# One Dimensional Kinematics - Chapter Outline

Mechanics

Nov 14, 2013 (4 years and 7 months ago)

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HONORS PHYSICS
FINAL

EXAM STUDY GUIDE

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IF A LINK IS BROKEN OR YOU WOULD LIKE EXTRA PRACTICE, IT CAN BE FOUND AT
www.physicsclassroom.com

in the

MULTIMEDIA PHYSICS STUDIOS,

MINDS ON PHYSICS (MOPS) INTERNET MODULES,

THE CALCULATOR PAD, and the

REVIEW SESSION.

One Dimensional Kinematics
-

Chapter Outline

Lesson 1 : Describing Motion with Words

a.

Introduction to the Language of Kinematics

(define mechanics, kinematics, READ ON TUTORIAL)

b.

Scalars and Vectors

(define each, ID quantities as scalar or vector, PRACTICE

ON TUTORIAL)

c.

Distance and Displacement

(differentiate between, PRACTICE ON TUTORIAL)

d.

Speed and Velocity

(differentiate between, instantaneous vs. average, calculate each, PRACTICE ON TUTORIAL)

e.

Acceleration

(define; calculate from data tables, graphs, word problems; understand direction of
acceleration

vector, PRACTICE ON TUTORIAL)

Lesson 2 : Describing Motion with Diagrams

a.

Introduction to Diagrams

(analyze ticker tape or “oil drop” and vector diagrams, READ ON TUTORI
AL)

b.

Ticker Tape Diagrams

(analyze “oil drop” diagrams and use to describe motion of objects, PRACTICE ON TUTORIAL)

c.

V
ector Diagrams

(analyze vector diagrams and use to describe motion of objects, READ ON TUTORIAL)

Lesson 3 : Describing Motion with Position vs. Time Graphs

a.

The Meaning of Shape for a
p
-
t Graph

(relate shape of slope to description of motion, link broken)

b.

The Meaning of Slope for a p
-
t Graph

(
calculate

slope

and use to describe motion of objects, link broken
)

c.

Determining the Slope on a p
-
t Graph

(calculate slope to calculate velocity, PRACTICE ON TUTORIAL)

Lesson 4 : Describing Motion with Velocity vs. Time Graphs

a.

The Meaning of Shape for a v
-
t Graph

(constant vs. changing velocity, direction of velocity, velocity vs. acceleration,

PRACTICE ON TUTORIAL)

b.

The Meaning of Slope for a v
-
t Graph

(slope of v
-
t graph is acceleration, link broken)

c.

Relating the Shape to the Motio
n

(use shape of line to describe motion, link broken)

d.

Determining the Slope on a v
-
t Graph

(calculate slope, PRACTICE ON TUTORIAL)

e.

Determining the Area on a v
-
t Graph

(Determine area of a rectangle, square, triangle, relate area to height, link

broken)

Lesson 5 : Free Fall and the Acceleration of Gravity

a.

Introduction to Free Fall

(define, know rate of free
-
fall on Earth, READ ON TUTORIAL)

b.

The Acceleration of Gravity

(g, know acceleration due to gravity on Earth, link broken)

c.

Representing Free Fall by Graphs

(recognize free fall on P
-
T and V
-
T graphs, READ ON TUTORIAL)

d.

How Fast? and How Far?

(calculate how far an object will fall in a certain time, calculate final velocity of free falling

object in certain time,
v
f

= g * t,

e.

The Big Misconception

(know t
he answer to “doesn't a more massive object accelerate at a greater rate than a

less massive object?” READ ON TUTORIAL)

Lesson 6 : Describing Motion with Equations

a.

The Kinematic
Equations

(Kinematics equations will be on reference, no need to memorize, READ ON TUTORIAL)

b.

Kinematic Equations and Problem
-
Solving

(utilize the FIVE problem
-
solving strategies, READ ON

TUTORIAL)

c.

Kinematic Equations and Free Fall

(know conceptual characteristics of free fall motion, READ ON TUTORIAL)

d.

Sample Problems and Solutions

(Solve problems using kinematics equations, PRACTICE ON TUTORIAL)

e.

Kinematic Equations and Graphs

(Sketch graphs on motion, analyze graphs and solve kinemat
ics problems,

PRACTICE ON WEBSITE)

THERE IS A HOMEWORK
ASSIGNMENT HIDDEN IN THIS
PACKET! DUE ON EXAM DAY!

All of these questions can be CHECKED on the
Physics Classroom

tutorial.

