2015 Final Exam
Cumulative
Topic
Scientific Reasoning:
Motion and graphs:
Momentum:
Forces:
Projectiles, FF and Circular motion:
6
Work, energy and power:
Energy sources/waves:
Total
# of questions
7
8
3
3
18
5
50
Schedule
• Thursday, May 14 – review for final (1
st
semester
content)
• Friday, May 15 – review for final (2
• Monday, May 18 – review for final
nd
– (sample test questions)
semester content)
Turn in MacBooks
in the morning
• Tuesday, May 19 – review for final
– Scientific Reasoning
– Work on weak areas
• Wednesday, May 20 – Take Final Exam
• Thursday, May 21 – Review exam results
• Friday, May 22 – Last ½ day!!
Motion Vocab
•
•
•
•
•
•
•
•
Position
Distance
Displacement
Speed
Velocity
Acceleration
Constant
Slope
Motion Diagram Example
A
Word Description
A. Positive constant velocity with
an initial position at 0.
0
+x
+x
B. Starting at a positive position,
slowing down, accelerating in
the opposite direction of motion.
+x
C. Starting at a positive position,
getting faster, accelerating in
the same direction as motion.
B
0
C
0
D
0
+x
D. Starting at a positive position,
moving at a constant negative
velocity for 3 time intervals, then
accelerates in the opposite
direction of motion to slow down
to stop before reaching 0.
20
Velocity
Velocity is the rate of change of position over
time. Velocity is more descriptive than speed
because velocity includes the direction of motion.
On an x vs. t graph, the slope of the line is the
average velocity.
The algebraic sign for velocity indicates the
direction of motion. A object with positive velocity
will move in the opposite direction than an object
with negative velocity.
Distance, Displacement, Speed
and Velocity
Distance:
Displacement:
-
- Solid line
- Is not path dependent
- Length of straight line from
start to end
- Specifies direction
- Is a vector
- Δx = xf - xi
- can be positive or negative
- (+) or (-) sign indicates
direction
Dashed line
Is path dependent
Does not specify direction
Is a scalar
Is always positive
Can include changes in
direction
Average Velocity
- rate of change of position over time.
Δx
-
is the average velocity over a time interval.
is relative to a reference point.
includes direction.
Dx x f - xi
is based on displacement.
v=
=
Dt t f - ti
Instantaneous Velocity
- velocity at a particular time (instant).
- is relative to a reference point.
- includes direction.
Animation at this site:
NOTE: THIS ANIMATION IS LABELED ‘SPEED’ SIMPLY BECAUSE DIRECTIONS ARE NOT SPECIFIED.
http://www.physicsclassroom.com/mmedia/kinema/trip.cfm
Speed:
- Does not specify direction
- Is a scalar
- Is based on distance
- Is always positive
- Speed = distance / time
- s = d/t
Average Velocity:
- Specifies direction
- Is a vector
- Is based on displacement
- Can be positive or negative
- V = Δx / Δt
- (+) or (-) sign indicates
direction
25
Information on Motion graphs when acceleration is
constant
x vs. t graphs
A horizontal (flat) line on a Position vs. time
graph indicates velocity is zero.
x
C
x vs. t
t
A slanted line on a Position vs. time graph
indicates constant velocity.
A curved line (parabola) on a Position vs.
time graph indicates constant acceleration.
v vs. t graphs
v
The slope of the line on a velocity vs. time
graph reveals acceleration.
D
v vs. t
C
t
a vs. t graphs
A slanted line on an velocity vs. time graph
reveals constant acceleration.
A steeper line on a velocity vs. time graph
means greater acceleration.
D
a
A horizontal (flat) line on a velocity vs. time
graph indicates acceleration is zero.
The area under the curve on a velocity vs.
time graph reveals the change in position
(displacement).
a vs. t
C
t
A horizontal line on an acceleration vs. time
graph reveals constant acceleration.
D
The area under the curve on an acceleration
vs. time graph reveals the change in velocity.
Be sure to review the basics about
 Calculating the area under the curve
on page 14.
Calculating the slope of the line on
30
Momentum vocab
•
•
•
•
•
•
Momentum
Velocity
Mass
Directly proportional
Inversely proportional
Law of Conservation of Momentum
Momentum
Variable:
p
S. I. Unit: kilogram meter / second = kg m/s
Formula: p = m v .
Definition: the product of an object’s mass and velocity;
the quantity of motion that an object has; mass in motion;
how hard it is to stop a moving object.
