Final Exam Review (Day 1)
PHYSICS
FINAL EXAM REVIEW: DAY 1 OVERVIEW

Energy Lecture Review
 Kinetic
& Potential Energy
 Net Work (Wnet = Fnet Dx = Fnet cos q)
 Work-Kinetic Energy Theorem (W = DKE)
 Conservation of Energy (KEi + PEi = KEf + PEf)

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 kx2)
 Chemical Potential (PE = nCvDT)

Kinetic Energy
 Energy
Achieved By An Object In Motion
 Kinetic Energy (KE = ½ mv2)
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

Wnet = Fnet Dx = Fnet cos q
WORK-KE THEOREM

Work Done On (Net External Force) An Object
Results In A Change In The Object’s Kinetic
Energy
= Force x Displacement or W = FDx
 Work-KE Theorem Is Equivelent To The Following
Expression:
 Work
W = KEf – KEi = ½ mvf2 – ½ mvi2
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.)
MEi = MEf
KEi + PEi = KEf + PEf
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 103 N, And
q = 20.0o.
What Is The Net Work
Done On The Boat By
The Two Locomotives?
PROBLEM #1: WORK
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.
Final Exam Review (Day 2)
PHYSICS
FINAL EXAM REVIEW: DAY 2 OVERVIEW

Momentum Lecture Review
(I = Fnett = Dp = pf – pi)
 Conservation Of Momentum (Pi = Pf)
 Collisions (Elastic & Inelastic)
 Circular Motion (ac = vt2/R)
 Gravitation (Fg = Gm1m2/d2)
 Impulse

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 = Fnett

The Object Will Thusly Experience A Change In
Velocity (Or Change In Momentum) As Shown
From Newton’s 2nd Law:
I = Fnett = Dp = pf – pi
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
Pi = P f
mv1i + mv2i = mv1f + mv2f
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
ac = vt2/R
GRAVITATION

Objects With Mass Are Seemingly Attracted To
Each Other Through The Gravitational Force
Fg = Gm1m2/d2

G Is The Gravitational Constant And Has An
Experimentally Determined Value of:
G = 6.67 x 10-11 Nm/kg2
PROBLEM #1: IMPULSE


During A Storm, Rain Comes
Straight Down With A Velocity Of
vo = -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 m1 = 0.250 kg And Velocity
v1i = +5.0 m/s Collides Head-on With A Ball Of
Mass m2 = 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?
Final Exam Review (Day 3)
PHYSICS
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)
Dx = xf - xi

Velocity Is Defined As The Displacement (Change In
Position) Of An Object Divided By The Change In Time
v = Dx/Dt

Acceleration Is The Change In Velocity Of An Object Over
The Change In Time
a = Dv/Dt
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?

What About Velocity Then?
 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 (Dx versus Dt)
Slope = Dx/Dt = Velocity
Dx
Dt

Velocity Versus Time (Dv versus Dt)
Dv
Slope = Dv/Dt = Acceleration
Dt
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
#1
Formula
v f  vi  aDt
Relationship
Velocity to Time
#2
1
2
Dx  vi Dt  aDt
2
Displacement to Time
#3
v f  vi  2aDx
Velocity to Displacement
#4
2
v
2
v f  vi
2
Dx

Dt
Average Velocity
FREEFALL

Freefalling Bodies Move Freely Under The
Influence Of Gravity ONLY!

The Acceleration Of An Object In Freefall Is
ALWAYS The Acceleration Of Gravity
ag = -9.81 m/s2

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?
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 Vix = Dx/Dt In The X-Direction
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 2nd Base
With A Velocity Of 10 m/s & Slides To A Stop At
3rd Base, What Is His Deceleration From 2nd To
3rd?
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 25.0o 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?
Final Exam Review (Day 4)
PHYSICS
FINAL EXAM REVIEW: DAY 4 OVERVIEW

Dynamics Lecture Review
Force Types (4 Major Forces)
 Newton’s Laws Of Motion

 1st Law (Freebody Diagrams)
 2nd Law (SF = Fnet = ma)
 3rd Law (F12 = -F21)

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
(FN)
An Applied Force (Mechanical or Electrical) Is One That
Is Applied To An Object Causing It To Move (FA)
The Resistive Force Acting On An Object In Contact With
Another Surface Is The Force Due To Friction


Static Friction (Fs = msFN)
Kinetic Friction (Fk = mkFN)
FORCE TYPES
Fk
FN
W
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: SF = MA
Second Law: The Net Force (Fnet = SF) Acting On An
Object Will Cause The Object To Accelerate
(Motion)
SF = ma
 Add Forces In Different Directions Vectorally

Fnet 2 = Fx2 + Fy2
(Magnitude)
Tan (q) = Fy/Fx
(Direction)
NEWTON’S 1ST & 3RD 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
F12 = -F21
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 2ND LAW
Two Forces, F1 & F2, Act On The 5.0 kg Block
Shown In The Drawing. The Magnitudes Of The
Forces Are F1 = 45.0 N And F2 = 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 mk =
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