Download Elastic Collisions Momentum is conserved m 1 ѵ 1i +

Momentum
&
Impulse
Momentum
The linear momentum of an object is defined as:
Momentum = mass x velocity
p=mxѵ
‘p’ is used because the word "impetus" (formally in place
of "momentum“) comes from the latin, "petere," to go
towards or rush upon...so therefore we get "p"
What are the units of momentum?
mxѵ=
So – the SI unit for momentum is defined as:
So let’s think about momentum…
Momentum is a measure of mass in motion.
So – think about:
car traveling at 55 mph vs. 18-wheeler at 55 mph
Which would you expect to have more momentum?
-Deyjah carries her violin to practice with a
velocity of .6m/s. If the mass of Deyjah & her
instrument combined is 66 kg, find her
momentum.
-Peter has a mass of 72 kg and is riding his 25.9 kg dirt bike
with a velocity of 4.5 m/s to the northwest.
What is Peter’s momentum?
What is the momentum of the bike?
What is the momentum of the two together?
Before we define ‘impulse,’ I would like to work
our way to it.
Impulse is defined as the change in
momentum. Let’s reason why…
p=mxѵ
So – how can we express change in momentum?
Δp = mѵf – mѵi
rewrite as:
From kinematics, what
equation do we know that
has the expression (ѵf – ѵi)?
Derive (ѵf – ѵi) by itself to get:
Substitute in for (ѵf – ѵi)
What equation = m x a?
Substitute in…
Your final equation is:
Impulse = Force x change in time
I = FΔt
The SI units of Impulse are:
(Are these the same units of momentum?)
Moreover, if Impulse = FΔt, then:
Impulse =
This is the ‘Impulse – Momentum Theorem’
Let’s discuss the idea of impulse…
If impulse is defined as the change in momentum,
then take an object, like an egg, that will:
-have a mass of .10 kg
-experience a change in velocity from 10 m/s to zero m/s.
In terms of the definition of change in momentum,
From the same height, compare the impulses of:
Egg falling on the pavement
vs.
Egg falling on a pillow
The impulses are the same!
So – why does one egg break and the other stay intact?
What is the true definition of impulse?
So, how are Force and Δt related?
Hmmmmm…. So – if broken egg and whole egg experienced the
same impulse, what was the difference?
How does impulse differ from force?
1. Force produces momentum; impulse produces acceleration.
2. Force is usually larger than momentum.
3. Force produces acceleration; impulse produces change in
momentum.
4. Momentum is larger than force.
5. Force produces acceleration; impulse produces momentum.
6. None of these
- A .40 kg soccer ball approaches Jennifer with a velocity of 18
m/s. Jennifer strikes the ball and causes it to move in the
opposite direction with a velocity of 22 m/s. What is the
impulse delivered by Jennifer?
-Noah throws a .50 kg football with a velocity of
15 m/s to the right. If Bryan catches the ball
and brings it to rest in .020 s, what is the force
exerted on Bryan?
Stopping Distance
- Riley slows her 2250 kg car to let a momma duck and her
ducklings cross the street. If Riley slows from 20.0 m/s to 5.0
m/s how long does it take her car to decelerate if the force on
the car is 8450 N in the opposite direction?
- Patrick drives his 3250 kg SUV to a stop from
20.0 m/s by a 6250 N braking force.
What is his vehicle’s velocity after 1.5 s?
How far does Patrick travel in 1.5 s?
How long does it take him to come to a complete stop?
Conservation of Momentum
Momentum is always conserved in collisions
(and also for objects pushing away from each other)
m1ѵ1 + m2ѵ2 = m1ѵ1 + m2ѵ2
initial
final
-Sam and Jose are standing face-to-face on a frozen lake. Jose
is carrying an extra 50kg on his back to give him a total mass
of 125 kg. Sam has a mass of 75kg. If Sam pushes off Jose at
2.3m/s, what is Jose’s velocity?
-Dillon counts the fish that he caught while sitting in his
rowboat next to the dock. If the boat has a mass of 45 kg
and Dillon has a mass of 57 kg, What is the final velocity of
the boat if Dillon steps on to the dock at 3.6 m/s?
-Andrew is standing on his 2.3 kg skateboard when he sees
Priscila drive by (she sees Andrew and speeds up! Haha).
Andrew attempts to throw his 7.7 kg backpack at her car with a
velocity of 2.9 m/s. If Andrew and his skateboard move in the
opposite direction at 2.5 m/s, find his mass.
- Yarelie (44 kg) is buckling on her rollerblades, when her
brother, Jesus, yells, “think fast!” He throws a 15 kg exercise
ball at her with a speed of 4.6 m/s, trying to knock her over.
Much to her brother’s surprise, Yarelie catches the ball.
Describe and calculate the motion she experiences after
catching the ball.
Collisions
There are 2 types of collisions:
Elastic – These collisions are characterized
by objects hitting and bouncing
apart.
Inelastic – Think of these as ‘not’ bouncing.
In fact, inelastic collisions occur when
objects collide and stick together.
Elastic
vs.
Inelastic
2 objects collide and bounce2 objects collide and stick
final velocities are in different
directions
move together as one mass
momentum is conserved
momentum is conserved
kinetic energy is conserved
kinetic energy is not conserved
Elastic Collisions
Momentum is conserved
m1ѵ1i + m2ѵ2i = m1ѵ1f + m2ѵ2f
initial
final
Kinetic Energy is conserved
½ m1ѵ1i2 + ½ m2ѵ2i2 = ½ m1ѵ1f2 + ½ m2ѵ2f2
Technically – most collisions are neither
perfectly elastic nor perfectly inelastic…
-most objects do not collide and stick together
-even in elastic collisions, such as a golf club hitting a
golf ball, there is some amount of deformation of
shape. This leads to kinetic energy loss in the form of
elastic potential energy.
- You might think that pool balls hitting each other
is a good example of elastic collisions with little or
no kinetic energy loss. However, think about the
sound pool balls make when they hit each other –
this is kinetic energy lost as ‘sound energy.’
-
A 4.0 kg bowling ball sliding to the right at 8.0 m/s has an
elastic head-on collision with another 4.0 kg bowling ball
initially at rest. The first ball stops after the collision.
- Find the velocity of the second ball after the collision.
-
Severin paddles a canoe (106 kg together) to the left at
12 m/s. He hits Bailey in a raft (55 kg together) traveling
to the right at 6.0 m/s. After the collision, Bailey travels
to the left at 18 m/s.
- Find the velocity of Severin after the collision
Perfectly Inelastic Collisions
-2 objects become one after colliding
Momentum is conserved
m1ѵ1i + m2ѵ2i = (m1+ m2)ѵf
initial
But kinetic energy is not
final
-
Billy drives his new truck (mass 1575 kg) right into Mr.
Engel’s bumper while he is sitting at a traffic light in his
car (mass 900kg). If Billy’s initial speed is 22m/s to the
north before the collision, what is the velocity of the
entangled mass after the collision?
-
How much kinetic energy is lost?
-
During practice, Yazmin kicks a .40 kg soccer ball
with a velocity of 8.5 m/s into a .15 kg bucket lying
on its side. The bucket and ball move together after
the collision. What is the final velocity of the final
mass?
-
What is the decrease in kinetic energy after the
collision?