Momentum is a vector; it is in the same direction as the
velocity.
Example:
mass
Law of Conservation of
Momentum
In Science, there are several ‘conservation laws’ that describe the way
certain measured values can shift around within a situation, yet the total
stays the same.
An important factor in considering conservation laws is the ‘system’ that is
under analysis. The system is defined by the observer to track changes
within the system.
A system is a set of interacting or
interdependent components
forming an integrated whole. The
image shown is a closed system
with a defined boundary.
velocity
A 7 kg medicine ball is thrown at a velocity of 3 m/s.
momentum = mass times velocity
p = mv
The Law of Conservation of Momentum states that the total momentum of
a closed system remains the same. The momentum can shift around in
the system, but the total remains the same.
p = (3kg) (7m/s) = 21 kg m/s
Special case:
The momentum of an object that is at rest is always 0.
For a full overview of momentum, visit:
http://www.physicsclassroom.com/Class/momentum/u4l2b.cfm
For a full overview of momentum, visit:
http://www.physicsclassroom.com/class/momentum/u4l1a.cfm.
38
Making Predictions using Formulas
Learning to use formulas to help you make predictions will
help you be successful in physics. For our course, there are
two ways that you will use to make predictions:
* Simple ratios
* Ratios with exponents
Ratio Example 1:
F = ma
If you double mass (m), how does force (F) change if acceleration(a)
stays the same?
Mass (m)
Acceleration
Force
F = ma
2 kg
0.5 m/s/s
1N
4kg
0.5 m/s/s
2N
12 kg
3 m/s/s
36 N
24 kg
3 m/s/s
72 N
Increasing mass by a factor of two from 2 kg
to 4 kg caused force to increase by a factor of
2 from 1 N to 2N. .
Doubling mass from 12 kg to 24 kg caused
force to double from 36 N to 72 N
Mass is directly proportional to Force.
Ratio Example 2:
a = F/m
If you triple mass (m), how does acceleration (a) change if force (F) stays
the same?
Mass
Force
Acceleration
a = F/m
2 kg
480 N
240 m/s/s
6kg
480 N
80 m/s/s
8 kg
480 N
60 m/s/s
24 kg
480 N
20 m/s/s
Increasing mass by a factor of three from 2
kg to 6 kg caused acceleration to decrease by
a factor of three from 240 m/s/s to 80 m/s/s
Tripling mass from 3 kg to 24 kg caused force
to decrease by a factor of three from 60
m/s/s to 20 m/s/s
Mass is indirectly proportional to
acceleration.
Predictions involving ratios with exponents
are similar to predictions involving ratios.
Exponents Example: EK = ½ m v2
If you triple velocity (v), how will kinetic energy (EK )change
if mass (m) stays the same?
Data
Set
velocity
mass
Kinetic Energy
EK = ½ m v2
A
1 m/s
12
kg
EK = 6 J
3 m/s
12
kg
EK = 54 J
B
5 m/s
12
kg
EK = 150 J
Examine data set B:
Increasing velocity by a factor
of 3 from 5 m/s/s to 15 m/s/s
caused Kinetic Energy to
increase by a factor of 32 (or
9) from 150 joules to 1,350
joules.
15 at
m/s
EK = 1,350
Let’s look
it with12the formula:
EKJ= ½ m v2
kg
When v = 5 m/s
When v = 3*5m/s = 15 m/s
EK = ½ (12 kg) (5m/s)2
EK = (6)(25) J
EK = 150 J
EK = ½ (12 kg) (3*5m/s)2
EK = ½ (12 kg) (15m/s)2
EK = (6 ) (225) J
EK = 1350 J
When velocity is 3 times larger, Kinetic Energy
is 32 times larger.
Or 9 times larger.
11
Forces vocab
•
•
•
•
•
•
•
Force
acceleration
Mass
1st Law
2nd Law
3rd Law
Force Diagram
Force Diagrams
Drawing a Force Diagram
Forces are vectors.
The elements of a force diagram:
- a point or small box that represents the object.
- forces are drawn pointing away from the point or box.
- forces are drawn pointing in the original direction.
- forces are labeled with names and/or magnitudes.
Vectors require a magnitude and a direction.
Scalars require only a magnitude (no directions needed).
When Force vectors are drawn, the length of the arrow
indicates the magnitude. The direction of the arrow
represents (you guessed it!) the direction that the force
is acting.
