Conceptual Physics
Energy Sources
Collisions
Lana Sheridan
De Anza College
July 7, 2015
Last time
• energy and work
• kinetic energy
• potential energy
• conservation of energy
• energy transfer
Overview
• simple machines
• efficiency
• discussion of energy sources
• momentum and collisions
Sources of Energy
Discussion!
Sources of Energy
Sources of energy:
• oil
• coal
• natural gas
• wood / charcoal / peat
• solar - photovoltaics and heating
• wind
• waves
• hydroelectric
• geothermal
• nuclear - thermonuclear, fission, and fusion(?)
Sources of Energy: Fraction of US Energy supply
1
US Energy Information Administration.
Sources of Energy: Costs
1
Wikipedia, NEA estimates.
Sources of Energy: Costs
1
Wikipedia, California Energy Commission estimates.
Carbon Dioxide
1
Graph from http://climate.nasa.gov/evidence/
Collisions
The conservation of momentum is very useful when analyzing what
happens to colliding objects.
In all collisions (with no external forces) momentum is conserved:
net momentum before collision = net momentum after collision
pnet,i = pnet,f
Types of Collision
There are two different types of collisions:
Elastic collisions
are collisions in which none of the kinetic energy of the colliding
objects is lost. (Ki = Kf )
Types of Collision
There are two different types of collisions:
Elastic collisions
are collisions in which none of the kinetic energy of the colliding
objects is lost. (Ki = Kf )
Inelastic collisions
are collisions in which energy is lost as sound, heat, or in
deformations of the colliding objects.
Types of Collision
There are two different types of collisions:
Elastic collisions
are collisions in which none of the kinetic energy of the colliding
objects is lost. (Ki = Kf )
Inelastic collisions
are collisions in which energy is lost as sound, heat, or in
deformations of the colliding objects.
When the colliding objects stick together afterwards the collision is
perfectly inelastic.
m1
Elastic Collisions
a
m2
Before the collision, the
particles move separately.
S
S
v1i collision, thev2i
After the
particles continue to move
m1
m2
separately
with new velocities.
a
S
S
v1f
v2f
After the collision, the
b particles continue to move
separately with new velocities.
Figure 9.7
ofSan
tation v
1f
Schematic represenS collielastic head-on
v
2f
ties, and
Because
al
alternativ
represente
tion of E
direction.
factor 12 iW
tive
it mo2
leftifand
In a typ
ties, and E
alternative
Factoring
tion
of Equ
factor 12 in
left and 2 o
Next,
lar way to
Factoring b
Example: Pool
A pool ball moving at 1 m/s to the right strikes a stationary pool
ball in an elastic collision. What is the final velocity of the two
pool balls? (Assume they have the same mass.)
1
Photo by Max Stansell via hsphysicslab.blogspot.com.
Example: Pool
A pool ball moving at 1 m/s to the right strikes a stationary pool
ball in an elastic collision. What is the final velocity of the two
pool balls? (Assume they have the same mass.)
The motional energy is just transferred from the first ball to the
second!
The first ball comes to rest after the collision, and the second
moves off to the right at 1 m/s.
Notice that momentum is conserved.
1
Photo by Max Stansell via hsphysicslab.blogspot.com.
Inelastic Collisions
For general inelastic collisions, some kinetic energy is lost.
But we can still use the conservation of momentum:
pi = pf
1
m2
ision, we can
Before the collision, the
Perfectly
Collisions
entum
of theInelastic
a particles move separately.
(9.15)
(9.14)
v 2i(9.15)
and S
particles
S
v 1f and
e system
S
ction
in S
v 1i and
v 2i
es
After theS
collision,S
vthe
2i
m1 v1i
particles move together.m2
a
S
v
After the collision, fthe
m1 !move
m2 together.
particles
b
Now the two particles stick together after colliding ⇒ same final
two particles
velocity!
S
vf
ities, S
v 1f and Figure 9.6 Schematic repre(9.16)
m
m
!
sentation
of
a
perfectly
inelastic
1
2
of the system
pi = pf collision
⇒ m1 v1ibetween
+ m2 v2i two
= (m1 + m2 )vf
direction in head-on
b
(9.17)
particles.
