# physics - La Quinta High School

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31 Οκτ 2013 (πριν από 4 χρόνια και 6 μήνες)

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PHYSICS

Final Exam Review (Day 1)

FINAL EXAM REVIEW: DAY 1 OVERVIEW

Energy Lecture Review

Kinetic & Potential Energy

Net Work (
W
net

=
F
net

D
x

F
net

cos

q
)

Work
-
Kinetic Energy Theorem (
W =
D

Conservation of Energy (
KE
i

+
PE
i

=
KE
f

+
PE
f
)

Problem Review (Group Problems)

Energy

Net Forces

ENERGY

Potential Energy

Stored Energy
In Which An Object May Use To
Perform Work On Another Object

Gravitational Potential (
PE =
mgh
)

Elastic Potential (
PE = ½ kx
2
)

Chemical Potential (
PE =
nC
v
D
q
)

Kinetic Energy

Energy Achieved By An Object
In Motion

Kinetic Energy (
KE = ½ mv
2
)

NET WORK

Work Done On An Object With Multiple Forces
Is The
Net Work

For A Net Force Applied At An Angle
, The
Net
Work

Is The Product Of The
Component Of
Force In The Direction Of Motion
& Its
Displacement

W
net

= F
net

D
x = F
net

cos
q

WORK
-
KE THEOREM

Work Done
On

(Net External Force) An Object
Results

In A Change In The Object’s
Kinetic
Energy

Work = Force x Displacement or
W = F
D
x

Work
-
KE Theorem Is Equivelent To The Following
Expression:

W = KE
f

KE
i

= ½ mv
f
2

½ mv
i
2

CONSERVATION OF
ENERGY

Total Mechanical Energy (
ME = KE + PE
) Of An
Object Remains Constant As The Object Moves

Assume
No Net Work Done
By
External Forces
(e.g.
Friction, Air Resistance, Pressure, etc.)

ME
i

= ME
f

KE
i

+ PE
i

= KE
f

+ PE
f

PROBLEM #1: WORK

The Drawing Shows A
Boat Being Pulled By
Two Locomotives
Through A Canal Of
Length 2.00 km. The
Tension In Each Cable
Is 5.00 x 10
3
N, And
q

= 20.0
o
.

What Is The Net Work
Done On The Boat By
The Two Locomotives?

PROBLEM #2: WORK & ENERGY

A 0.075 kg Arrow Is Fired Horizontally. The
Bowstring Exerts An Average Force Of 65 N On
The Arrow Over A Distance Of 0.90 m.

With What Speed Does The Arrow Leave The
Bow?

PROBLEM #3: ENERGY

A Cyclist Approaches The Bottom Of A gradual
Hill AT A Speed Of 11 m/s. The Hill Is 5.0 m
High, And The Cyclist Estimates That She Is
Going Fast Enough To Coast Up And Over It
Without Peddling.

Ignoring Air Resistance And Friction, Find The
Speed AT Which The Cyclist Crests The Hill.

PHYSICS

Final Exam Review (Day 2)

FINAL EXAM REVIEW: DAY 2 OVERVIEW

Momentum Lecture Review

Impulse (
I =
F
net
t

=
D
p

p
f

p
i
)

Conservation Of Momentum (
P
i

= P
f
)

Collisions (
Elastic & Inelastic
)

Circular Motion (
a
c

= v
t
2
/R
)

Gravitation (
F
g

= Gm
1
m
2
/d
2
)

Problem Review (Group Problems)

Momentum

Collisions

Circular Motion

IMPULSE

When A
Large Force

Acts on An Object For A
Sufficient Amount Of Time
, Their Product Is The
Impulse

Of The Force

I =
F
net
t

The Object Will Thusly Experience A Change In
Velocity (Or
Change In Momentum
) As Shown
From Newton’s 2
nd

Law:

I =
F
net
t

=
D
p

p
f

p
i

MOMENTUM

The
Total Linear Momentum
Of An Isolated
System Remains
Constant

An
Isolated System
Is One For Which The Vector
Sum Of The
External Forces
Acting On The System
Is
Zero

P
i

= P
f

mv
1i

+ mv
2i
= mv
1f

+ mv
2f

COLLISIONS

Elastic Collision
Is One In
Which The Total KE Of The
System After The Collision
Is
Equal

To The Total KE
Before The Collision

Inelastic Collision
Is One
In Which The Total KE Of
The System After The
Collision Is
Not Equal
To
The Total KE Before The
Collision

CIRCULAR MOTION

Uniform Circular Motion Is The Motion Of An
Object Traveling At A Constant (Uniform) Speed
On A Circular Path