Example:
FAPP
Ff
FN
Force Diagram Examples:
FT
FT
FN
FN
2N
Fg
FN
Fg
2N
Fg
FN
12 N
12 N
FN
FAPP
Ff
Fg
FN
The force diagram for the car shows
it is accelerating to the right since
FAPP is larger than Ff. Each of the
normal forces shown is ½ the
magnitude of the car’s Fg (or
weight). It must be a two wheeled
car – get it?? Since there are only two
FN’s, it must have only 2 wheels. . .
42
Mass, Weight, & Force due to Gravity
Mass is the amount of matter in an object, or the amount
of ‘stuff’.
Symbol or variable:
m
S.I. Unit
kilogram (kg)
Force to due Gravity is the pull on an object from a
gravitational field.
Symbol or variable:
Fg
S.I. Unit:
Newton (N)
Weight is the ‘non-physics’ person’s name for the Force
due to Gravity.
Symbol or variable:
Fg
S.I. Unit:
Newton (N)
Relationship between m and Fg
Mass does not depend on the gravitational field. A 70 kg
astronaut on the Earth will be a 70 kg astronaut on the
Moon or Jupiter or Mars.
But. . . the same 70 kg astronaut will have different weights
on Earth, Moon, Jupiter and Mars because each one has a
different gravitational field strength. Later, you will learn
why gravitational fields vary, but for now we will concentrate
on just mass and weight.
The Force due to gravity (or weight) is the pull on an object
from a gravitational field, Fg will depend on the strength of
the gravitational field since mass is the same everywhere.
On Earth, the gravitational field strength (gE) is 9.8 m/s2.
gE = 9.8 m/s2 ( or about 10 m/s2)
To find the Force due to Gravity (Weight), multiply an
object’s mass by gE .
Fg = m gE
Example: Find the weight on Earth of a 4 kilogram object:
Mass and Weight are NOT the same thing.
Fg =
m
gE
= ( 4 kg ) ( 9.8 m/s2)
= 39.2 N
16
A 4 kilogram object weighs 39.2 Newtons (or about 40 N).
Newton’s Laws
Third Law of Motion
Second Law of Motion
First Law of Motion
An object at rest will remain at rest
until a net force accelerates it.
When a net force is applied to an object, it
produces a proportional acceleration.
An object moving at constant speed in
a straight line will keep moving at
constant speed in a straight line until a
net force accelerates it.
constant velocity
Forces are balanced, so object is in
equilibrium.
V ≠ 0 m/s a = 0 m/s2
LAW OF INERTIA
“An object will keep doing what its doing until
something changes it. “
Forces on individual objects.
V = 0 m/s a = 0 m/s2
FNET = m*a
Σ F = m*a
When a net forces are balanced:
FNET = 0
or
F
-F
ΣF =0
Equilibrium
When a net forces are not balanced:
FNET ≠ 0
Whenever a large mass and small mass interact,
the forces on them will be equal but their
resulting accelerations will be different.
or
ΣF ≠0
ACCELERATION
Disequilibrium
Action- reaction outcomes.
a
<
Forces between two objects
at rest.
Forces are balanced, so object is in
equilibrium.
Whenever one object exerts a force F on a 2nd
object , the 2nd exerts a force −F on the 1st object .
F and −F are equal in
magnitude and opposite in direction.
a
The acceleration will be
directly proportional
to the net force.
The acceleration will be
inversely proportional
to mass.
46
Projectile, FF & circular motion vocab
•
•
•
•
•
•
•
•
Force
acceleration
Mass
Terminal velocity
Range
Peak height
Launch angle
Horizontal launch
• Centripetal force
• Centripetal
acceleration
• Tangential velocity
Circular Motion:
Force, acceleration & velocity vectors:
To understand the motion of an object travelling in a circular path,
begin by recalling the definition acceleration:
o Getting faster
o Getting slower
o Changing
directions.
Since objects moving along a curved path are constantly
changing directions, they must be accelerating. Accelerating
objects are acted upon by unbalanced forces.
Acceleration means:
Recall Newton’s second law:
SF = ma
Based on the second law, the force that keeps an object moving in a
curved path is the CENTRIPETAL force. Since objects accelerate in
the direction of the unbalanced force, CENTRIPETAL acceleration
(ac) is in the same direction as CENTRIPETAL force (Fc).
What happens when the centripetal force disappears?
If there is no net force keeping the object in a circular path,
it will move in a straight line at constant speed.