Inelastic Collision Example
From page 91-92 of Hewitt:
Two freight rail cars collide and lock together. Initially, one is
moving at 10 m/s and the other is at rest. Both have the same
mass. What is their final velocity?
Inelastic Collision Example
From page 91-92 of Hewitt:
Two freight rail cars collide and lock together. Initially, one is
moving at 10 m/s and the other is at rest. Both have the same
mass. What is their final velocity?
pnet,i
mvi
= pnet,f
= (2m)vf
10m = 2mvf
The final mass is twice as much, so the final speed must be only
half as much: vf = 5 m/s.
Collision Question
Two objects collide and move apart after the collision. Could the
collision be inelastic?
(A) Yes.
(B) No.
Collision Question
Two objects collide and move apart after the collision. Could the
collision be inelastic?
(A) Yes.
(B) No.
←
Question
In a perfectly inelastic one-dimensional collision between two
moving objects, what condition alone is necessary so that the final
kinetic energy of the system is zero after the collision?
(A) The objects must have initial momenta with the same
magnitude but opposite directions.
(B) The objects must have the same mass.
(C) The objects must have the same initial velocity.
(D) The objects must have the same initial speed, with velocity
vectors in opposite directions.
1
Serway & Jewett, page 259, Quick Quiz 9.5.
Question
In a perfectly inelastic one-dimensional collision between two
moving objects, what condition alone is necessary so that the final
kinetic energy of the system is zero after the collision?
(A) The objects must have initial momenta with the same
magnitude but opposite directions.
←
(B) The objects must have the same mass.
(C) The objects must have the same initial velocity.
(D) The objects must have the same initial speed, with velocity
vectors in opposite directions.
1
Serway & Jewett, page 259, Quick Quiz 9.5.
600 N/m
served when t
implies that th
important sub
m1
Finalize This answer is not the maximum compression of the spring because
the two
iar example
in
m2
example,
theshown
caseinofFigure
a glancing
each otherconsider
at the instant
9.10b. Cancollision.
you determine
thesurface.
maximum
Forcom
su
a
for conservatio
numerical values:
S x 5 0.173 m
More Complicated Collisions
As an
S
v1i
After the collision
9.5 Collisions in Two
Dimension
v
S
1f
v1f sin
where the thr
θ
In Section 9.2, we
showed
that the momentum
of
respectiv
served when the system is isolated. sent,
For any
collis
S
v1i
thedirecti
veloci
v1f cos
implies that the momentum
inθ each and
of the
θ
Let
usplane.
consi
important
subset
of
collisions
takes
place
in
a
m1
collides
with p
φ multiple collisions
iar example involving
of
object
v2f cos φ
m2
(Fig. 9.11b),
surface. For such two-dimensional collisions,
wepa
ob
a
moves at an an
for conservationvofsin
momentum:
φ
2f
S
sion. Applying
v2f
m1v1ix 1 m 2vthat
m1initial
v1fx 1
After the collision
2ix 5
the
b
You would find the total initial momentum
by adding the initial
m1v1iy 1 m 2v 2iy 5 m1v1fy 1
S
Dp
v1f
momentum vectors.
Figure 9.11 An elastic, glancing
v1f sin θ
where
the three
subscripts
on the velocity compo
Dp
collision
between
two particles.
sent, respectively, the identification of the object (1
The final momentum is vfound
by
adding
the
final
momentum
and the velocity component (x, y).
1f cos θ
θ
vectors.
