III
II
Jn= Negative impulse
JNet = Net Impulse JNet = Jp + Jn
t
Calculate the Impulse from:
1. 0-10
2. 10-17
3. 17-20
4. 20-25 seconds.
10
5
F(N)
10
17
20
25
Time (s)
Force on a rubber ball during a bounce
Constant force
What would the graph be for a
rigid ball hitting the wall?
Force on a human during a jump
Force (N)
Time (sec)
1. In which case (A or B) is the change in momentum the
greatest? Explain.
2. In which case (A or B) is the impulse the greatest? Explain
3. In which case (A or B) is the force which acts upon the ball
the greatest (assume contact times are the same in both
cases)? Explain
Lucky
Lara, mass 60 kg, is riding at 25 m/s in her sports car when
she must suddenly slam on the brakes to avoid hitting a dog crossing
the road. She strikes the air bag, which brings her body to a stop in
0.4 s . Lara then picks up the “Lucky” puppy and they live happily
ever after.
1. What average force does the seat belt exert on her?
2. If Lara had not been wearing her seat belt and not had an air bag,
the windshield would have stopped her head in 0.001 s. What
average force would the windshield have exerted on her?
80N
1. A hockey player applies an average force of 80 N to a 0.25 kg
hockey puck for a time of 0.10 seconds. Determine the impulse
experienced by the hockey puck.
2. If a 5 kg object experiences a 10 N force for a duration of 0.1
second, then what is the momentum change of the object?