One Dimensional Kinematics

LESSON 1B:

Scalars and Vectors

Categorize
each quantity as being either a vector or a scalar. Click the button to see the answer.

website.

Quantity

Category

a. 5 m

b. 30 m/sec, East

c. 5 mi., North

d. 20 degrees Celsius

e. 256 bytes

f. 4000 Calories

LESSON
1c:

Distance and Displacement

Determine the DISTANCE traveled and the DISPLACEMENT for each example. Check answers on website.

Distance = _______ Displacement = _______

Distance = _______ Displacement = _______

Distance = _______
Displacement = _______

What is the displacement of the cross
-
country team if they begin at the school, run 10 miles and finish back at the school?

What is the distance and the displacement of the race car drivers in the Indy 500?

LESSON 1d:

Speed and
Velocity

Q: While on vacation, Lisa Carr traveled a total distance of 440 miles. Her trip took 8 hours. What was her average speed?

Q:
Use the diagram to determine the average speed and the average

velocity of the skier during thes
e three minutes.

SEE

IF YOUR ANSWERS ARE CORRECT ON THE
PHYSICS CLASSROOM TUTORIAL!!!

ALL ANSWERS CAN BE
CHECKED AT THE PHYSICS
CLASSROOM TUTOIAL!!!!

What is the coach's average speed and average velocity?

LESSON 1e:

Acceleration

Use the equation for acceleration to determine the acceleration for the following two motions.

LESS
ON 2b:

TICKER TAPE DIAGRAMS

Analyze the following ticker tape diagrams.

1.

2.

3.

LESSON 3c:

Determining slope on a P
-
T graph

Determine the velocity (i.e., slope) of the object as portrayed by the graph below.

CORRECT ON THE
PHYSICS CLASSROOM TUTORIAL!!!

LESSON 4a
: The Meaning of Shape for a V
-
T Graph

Consider the graph at the right. The object whose motion is represented by this graph is ... (include all that are true):

a.

moving in the positive direction.

b.

mov
ing with a constant velocity.

c.

moving with a negative velocity.

d.

slowing down.

e.

changing directions.

f.

speeding up.

g.

moving with a positive acceleration.

h.

moving with a constant acceleration.

LESSON 4d
: Describing Motion with V
-
T Graphs

Consider the veloc
ity
-
time graph below. Determine the acceleration (i.e., slope) of the object as portrayed by the graph. Click the

LESSON 6D: Kinematics Sample Problems

An airplane accelerates down a runway at 3.20 m/s
2

for 32.8 s until is f
inally lifts off the ground. Determine the distance traveled
before takeoff.

A car starts from rest and accelerates uniformly over a time of 5.21 seconds for a distance of 110 m. Determine the accelerat
ion of
the car.

Upton Chuck is riding the Giant Drop at Great America. If Upton free falls for 2.6 seconds, what will be his final velocity a
nd how far
will he fall?

A race car accelerates uniformly from 18.5 m/s to 46.1 m/s in 2.47 seconds. Determine the acceleration o
f the car and the distance
traveled.

A feather is dropped on the moon from a height of 1.40 meters. The acceleration of gravity on the moon is 1.67 m/s
2
. Determine
the time for the feather to fall to the surface of the moon.

Rocket
-
powered sleds are us
ed to test the human response to acceleration. If a rocket
-
powered sled is accelerated to a speed of
444 m/s in 1.8 seconds, then what is the acceleration and what is the distance that the sled travels?

MORE ON TUTORIAL WEBSITE!

LESSON 6e
: Kinematics
Equations and Graphs

Rennata Gas is driving through town at 25.0 m/s and begins to accelerate at a constant rate of
-
1.0 m/s
2
. Eventually Rennata
comes to a complete stop. Represent Rennata's accelerated motion by sketching a velocity
-
time graph. Use the
velocity
-
time graph
to determine this distance.

2. Use kinematic equations to calculate the distance that Rennata travels while decelerating.

MORE PROBLEMS ON WEBSITE!

Newton's Laws
-

Chapter Outline

Lesson 1: Newton's First Law of Motion

a.

Newton's First Law

(Define, apply to real
-
world situations, READ ON TUTORIAL)

b.

Inertia and Mass

(know relationship between,

gravitational and frictional influences, PRACTICE ON TUTORIAL

c.

State of Motion

(define inertia, PRACTICE ON TUTORIAL)

d.

Balanced and Unbalanced Forces

(Forces cause accelerations, not motions; ID balanced & unbalanced forces, define

equilibrium, PRACTICE ON TUTORIAL)

Lesson 2: Force and Its Represen
tation

a.