P
If the centripetal force
disappears at point P , the object
will move in a straight line at a
constant speed in the direction it
was moving at the instant the
centripetal force disappeared.
vt
Fc
vt
ac
vt
Centripetal Force (Fc) and centripetal acceleration (ac) ALWAYS point
toward the center of rotation.
Tangential velocity (vt) is the velocity at a given point along the curved
and is ALWAYS perpendicular to Fc and ac.
Centripetal
Force
Centripetal
Acceleration
Tangential
Velocity
50
Great Stuff to know about Projectiles!!
Horizontal Motion
Vx is constant.
ΣFx = 0
Since the horizontal forces are balanced, a
projectile is in constant velocity in the
horizontal direction.
Predictable patterns in Projectile motion.
1.Vertical velocity at the peak is 0.
2.The magnitude of the vertical velocity is the
same at symmetrical points on the trajectory,
so |VyB| = |VyD|
3. The horizontal velocity is the same
everywhere.
4. The time to go from A to C is equal to the
time to go from C to E since A and E are ‘at the
same level’.
5.The time to move from A to E is the same
when analyzing horizontal or vertical motions.
Vertical Motion
Vyis changes.
ΣFy ≠ 0
Since the vertical forces are unbalanced, a
projectile accelerates in the vertical
direction.
Using “INTERVALS’ of motion: Many projectile problems are easier to solve if we
analyze the up interval (Launch-to-peak) or down interval (peak –to-landing)
instead of launch-to-landing.
56
Work, Energy & Power vocab
•
•
•
•
•
•
•
Work
Force
distance
Mass
Power
height
velocity
• Gravitational Potential
Energy
• Kinetic Energy
• Law of Conservation of
Energy
• % efficiency
Making Predictions using Formulas
Learning to use formulas to help you make predictions will
help you be successful in physics. For our course, there are
two ways that you will use to make predictions:
* Simple ratios
* Ratios with exponents
Ratio Example 1:
F = ma
If you double mass (m), how does force (F) change if acceleration(a)
stays the same?
Mass (m)
Acceleration
Force
F = ma
2 kg
0.5 m/s/s
1N
4kg
0.5 m/s/s
2N
12 kg
3 m/s/s
36 N
24 kg
3 m/s/s
72 N
Increasing mass by a factor of two from 2 kg
to 4 kg caused force to increase by a factor of
2 from 1 N to 2N. .
Doubling mass from 12 kg to 24 kg caused
force to double from 36 N to 72 N
Mass is directly proportional to Force.
Ratio Example 2:
a = F/m
If you triple mass (m), how does acceleration (a) change if force (F) stays
the same?
Mass
Force
Acceleration
a = F/m
2 kg
480 N
240 m/s/s
6kg
480 N
80 m/s/s
8 kg
480 N
60 m/s/s
24 kg
480 N
20 m/s/s
Increasing mass by a factor of three from 2
kg to 6 kg caused acceleration to decrease by
a factor of three from 240 m/s/s to 80 m/s/s
Tripling mass from 3 kg to 24 kg caused force
to decrease by a factor of three from 60
m/s/s to 20 m/s/s
Mass is indirectly proportional to
acceleration.
Predictions involving ratios with exponents
are similar to predictions involving ratios.
Exponents Example: EK = ½ m v2
If you triple velocity (v), how will kinetic energy (EK )change
if mass (m) stays the same?
Data
Set
velocity
mass
Kinetic Energy
EK = ½ m v2
A
1 m/s
12
kg
EK = 6 J
3 m/s
12
kg
EK = 54 J
B
5 m/s
12
kg
EK = 150 J
Examine data set B:
Increasing velocity by a factor
of 3 from 5 m/s/s to 15 m/s/s
caused Kinetic Energy to
increase by a factor of 32 (or
9) from 150 joules to 1,350
joules.
15 at
m/s
EK = 1,350
Let’s look
it with12the formula:
EKJ= ½ m v2
kg
When v = 5 m/s
When v = 3*5m/s = 15 m/s
EK = ½ (12 kg) (5m/s)2
EK = (6)(25) J
EK = 150 J
EK = ½ (12 kg) (3*5m/s)2
EK = ½ (12 kg) (15m/s)2
EK = (6 ) (225) J
EK = 1350 J
When velocity is 3 times larger, Kinetic Energy
is 32 times larger.
Or 9 times larger.
11
The Law of Conservation of Energy
The Law of Conservation of Energy states that
energy cannot be created or destroyed;
it simply changes form.
Consider the closed system at the left. In a
closed system, energy does not flow in or out.