Let us consider a specific two-dimensional proble
collides with particle 2 of mass m2 initially at rest as i
φ
v2f cos φ
(Fig. 9.11b), particle 1 moves at an angle u with respec
moves at an angle f with respect to the horizontal. T
Before the collision
v2f sin φ
S
600 N/m
served when t
implies that th
important sub
m1
Finalize This answer is not the maximum compression of the spring because
the two
iar example
in
m2
example,
theshown
caseinofFigure
a glancing
each otherconsider
at the instant
9.10b. Cancollision.
you determine
thesurface.
maximum
Forcom
su
a
for conservatio
numerical values:
S x 5 0.173 m
More Complicated Collisions
As an
S
v1i
After the collision
9.5 Collisions in Two
Dimension
v
S
1f
v1f sin
where the thr
θ
In Section 9.2, we
showed
that the momentum
of
respectiv
served when the system is isolated. sent,
For any
collis
S
v1i
thedirecti
veloci
v1f cos
implies that the momentum
inθ each and
of the
θ
Let
usplane.
consi
important
subset
of
collisions
takes
place
in
a
m1
collides
with p
φ multiple collisions
iar example involving
of
object
v2f cos φ
m2
(Fig. 9.11b),
surface. For such two-dimensional collisions,
wepa
ob
a
moves at an an
for conservationvofsin
momentum:
φ
2f
S
sion. Applying
v2f
m1v1ix 1 m 2vthat
m1initial
v1fx 1
After the collision
2ix 5
the
b
You would find the total initial momentum
by adding the initial
m1v1iy 1 m 2v 2iy 5 m1v1fy 1
S
Dp
v1f
momentum vectors.
Figure 9.11 An elastic, glancing
v1f sin θ
where
the three
subscripts
on the velocity compo
Dp
collision
between
two particles.
sent, respectively, the identification of the object (1
The final momentum is vfound
by
adding
the
final
momentum
and the velocity component (x, y).
1f cos θ
θ
vectors.
Let us consider a specific two-dimensional proble
collides with particle 2 of mass m2 initially at rest as i
φ
v cos φ
What will pnet,f be in this2f case? (Fig. 9.11b), particle 1 moves at an angle u with respec
moves at an angle f with respect to the horizontal. T
Before the collision
v2f sin φ
S
Example 9.8 - Car collision
A 1500 kg car traveling east with a speed of 25.0 m/s collides at
Collisions an intersection with a 2500 kg truck traveling north at a speed of
20.0 m/s. Find the direction and magnitude of the velocity of the
wreckage after the collision, assuming the vehicles stick together
after the collision.
nceptualize the situation before
along the positive x direction and
mediately before and immediately
l, we ignore the small effect that
and model the two vehicles as an
nore the vehicles’ sizes and model
stic because the car and the truck
ing momentum in the x direction
l initial momentum of the system
the car. Similarly, the total initial
of the truck. After the collision, let
respect to the x axis with speed vf .
1
y
S
vf
25.0iˆ m/s
u
x
20.0jˆ m/s
Figure 9.12 (Example 9.8) An
eastbound car colliding with a northbound truck.
Serway & Jewett, page 265.
Example 9.8 - Car collision
This is an inelastic collision.
Example 9.8 - Car collision
This is an inelastic collision.
Initial momentum = initial momentum of car
+ initial momentum of truck
pnet,i = (1500 kg) (25.0 m/s) i + (2500 kg) (20.0 m/s) j
pnet,f = (1500 + 2500 kg) vf
Example 9.8 - Car collision
This is an inelastic collision.
Initial momentum = initial momentum of car
+ initial momentum of truck
pnet,i = (1500 kg) (25.0 m/s) i + (2500 kg) (20.0 m/s) j
pnet,f = (1500 + 2500 kg) vf
θ = 53.1◦ (as marked in diagram)
and
vf = 15.6 m/s
Summary
• sources of energy
• rotational motion
Essay Homework due July 13th.
• Describe the design features of cars that make them safer for
passengers in collisions. Comment on how the design of cars
has changed over time to improve these features. In what
other circumstances might people be involved in collisions?
What is / can be done to make those collisions safer for the
people involved? Make sure use physics principles
(momentum, impulse) in your answers!
Homework Hewitt,
• Ch 6, onward from page 96, Plug and chug: 1, 3, 5, 7;
Ranking: 1; Exercises: 5, 7, 19, 31, 47
• Ch 7, onward from page 119. Exercises: 57, 59; Probs: 7, 9