Can momentum change?
∆p = m ∆v
Change in momentum = mass x change in velocity
(Units) kg•m/s = kg
x
m/s
To stop an object, we have to apply a force
to the object over a period of time.
This is called IMPULSE.
J = F ∆t
Impulse = Force x change in time
N•s
=
N
x
s
Combine these two formulas and
simplify:
F = ma
a = ∆v/∆t
Useful Form
F∆t = m∆v
SO……
J = ∆p
F = ∆p/ ∆t
Short Form
An egg dropped on a tile floor breaks, but an
egg dropped on a pillow does not. Why?
FΔt= mΔv
Hint 1: In both cases, m and Δv are the same.
Hint 2: If Δt goes up, what happens to F, the force?
Answer: When dropped on a pillow, the egg
starts to slow down as soon as it touches it.
A pillow increases the time the egg takes to
stop.
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.
http://techdigestuk.typepad.com/photos/uncategorized/car_crash.JPG
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.
Apply the force for a long time.
∆t
F
Apply the force for a short
time.
F
∆t
Helmet and bare head stop a 90 mph fastball,
m∆v is the same for both situations
It’s all about
time!!!
F
= mDv
t
Small “t”
for head
without
helmet
Big Force
F= mDv
t
Big “t” for
head with
helmet
Small Force
Collisions that take a
long time are better,
because they allow for
smaller forces.
How do we
increase the time
of a collision?
5 kg mass is dropped onto an
athletic surface
Height of the bounce is
measured
Gmax value is determined
The bigger the bounce the
harder the surface
Different surface has different
allowable Gmax values
basketball court > football field
Large amounts of
time in a collision,
results in a
smaller force.
Collisions are about
momentum, and Newton’s
2nd and 3rd Laws.
Newton’s Laws help us
predict changes in motion.
Motion can be
described by
position, velocity
and momentum.
Changes in
motion can be
described by
acceleration
and changes
in momentum.
Changes in motion
are caused by forces.
You drive around a curve in a narrow
one-way street at 30 mph when you see
an identical car heading straight toward
you at 30 mph. You have two options: hit
the car head-on or swerve into a massive
concrete wall (also head-on). What
should you do?
1) hit the other car
2) hit the wall
3) makes no difference
4) call your physics prof!!
5) get insurance!
You drive around a curve in a narrow
one-way street at 30 mph when you see
an identical car heading straight toward
you at 30 mph. You have two options: hit
the car head-on or swerve into a massive
concrete wall (also head-on). What
should you do?
1) hit the other car
2) hit the wall
3) makes no difference
4) call your physics prof!!
5) get insurance!
In both cases your momentum will decrease to zero in the collision. Given
that the time Dt of the collision is the same, then the force exerted on YOU will
be the same!!
If a truck is approaching at 30 mph, then you’d be better off hitting the wall
in that case. On the other hand, if it’s only a mosquito, well, you’d be better
off running him down...
Two boxes, one heavier than the
other, are initially at rest on a
horizontal frictionless surface. The
same constant force F acts on each
one for exactly 1 second. Which box
has more momentum after the force
acts ?
F
light
1) the heavier one
2) the lighter one
3) both the same
F
heavy
Two boxes, one heavier than the
other, are initially at rest on a
horizontal frictionless surface. The
same constant force F acts on each
one for exactly 1 second. Which box
has more momentum after the force
acts ?
We know:
Dp ,
Fav =
Dt
so impulse Dp = Fav Dt.
In this case F and Dt are the
same for both boxes!
Both boxes will have the
same final momentum.
F
light
1) the heavier one
2) the lighter one
3) both the same
F
heavy
In the previous question, which
1) the heavier one
box has the larger velocity after
2) the lighter one
the force acts?
3) both the same
In the previous question, which
1) the heavier one
box has the larger velocity after
2) the lighter one
the force acts?
3) both the same
The force is related to the acceleration by Newton’s Second
Law (F = ma). The lighter box therefore has the greater
acceleration and will reach a higher speed after the 1-second
time interval.
Follow-up: Which box has gone a larger distance after the force acts?
Follow-up: Which box has gained more KE after the force acts?
A small car and a large truck
1) the car
collide head-on and stick
2) the truck
together. Which one has the
larger magnitude of momentum
change?
3) they both have the same
momentum change
4) can’t tell without knowing the
final velocities
A small car and a large truck
1) the car
collide head-on and stick
2) the truck
together. Which one has the
larger magnitude of momentum
change?
3) they both have the same
momentum change
4) can’t tell without knowing the
final velocities
Because the total momentum of the system
is conserved, that means that Dp = 0 for the
car and truck combined. Therefore, Dpcar
must be equal and opposite to that of the
truck (–Dptruck) in order for the total
momentum change to be zero. Note that
this conclusion also follows from Newton’s
Third Law.
Follow-up: Which one feels
the larger acceleration?
You are lying in bed and you want to
shut your bedroom door. You have a
1) the superball
superball and a blob of clay (both
2) the blob of clay
with the same mass) sitting next to
3) it doesn’t matter—they will
be equally effective
you. Which one would be more
effective
close it?
to throw at your door to
4) you are just too lazy to throw
anything
You are lying in bed and you want to
shut your bedroom door. You have a
1) the superball
superball and a blob of clay (both
2) the blob of clay
with the same mass) sitting next to
3) it doesn’t matter—they will
be equally effective
you. Which one would be more
effective
to throw at your door to
close it?
4) you are just too lazy to throw
anything
The superball bounces off the door with almost no loss of speed, so its
Dp (and that of the door) is 2mv.
The clay sticks to the door and continues to move along with it, so its
Dp is less than that of the superball, and therefore it imparts less Dp
to the door.