Even Though An Object In Circular Motion Has A
Constant Velocity (VT) It Experiences An
Acceleration Toward The Center Of The Circular
Path

a
c

= v
t
2
/R

GRAVITATION

Objects With Mass
Are Seemingly
Attracted To
Each Other

Through The
Gravitational Force

F
g

= Gm
1
m
2
/d
2

G
Is The Gravitational Constant And Has An
Experimentally Determined Value of:

G = 6.67 x 10
-
11

Nm/kg
2

PROBLEM #1: IMPULSE

During A Storm, Rain Comes
Straight Down With A Velocity Of
v
o

=
-
15 m/s

And Comes To Rest
After Impacting The Car. If The
Rain Drops Have A Mass Of
0.060 kg & It Takes 1.0s To
Come To A Rest,
What Is The
Force Exerted By The Rain On
The Car Roof?

If Hail Fell Instead Of Rain,
Would The Force On The Roof
Be Smaller Than, Equal To , Or
Greater Than That Of The
Raindrop?

PROBLEM #2: MOMENTUM

A Ball Of Mass m
1

= 0.250 kg And Velocity
v
1i

-
on With A Ball Of
Mass m
2

= 0.800 kg That Is Initially At Rest.
No External Forces Act On The Balls.

If The Collision Is Elastic, What Are The
Velocities Of The Balls After The Collision?

PROBLEM #3: CIRCULAR MOTION

How Long Does It Take A Plane, Traveling At A
Constant Speed Of 110 m/s, To Fly Once
Around A Circle Whose Radius Is 2850 m?

PHYSICS

Final Exam Review (Day 3)

FINAL EXAM REVIEW: DAY 3 OVERVIEW

Kinematics Lecture Review

Displacement, Velocity & Acceleration

Speed Versus Velocity

Graphical Models Of Motion

Kinematic Equations

Freefall

2
-
D Kinematics

Horizontal Projectile Motion

Projectile Motion @ Angle

Problem Review (Group Problems)

1
-
D Kinematics

2
-
D Kinematics

DISPLACEMENT, VELOCITY & ACCELERATION

Displacement

Is A Vector That Points From An Object’s
Initial Position Toward Its Final Position (Shortest
Distance

Between Two Points)

D
x

x
f

-

x
i

Velocity

Is Defined As The Displacement (Change In
Position) Of An Object Divided By The Change In Time

v =
D
x
/
D
t

Acceleration

Is The Change In Velocity Of An Object Over
The Change In Time

a =
D
v
/
D
t

SPEED VERSUS VELOCITY

What Is Speed?

Speed Is An Average Velocity

If I Asked How Fast You Drove From Home To School
Today What Would You Say?

Velocity Is Instantaneous, It Changes From One
Second To The Next

Watch Your Speedometer Next Time You’re Driving!

GRAPHICAL MODELS OF MOTION

Position Versus Time (
D
xversu猠
D
t
)

Velocity Versus Time (
D
vversu猠
D
t
)

Slope =
D
x/
D
t = Velocity

Slope =
D
v/
D
t = Acceleration

D
t

D
t

D
x

D
v

KINEMATIC EQUATIONS

Kinematics

is the study of objects’ motion at
constant acceleration

There are
4 kinematic equations

Use these to
solve all 1
-
D and 2
-
D motion
problems!

KINEMATIC EQUATIONS

Equation

Formula

Relationship

#1

Velocity to Time

#2

Displacement to Time

#3

Velocity to

Displacement

#4

Average Velocity

Freefalling Bodies
Move
Freely

Under The
Influence Of
Gravity ONLY
!

The Acceleration Of An Object In Freefall Is
ALWAYS The Acceleration Of Gravity

a
g

=
-
9.81 m/s
2

Use Kinematic Equations To Solve Freefall
Problems

What Is The Acceleration Of An Object Thrown
Upwards?

What Is The Velocity Of An Object At The Peak
Of Its Motion?

FREEFALL

2
-
D KINEMATICS

Projectile Motion

Horizontal Projectile Motion

Projectile Motion At An Angle

Problem Solving Method

First Commandment Of Physics
(Keep X & Y
Directions Separate)

Solve For
Time
In
Y
-
Direction

Using A Kinematic
Equation

Use
V
ix

=
D
x
/
D
t

I渠周q
X
-
䑩rection

PROBLEM #1: GRAPHICAL MODELS

What Is The Acceleration At

The Following Points:

a). 0 to 5 s

b). 5 to 15 s

c). 15 to 20 s

PROBLEM #2: 1
-
D KINEMATICS

A Baseball Player Hits A Triple And Ends Up On
Third Base. A Baseball “Diamond” Is A Square,
Each Side Of Length 27.4 m. What is The
Magnitude Of His Displacement?