The Meaning of Force

(define force, identify common forces F
frict
, F
norm
, F
grav
, etc, READ ON TUTORIAL)

b.

Types of Forces

(identify common forces F
frict
, F
norm
, F
grav
, etc, link broken)

c.

Drawing Free
-
Body Diagrams

(understand free
-
body diagrams show forces, not motions; draw free
-
body dia
grams for

real
-
world situations, PRACTICE ON TUTORIAL)

d.

Determining the Net Force

(define net force, analyze diagrams to determine of net force exists, analyze free
-
body

diagra
ms to determine if net force exists, PRACTICE ON TUTORIAL)

Lesson 3 : Newton's Second Law of Motion

a.

Newton's Second Law

b.

The Big Misconception

(know the answer to, “does sustaining a motion require a continued force?”, READ ON

TUTORIAL, Take “quiz” to see if you are infected with the misconception)

c.

Finding Acceleration

(The three major equations that will be useful are the equation for net force (
Fnet = m•a
), the

equation for
gravitational force

(F
grav

= m•g), and the equation for
frictional force

(F
frict

= μ•F
norm
)
,
PRACTICE ON TUTORIAL).

d.

Finding Individual Forces

(find sum of individual forces acting on a object, PRACTICE ON TUTORIAL)

e.

Free Fall and Air Resistance

(determine net force and net acceleration, define terminal velocity. PRACTICE ON

TUTORIAL)

f.

Double Trouble (a.k.a., Two Body Problems)

(will not be covered)

Lesson 4 : Newton's Third Law of Motion

a.

Newton's Third Law

(define, compare forces apply to real
-
world pr
oblems, PRACTICE ON TUTORIAL)

b.

Identifying Action and Reaction Force Pairs

(ID action and reaction pairs. PRACTICE ON TUTORIAL)

Newton's Laws

LESSON 1b
: Inertia and Mass

Imagine

a place in the
cosmos

far from all gravitational and frictional influences. Suppose that you visit that place (just suppose)
and throw a rock. The rock will

b. continue in motion in the same direction at constant speed.

A 2
-
kg

object is moving horizontally with a speed of 4 m/s. How much net force is required to keep the object moving at this speed
and in this direction?

Mac and Tosh are arguing in the cafeteria. Mac says that if he flings the Jell
-
O with a greater speed it w
ill
have a greater inertia. Tosh argues that inertia does not depend upon speed, but rather upon mass. Who do
you agree with? Explain why.

Supposing you were in space in a
weightless environment
, would it require a force to set an object in
motion?

Fred

spends most Sunday afternoons at rest on the sofa, watching pro football games and consuming large

quantities of food. What effect (if any) does this practice have upon his inertia? Explain.

MORE ON TUTORIAL!

LESSON 1c:

State of MOTION

A group of physics teachers is taking some time off for a little putt
-
putt golf. The 15th hole at the Hole
-
In
-
One Putt
-
Putt Golf Course has a large metal rim that putters must use to guide their ball towards the
hole. Mr. S guides a golf ball around the m
etal rim When the ball leaves the rim, which path (1, 2, or 3)
will the golf ball follow?

A 4.0
-
kg object is moving across a friction
-
free surface with a constant velocity of 2 m/s. Which one of
the following horizontal forces is necessary to maintain th
is state of motion?

a. 0 N

b. 0.5 N

c. 2.0 N

d. 8.0 N

a.

depends on the speed.

LESSON 1d
: Balanced and Unbalanced Forces

Luke Autbeloe

drops an approximately 5.0 kg fat cat (weight = 50.0 N) off the roof of his house into the swimming pool below.
Upon encountering the pool, the cat encounters a 50.0 N upward resistance force (assumed to be constant). Use this descriptio
n to
llowing questions. Click the button to view the correct answers.

1. Which one of the velocity
-
time graphs best describes the motion of the cat? Support your answer with sound reasoning.

2. Which one of the following dot diagrams best describes the
motion of the falling cat from the time that they are dropped to the
time that they hit the bottom of the pool? The arrows on the diagram represent the point at which the cat hits the water. Sup
port

3. Several of L
uke's friends were watching the motion of the falling cat. Being "physics types", they began discussing the motion
and made the following comments. Indicate whether each of the comments is correct or incorrect? Support your answers.

a. Once the
cat hits the water, the forces are balanced and the cat will stop.

b. Upon hitting the water, the cat will accelerate upwards because the water applies an upward force.

c. Upon hitting the water, the cat will bounce upwards due to
the upward force.