The Law of Conservation of Energy is helpful in
analyzing the flow of energy in many systems.
In the food chain, energy is dissipated as each
organism provides nourishment for the next one
on the chain. The energy is not lost. It is
converted to tissue, heat or waste.
If the clay had 40 J of EGRAV before it was
dropped, there would be 40 J of energy later
but not all of it would be EGRAV. It could be EK
(when it is moving), EEL (when it compresses
the spring) or a combination.
Consider the closed system at the right.
Remember  In a closed system, energy does
not flow in or out.
If the clay had 40 J of EGRAV before it was
dropped, there would be 40 J of energy
after it hit the ground.
However, the kinds of energy in the system at the end are kinds that
cannot be easily recovered: sound and heat. When energy changes to a
type of energy that we cannot recover or use, this is called Dissipated
energy (EDISS). Energy is not ‘gone’; it changed to a form we cannot use.
In mechanical systems, energy is transformed to
accomplish a task. When mechanical systems
‘waste’ energy, the energy that is ‘lost’ is not
really lost at all. The ‘wasted’ energy which
may be due to friction, vibration or sound is
considered EDISS since it is energy that does not
contribute to the task the mechanical system is
intended to perform.
63
Work
Work done against gravity:
Work is the measure of the
transfer of energy.
The weightlifter raises the
bar bell 2 meters. The 50 kg
Barbell weighs 500 N.
(Hint: weight is Fg = m g = (50kg)(10m/s2)
For Work to be done by a given force, two
conditions must be met:
1st condition:
The force (F) must cause a displacement
(∆x) of the object
2nd condition:
A components of a force (F)must be
parallel to the displacement (∆x).
Formula:
Work = Force 
displacement
W = F · d or W = F · ∆x
Where the Force & Displacement are
parallel..
S. I. Units:
Joules
W= F*d
Where F is the weight & d is 2 m.
W = (500N)(2m) = 1000 Joules
The lifter does 1000 joules of Work on the 50 kg
barbell to lift it 2 meters.
Work done against friction:
A 65 N ball player slides into base. He slides
1.5 meters while a friction force of 4 Newtons
slows him down.
W= F*d
Where F is the Friction force (not his
weight)
and d is 1.5 meters.
W = (4N)(1.5m) = 6 Joules
The players weight is not parallel to his motion so no
work is done by the player’s weight.
57
Examples:
Power
Power is the rate at which Work is
done.
Formula:
Power = Work / timt
P=
W
t
P=
First: Over a 7 second period, 35 joules of work
were expended to raise a crate. How much power is
consumed?
35Joules
S: P =
= 5Watts
G: t = 7 s, W = 38 J
7seconds
U: P, power
S: 5 Watts of Power are
W
E:
P=
consumed to raise the crate.
t
Fd
t
Second: A crane raises a 67 N crate is raised 10 meters in
2 seconds. What is the minimum power output of the
machine?
S. I. Units:
Watts
GENERAL RELATIONSHIPS:
Power will increase when work is done over a shorter amount of time.
G: F = 67 N, d = 10 m,
t=2s
U: P, power
E:
Fd
P=
Power will decrease when work is done over a longer amount of time.
Power will increase when more work is done over the same amount of time.
Power will decrease when less work is done over the same amount of time.
t
67N ´10m
= 335Watts
2seconds
S: 335 Watts of Power are
consumed to raise the crate.
S:
P=
58
Efficiency
Efficiency is the ratio of the work
input to a system to the work
output of the same system.
Formula:
First: If 40 Joules of work are done on a system, yet
the work output by the system is 30 Joules, find the
efficiency of the system.
Efficiency =
Efficiency =
(workout )
(workin )
There are no units for efficiency
……………………………………………..since it is a ratio.
S. I. Units:
Examples:
(workout ) 30Joules
=
= 75 0 0
(workin ) 40Joules
Second: Two systems are compared that require the
same work input. If system X has a lower work output
than system Q, which system has greater efficiency?
System Q will have greater efficiency.
GENERAL RELATIONSHIPS:
Efficiency will increase when work output increases (as long as work input
stays the same).
Efficiency will decrease when work output decreases (as long as work input
stays the same).
Efficiency will increase when work input decreases (as long as work output
the same).
Efficiency will decrease when work input increases (as long as work output
stays the same).
59
Mechanical energy: Potential Energy
Potential energy (PE) is the energy stored by an object due
position. There are several forms of potential energy.
The food stores Chemical potential energy (ECHEM).