If The Same Baseball Player Rounds 2
nd

Base
With A Velocity Of 10 m/s & Slides To A Stop At
3
rd

Base, What Is His Deceleration From 2
nd

To
3
rd
?

PROBLEM #3: 2
-
D KINEMATICS

A Quarterback Throws A Pass To A Receiver,
Who Catches It At The Same Height As The
Pass Is Thrown. The Initial Velocity Of The Ball
Is 15.0 m/s, At An Angle Of 25.0
o

Above The
Horizontal. What Is The Horizontal Component
Of The Ball’s Velocity When The Receiver
Catches It?

PROBLEM #4: 2
-
D KINEMATICS

Given The Last Problem, How Far Did The
Receiver Have To Run Before Making The
Catch?

PHYSICS

Final Exam Review (Day 4)

FINAL EXAM REVIEW: DAY 4 OVERVIEW

Dynamics Lecture Review

Force Types (4 Major Forces)

Newton’s Laws Of Motion

1
st

Law (
Freebody

Diagrams
)

2
nd

Law (
S
F =
F
net

= ma
)

3
rd

Law (
F
12
=
-
F
21
)

Problem Review (Group Problems)

Net Force

Newton’s Second Law I

Newton’s Second Law II

FORCE TYPES

An
Object With Mass
(Takes Up Space) In The
Presence
Of Gravity
Has
Weight
.

W = mg

Any Object In Contact With A Surface Experiences A
Force Normal To The Surface Called The
Normal Force
(F
N
)

An
Applied Force
(Mechanical or Electrical) Is One That
Is Applied To An Object Causing It To Move (
F
A
)

The Resistive Force Acting On An Object In Contact With
Another Surface Is The Force Due To Friction

Static Friction (
F
s

=
m
s
F
N
)

Kinetic Friction (
F
k

=
m
k
F
N
)

FORCE TYPES

F
k

W

F
N

FREEBODY

DIAGRAMS

Draw The
Freebody

(The Object Separated From
Its Surroundings)

Draw Relevant Forces
Acting On The
Freebody

From The Center Of The Object

Does The Body Have
Mass In The Presence Of
Gravity?

Is The Object In
Contact With A Surface?

If Yes
, Is The Contact Surface
Frictionless

or Is
Friction

Present?

Is There An
Applied Force?

NEWTON’S SECOND LAW:
S
F

= MA

Second Law:

The
Net Force
(
F
net

=
S
F
)ActingOn⁁n
Object Will Cause The Object To
Accelerate

(
Motion
)

S
F = ma

Vectorally

F
net

2

= F
x
2

+ F
y
2

(Magnitude)

Tan (
q
) =
F
y
/
F
x

(
Direction
)

NEWTON’S 1
ST

& 3
RD

LAWS:

First Law

An
Object In Motion
Will Stay In Motion Until Acted
Upon By An External Net Force

An
Object At Rest
Will Remain At Rest Until Acted
Upon By An External Net Force

Third Law

Two Objects In Contact Will Apply Forces Equal In
Magnitude But Opposite In Direction

F
12

=
-
F
21

PROBLEM #1: NET FORCE

A Person With A Blackbelt In Karate Has A Fist
That Has A Mass Of 0.70 kg. Starting From
Rest, This Fist Attains A Velocity Of 8.0 m/s In
0.15 s. What Is The Magnitude Of The Average
Net Force Applied To The Fist To Achieve This
Level Of Performance?

PROBLEM #2: VECTOR NATURE OF 2
ND

LAW

Two Forces,
F
1

&
F
2
, Act On The 5.0 kg Block
Shown In The Drawing. The Magnitudes Of The
Forces Are F
1

= 45.0 N And F
2

= 25.0 N. What
Is The Horizontal Acceleration (Magnitude &
Direction) Of The Block?

PROBLEM #3: FRICTION

A 92 kg Baseball Player Slides Into Second
Base. The Coefficient Of Kinetic Friction
Between The Player And The Ground Is
m
k

=
0.61.

a). What Is The Magnitude Of The Frictional

Force?

b). If The Player Comes To Rest After 1.2 s,

What Is His Initial Speed?

PROBLEM #4: TENSION

Given The Following Atwood Machine With
Masses
M

and
m
,
Determine The Acceleration
Of Mass m
.

m