4. If the forces acting upon an object are balanced, then the object

a. must not be moving.

b. must be moving with a constant velocity.

c. must not be accelerating.

d. none of these

LESSON 2c
:

Free Body Diagrams

A book is at rest on a tabletop. Diagram the forces acting on the book.

A girl is suspended motionless from the ceiling by two ropes. Diagram the forces acting on the combination of girl and
bar.

An egg is free
-
falling from a nest in a tree. Neglect air resistance. Diagram the forces acting on the egg as it is falling.

A flying squirrel is gliding (no
wing

flaps
) from a tree to the ground at constant velocity. Consider air resistance.
Diagram the

forces acting on the squirrel.

A rightward force is applied to a book in order to move it across a desk with a rightward acceleration. Consider frictional
forces. Neglect air resistance. Diagram the forces acting on the book.

MORE ON TUTORIAL

LESSON

3c
: Finding Acceleration

An applied force of 50 N is used to accelerate an object to the right across a frictional surface. The object encounters 10 N

of
friction. Use the diagram to determine the normal force, the net force, the mass, and the
acceleration of the object. (Neglect air
resistance.)

An applied force of 20 N is used to accelerate an object to the right across a frictional surface. The object encounters 10 N

of
friction. Use the diagram to determine the normal force, the net
force, the coefficient of friction (μ) between the object and the
surface, the mass, and the acceleration of the object. (Neglect air resistance.)

A 5
-
kg object is sliding to the right and encountering a friction force that slows it down. The coefficient

of friction (μ) between the
object and the surface is 0.1. Determine the force of gravity, the normal force, the force of friction, the net force, and th
e
acceleration. (Neglect air resistance.)

1. Edwardo applies a 4.25
-
N rightward force to a 0.765
-
kg

book to accelerate it across a tabletop. The coefficient of friction
between the book and the tabletop is 0.410. Determine the acceleration of the book.

2. In a physics lab, Kate and Rob use a hanging mass and pulley system to exert a 2.45 N rightward for
ce on a 0.500
-
kg cart to
accelerate it across a low
-
friction track. If the total resistance force to the motion of the cart is 0.72 N, then what is the cart's
acceleration?

LESSON 3d
: Finding Individual Forces

Practice #1

Free
-
body diagrams for four situa
tions are shown below. The net force is known for each situation. However, the magnitudes of a
few of the individual forces are not known. Analyze each situation individually and determine the magnitude of the unknown fo
rces.

A rightward force is
applied to a 6
-
kg object to move it across a rough surface at constant velocity. The object encounters 15 N of
frictional force. Use the diagram to determine the gravitational force, normal force, net force, and applied force. (Neglect
air
resistance.)

A rightward force is applied to a 10
-
kg object to move it across a rough surface at constant velocity. The coefficient of friction
between the object and the surface is 0.2. Use the diagram to determine the gravitational force, normal force, applied force,

frictional force, and net force. (Neglect air resistance.)

MORE ON TUTORIAL!

LESSON 3e
: Free fall and Air Resistance

In the diagrams below, free
-
body diagrams showing the forces acting upon an 85
-
kg skydiver (equipment included) are shown. For
each ca
se, use the diagrams to determine the net force and acceleration of the skydiver at each instant in time. Then use the
button to view the answers.

Lesson 4a
: Newton’s Third Law

While driving down the road, a firefly strikes the windshield of a bus
and makes a quite obvious
mess in front of the face of the driver. This is a clear case of Newton's third law of motion. The
firefly hit the bus and the bus hits the firefly. Which of the two forces is greater: the force on the
firefly or the force on the
bus?

For years, space travel was believed to be impossible because there was nothing that rockets
could push off of in space in order to provide the propulsion necessary to accelerate. This inability
of a rocket to provide propulsion is because ...

a. ... space is void of air so the rockets have nothing to push off of.

b. ... gravity is absent in space.

c. ... space is void of air and so there is no air resistance in space.

d. ... nonsense! Rockets do accelerate
in space and have been able to do so for a long time.

Many people are familiar with the fact that a rifle recoils when fired. This recoil is the result of action
-
reaction force pairs. A gunpowder explosion creates hot gases that expand outward allowing
the rifle to
push forward on the bullet. Consistent with Newton's third law of motion, the bullet pushes backwards
upon the rifle. The acceleration of the recoiling rifle is ...

a. greater than the acceleration of the bullet.

b. smalle
r than the acceleration of the bullet.

c. the same size as the acceleration of the bullet.

