7-3 Collisions and Impulse
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Transcript 7-3 Collisions and Impulse
Chapter 7
Linear Momentum
Objectives
• Define impulse, and relate to momentum.
• Give examples of how both the size of the force and
length of time applied affect the change in momentum.
• Solve momentum and impulse problems.
Warm-Up
Knowing how to find momentum, how do you
think one can find the change in momentum?
Engagement / Exploration
• Demo – egg and sheet
• https://www.youtube.com/watch?v=7RSUj
xiZnME
Exploration – Interpret the diagram
Impulse
• When an object experiences a net force, its momentum
will change!
• Impulse is a change in momentum!
J=Δp
• Impulse = Force * Time
J=Ft
Ft=Δp
F t = m Δv
F t = m (vf - vi)
Impulse changes Momentum
A greater impulse exerted on an object
A greater change in momentum
OR
Impulse = Change in momentum
OR
Impulse = Δ(mv)
Greek symbol “Delta”
Means “the change in…”
Impulse can be exerted on an object to either INCREASE or
DECREASE its momentum.
Impulse-Momentum Theorem
The theorem states that the impulse
acting on the object is equal to the
change in momentum of the object
•
F (t 2 t1) p 2 p1
• Impulse=change in momentum
(vector!)
• If the force is not constant, use the
average force applied
Air Bags
The air bag increases
the time of the
collision
It will also absorb
some of the energy
from the body
It will spread out the
area of contact
• decreases the
pressure
• helps prevent
penetration wounds
Case 1: Increasing Momentum
Examples:
Hitting a golf ball:
Baseball and bat:
Apply the greatest force
possible for the longest time
possible.
Accelerates the ball from 0
to high speed in a very short
time.
The impulse of the bat
decelerates the ball and
accelerates it in the opposite
direction very quickly.
Video: Changing Momentum – Follow Through
Case 2: Decreasing Momentum
It takes an impulse to change momentum, and
Remember … Impulse = F x t
If you want to stop something’s motion, you can apply a LOT of force over a short
time,
Or, you can apply a little force over a longer time.
Remember, things BREAK if you apply a lot of force to them.
Case 3: Decreasing Momentum
over a Short Time
If the boxer moves away from the punch, he extends the
time and decreases the force while stopping the punch.
If he moves toward the punch, he decreases the time
and increases the force
The airbag extends the time over which the impulse is
exerted and decreases the force.
Hitting the bricks with a sharp karate blow very
quickly maximizes the force exerted on the bricks
and helps to break them.
7-3 Collisions and Impulse
During a collision, objects
are deformed due to the
large forces involved.
Since
write
, we can
(7-5)
The definition of impulse:
Same Impulse
• If an object experiences a change in
momentum, how can you minimize the
force on the object?
• Extending the time, there by minimizing
the force.
J=
F
t
J= F
t
7-3 Collisions and Impulse
Since the time of the collision is very short, we
need not worry about the exact time dependence
of the force, and can use the average force.
7-3 Collisions and Impulse
The impulse tells us that we can get the same
change in momentum with a large force acting for a
short time, or a small force acting for a longer time.
This is why you should bend
your knees when you land;
why airbags work; and why
landing on a pillow hurts less
than landing on concrete.
Impulse examples
Follow through increases the
time of collision and the
impulse
small
large
I
Problem
•
Bobo hits a 0.050 kg golf ball, giving it a
speed of 75 m/s. What impulse did he
impart on the ball? Assume the initial
speed of a ball was 0 m/s.
•
•
J = change in momentum (mv)
J = 3.75 kg m/s
Questions
• Pick one to run into, a brick wall or a
haystack.
• Catch a baseball, what do you do?
• Jump off a table, what do you do?
• On which surface is a dropped glass less
likely to break: carpet or sidewalk?
• Why do boxers use short, fast jabs?
Conservation of Momentum
If no net external force (same as saying “no net impulse”) acts
on a system, the system’s momentum cannot change.
Momentum = 0 before the shot
Cannon’s
momentum
And after the shot
Shell’s
momentum
(equal and
opposite)
Example 7-6
• Advantage of bending knees when landing!
a) m =70 kg, h =3.0 m
Impulse: p = ?
Just before he
hits the ground
Ft= p = m(0-v)
First, find v (just before
hitting): KE + PE = 0
Just after he
hits the ground
m(v2 -0) + mg(0 - h) = 0
v = 7.7 m/s
Impulse: p = mv
p = -540 N s
Opposite the person’s momentum
• Advantage of bending knees when landing!
Impulse: p = -540 N s
m =70 kg, h =3.0 m, F = ?
b) Stiff legged: v = 7.7 m/s to
v = 0 in d = 1 cm (0.01m)!
vavg = (½ )(7.7 +0) = 3.9 m/s
Time t = d/v = 2.6 10-3 s
F = p/t = 540 Ns/2.6 10-3 s
= 2.1 105 N
(Net force upward on person)
From free body diagram,
F = Fgrd - mg 2.1 105 N
Fgrd =F + mg = 2.1 105 N + (70kg x 9.80 m/s/s)
Enough to fracture leg bone!!!
2.1 105 N
• Advantage of bending knees when landing!
Impulse: p = -540 N s
m =70 kg, h =3.0 m, F = ?
c) Knees bent: v = 7.7 m/s to
v = 0 in d = 50 cm (0.5m)
vavg = (½ )(7.7 +0) = 3.8 m/s
Time t = d/v = 0.13 s
F = p/t = 4.2 103 N
(Net force upward on person)
From free body diagram,
F = Fgrd - mg 4.9 103 N
Leg bone does not break!!!
Practice Problem
A 57 gram tennis ball falls on a tile floor. The ball
changes velocity from -1.2 m/s to +1.2 m/s in
0.02 s. What is the average force on the ball?
Identify the variables:
Mass = 57 g = 0.057 kg
Δvelocity = +1.2 – (-1.2) = 2.4 m/s
Time = 0.02 s
using FΔt= mΔv
F x (0.02 s) = (0.057 kg)(2.4 m/s)
F= 6.8 N
Example: Crash Test
• Crash test: Car, m = 1500 kg, hits
wall. 1 dimensional collision. +x is to
the right. Before crash, v = -15 m/s.
After crash, v = 2.6 m/s. Collision
lasts Δt = 0.15 s. Find: Impulse car
receives & average force on car.
Assume: Force exerted by wall is large
compared to other forces
Gravity & normal forces are perpendicular
& don’t effect the horizontal momentum
Use impulse approximation
p1 = mv1 = -22500 kg m/s, p2 = mv2 = 3900 kg m/s
J = Δp = p2 – p1 = 2.64 104 kg m/s
(∑F)avg = (Δp/Δt) = 1.76 105 N
Closure - Car Crash
Would you rather be in a
head on collision with an
identical car, traveling at
the same speed as you, or
a brick wall?
Assume in both situations you
come to a complete stop.
Take a guess
http://techdigestuk.typepad.com/photos/uncategorized/car_crash.J
PG
Car Crash (cont.)
Everyone should vote now
Raise one finger if you think
it is better to hit another
car, two if it’s better to
hit a wall and three if it
doesn’t matter.
And the answer is…..
Car Crash (cont.)
The answer is…
It Does Not Matter!
Look at FΔt= mΔv
In both situations, Δt, m, and Δv
are the same! The time it
takes you to stop depends on
your car, m is the mass of
your car, and Δv depends on
how fast you were initially
traveling.
Homework
Chapter 7
problems
15, 16, 17, 19, 20
Kahoot 7-3