The position of atoms in molecules stores energy
in molecular bonds. When those bonds are
broken, energy is released. Batteries also store
energy as Chemical potential energy (ECHEM).
Nuclear potential energy is the potential energy of the particles
positioned inside an atomic nucleus. These particles are bond
together by the strong nuclear force.
Magnetic and electrical potential energies also store energy based
on the position of electric charges and magnetic fields.
Elastic potential energy (EEL). Is due
to the position of a spring or elastic band.
When it is deformed (stretched or
compressed), energy is stored.
Formula:
EEL = ½ k x2
Where “k” is the stiffness of the spring and
“x” is the change in the spring or elastic band’s
length.
Gravitational potential energy (Egrav) is the stored
energy due to the vertical position of an object within
Earth's gravitational field.
Formula:
EGRAV = mgh
Where “m” is the object’s mass, “h” is the height
and “g” is the strength of the gravitational field.
A familiar story exists about Isaac
Newton being struck on the head
by an apple.
If the apple was 2 meters above the
ground and its mass was 0.5 kg,
what was the apple’s Gravitational
potential energy?
G: m = 0.5 kg, h = 2 m, g = 9.8 m/s/s
U: EGRAV
E: EGRAV = mgh
S: EGRAV = (o.5kg) (2 m) (9.8 m/s/s)
S: The apple’s gravitational potential energy
was 9.8 joules.
When mass changes by a factor, EGRAV
changes by the same factor.
When height changes by a factor, EGRAV
changes by the same factor.
61
Mechanical energy: Kinetic Energy
Kinetic energy (KE) is defined as the energy possessed by
an object due to its motion. Temperature is due to the
kinetic energy of the molecules in a substance. When
temperature increases, the molecules move faster. Similarly,
a decrease in temperature will mean the molecules move
more slowly. So, temperature is one measure of kinetic
energy.
An object must be moving to possess kinetic energy. The
amount of kinetic energy (KE) possessed by a moving object
is dependent upon mass and speed.
Formula:
EK= ½ m v2
Where “m” is the mass of the object and
“v” is the object’s velocity.
Examples:
Determine the Kinetic energy of
a 60. kg man moving at 3.0 m/s.
G: m =60kg, v = 3 m/s
U: EK
E: EK= ½ m v2
S: EK = ½ (60. kg) (3.0 m/s)2
S: The man’s kinetic energy is 270 joules.
Determine the Kinetic energy of
a 0.0003032 kg bullet moving at 1256.8 m/s.
G: m =0.0003032kg, v = 1256.8 m/s
U: EK
E: EK= ½ m v2
S: EK = ½ (0.0003032kg) (1256.8 m/s)2
S: The bullet’s kinetic energy is 239.6 joules.
When mass changes by a factor, EK
changes by the same factor.
When velocity changes by a factor, EK
changes by the factor squared.
62
Energy Transformations & The Law of Conservation of Energy
The Law of Conservation of Energy states that energy cannot be created or destroyed; it simply changes
form. For the example below, the coaster is frictionless. The roller coaster below shows how the
gravitational potential energy of the car at A is converted to kinetic energy as the car reaches B. When the
car rolls downhill (EGRAV decreases), it speeds up (EK increases). As the coaster rolls uphill from B to C, the
coaster slows down (EK decreases) as it moves upward (EGRAV increases).
At A:
Car stopped at the highest point
At C:
Car stopped at the highest point
EGRAV = 25,000 Joules EK = 0 Joules E
Car slowing down as it moves up hill
EK = 0 Joules
GRAV = 2500 Joules
EGRAV = 20,000 Joules EK = 5,000 Joules
A
C
At B:
Car moving
at the lowest point
EGRAV = 0 Joules
EK = 25,000 Joules
hA = 50. m
mcoaster = 50.
kg
g = 10 m/s/s
hB = 0.0 m
h=0m
h=0m
B
hC= 40. m
h=
0m
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Energy Sources & Waves vocab
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Nuclear
Chemical
Electromagnetic
Mechanical
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Frequency
Wavelength
• Fission
• Fusion
Electromagnetic Spectrum
Electromagnetic (EM) waves do not transfer energy the same way that mechanical waves do. Mechanical waves
require a medium, but EM waves do not. EM waves can transfer energy through the vacuum of space.
Electromagnetic (EM) waves are self-propagating waves that are pushed by perpendicular electric and magnetic
fields.
High frequency
High energy
Short wavelength
Low frequency
Low energy
Long wavelength
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