In the top picture (below), Kent Budgett is pulling upon a rope that is attached to a wall. In the bottom picture, the Kent i
s pulling
upon a rope that i
s attached to an elephant. In each case, the force scale reads 500 Newton. Kent is pulling ...

a. with more force when the rope is attached to the wall.

b. with more force when the rope is attached to the elephant.

c. the same force in each case.

LESSON 4b
: Identifying Action and Reaction Force Pairs

Consider the interaction depicted below between foot A, ball B, and foot C. The three objects interact simultaneously (at the

same
time). Identify the
two pairs

of action
-
reaction forces. Use the notat
ion "foot A", "foot C", and "ball B" in your statements. Click the
button to view the answer.

2. Identify at least six pairs of action
-
reaction force pairs in the following diagram.

1
-

2
-

3
-

4
-

5
-

6
-

CORRECT ON THE
PHYSICS CLASSROOM TUTORIAL!!!

Vectors: Motion and Forces in Two Dimensions
-

Chapter Outline

Lesson 1: Vectors
-

Fundamentals and Operations

a.

Vectors and Direction

(Draw

scaled vectors, be able to use the counterclockwise convention)

b.

(add vectors using pythagorean theorem and calculus)

c.

Resultants

(know how to determine resultant magnitude and direction)

d.

Vector Components

(know how to work backwared...identify the vectors that make up a resultant
)

e.

Vector Resolution

(link broken; know hoe to break a vector into components; hanging pictures,

dog chains, airplane flights)

f.

Component Method of Vector Addition

(link broken; be able to use pythagorean theorem, add three

or more vectors tail
-
to
-
tip, etc.)

g.

Relative Velocity and Riverboat
Problems

(Solve riverboat problems)

h.

Independence of Perpendicular Components of Motion

(vector resoluntion involving riverboat problems)

Lesson 2: Projectile Motion

a.

What is a Projectile?

(Analyze presence of forces, accelerations, and velocity in both components of

a projectile)

b.

Characteristics of a Projectile's Trajectory

(analyze projectiles for initial; and final velocity, horizontal

and vertical acceleration, and net force)

c.

Describing Projectiles with Numbers

1.

Horizontal and Vertical Components of Velocity

(use kinematics equations to solve for velocity)

2.

Horizontal and Vertical Components of Displacement

(use kinematics equation to

solve for

displacement)

d.

Initial Velocity Components

(link broken; be able to resolve the trajectory of a projectile using

Pythagorean theorem and calculus)

e.

Horizontally Launched Projectiles
-

Problem
-
Solving

(be able to use kinematics equations to solve

problem about projectiles launched horizontally)

f.

Non
-
Horizontally Launched Projectiles
-

Problem
-
Solving

(link broken, there are additional problems in

“The Calculator Pad” section of the website; be able to use kinematics equations

to

solve problem about projectiles launched vertically)

Lesson 3 : Forces in Two Dimensions

a.

(Review of previous concepts)

b.

Resolution of Forces

(Review of breaking forces into components)

c.

Equilibrium and Statics

(be able to determine wei
ght of hanging picture,
then determine the tension

in the diagonal cable that supports its weight.

d.

Net Force Problems Revisited

( Be able to
calculate F
net
= m • a problems involving f
orces at angles
)

e.

Inclined Planes

( Be able to u
se the principles of vector resolution to determine the net force and

acceleration of
objects on an incline)

f.

Double Trouble (a.k.a. Two Body Problems)

(Do the following HW assignments and then go to sleep)

HW:

Due on exam day. Previously distributed in class. All were present

I put them on the website in case you lost them!

1)

Circular Motion and Satellite Motion, Lesson 3.

2)

Momentum an It’s Conservation, Lesson 1

Vectors: Motion and Forces in Two Dimensions

Lesson 1a
:
Vectors and Direction

1)
Given the
SCALE: 1 cm = 50 km/hr
, determine the magnitude and direction of this vector.

2) Given the
SCALE: 1 cm = 15 m/s
, represent the vector 120 m/s, 240
-
d
egrees by a scaled vector diagram.

Lesson 1
b
:
Vector

Does the order in which vectors are added tail to tip have any effect on the resultant vector’s magnitude or
direction?

Lesson 1g: Relative Velocity and Riverboat Problems

Example 2
A motorboat traveling 4 m/s, East encounters a current traveling 3.0 m/s, North.

a.

What is the resultant velocity of the motorboat?

b.

If the width of the river is 80 meters wide, then how much time does it take the boat to travel shore to shore?

c.

What distance downstream does the boat reach the opposite shore?

Example 2
A motorboat traveling 4 m/s, East encounters a current traveling 7
.0 m/s, North.

a.

What is the resultant velocity of the motorboat?

b.

If the width of the river is 80 meters wide, then how much time does it take the boat to travel shore to shore?

c.

What distance downstream does the boat reach the opposite shore?

Check Your
Understanding

1. A plane can travel with a speed of 80 mi/hr with respect to the air. Determine the resultant velocity of the plane (magnit
ude
only) if it encounters a

a. 10 mi/hr headwind.

b. 10 mi/hr tailwind.

c. 10 mi/hr crosswind.

d. 60 mi/hr
crosswind.

2. A motorboat traveling 5 m/s, East encounters a current traveling 2.5 m/s, North.

a. What is the resultant velocity of the motor boat?

b. If the width of the river is 80 meters wide, then how much time does it take the boat to travel shore to

shore?

c. What distance downstream does the boat reach the opposite shore?

3. A motorboat traveling 5 m/s, East encounters a current traveling 2.5 m/s, South.

a. What is the resultant velocity of the motor boat?

b. If the width of the river is 80 meters

wide, then how much time does it take the boat to travel shore to shore?

c. What distance downstream does the boat reach the opposite shore?

4. A motorboat traveling 6 m/s, East encounters a current traveling 3.8 m/s, South.

a. What is the resultant veloc
ity of the motor boat?

b. If the width of the river is 120 meters wide, then how much time does it take the boat to travel shore to shore?

c. What distance downstream does the boat reach the opposite shore?

5. If the current velocity in question #4 were i
ncreased to 5 m/s, then

a. how much time would be required to cross the same 120
-
m wide river?

b. what distance downstream would the boat travel during this time?

Lesson 1h
:

Indepen
dence of Perpendicular Components of Motion

1. A plane flies northwest out of O'Hare Airport in Chicago at a speed of 400 km/hr in a direction of 150
degrees (i.e., 30 degrees north of west). The Canadian border is located a
distance of 1500 km due north
of Chicago. The plane will cross into Canada after approximately ____ hours.

a. 0.13

b. 0.23

c. 0.27

d. 3.75

e. 4.33

f. 6.49

g. 7.50

h. None of these are even close.

2. Suppose that the plane in question 1 was flying
with a velocity of 358 km/hr in a direction of 146 degrees (i.e., 34 degrees north
of west). If the Canadian border is still located a distance of 1500 km north of Chicago, then how much time would it take to

cross
the border?

3.
TRUE
or
FALSE
:

A boat
heads straight across a river. The river flows north at a speed of 3 m/s. If the river current were greater, then the time
required for the boat to reach the opposite shore would not change. _______________________

4. A boat begins at point A and heads s
traight across a 60
-
meter wide river with a speed of 4 m/s
(relative to the water). The river water flows north at a speed of 3 m/s (relative to the shore). The
boat reaches the opposite shore at point C. Which of the following would cause the boat to reac
h
the opposite shore at a location SOUTH of C?

a. The boat heads across the river at 5 m/s.

b. The boat heads across the river at 3 m/s.

c. The river flows north at 4 m/s.

d. The river flows north at 2 m/s.

e. Nonsense! None of these affect the location

where the boat lands.

Lesson 2
b
:
Characteristics of a Projectile’s Trajectory

Use your understanding of projectiles to answer the following questions. When finished, click the button to view your answers
.

1. Consider these
diagrams in answering the following questions.

Which diagram (if any) might represent ...

a. ... the initial horizontal velocity?

b. ... the initial vertical velocity?

c. ... the horizontal acceleration?

d. ... the vertical acceleration?

e. ... t
he net force?

2. Supposing a snowmobile is equipped with a flare launcher that is capable of launching a sphere vertically (relative to the

snowmobile). If the snowmobile is in motion and launches the flare and maintains a constant horizontal velocity aft
er the launch,
then where will the flare land (neglect air resistance)?

a. in front of the snowmobile

b. behind the snowmobile

c. in the snowmobile

3. Suppose a rescue airplane drops a relief package while it is moving with a
constant horizontal s
peed at an elevated height. Assuming that air resistance
is negligible, where will the relief package land relative to the plane?

a. below the plane and behind it.

b. directly below the plane

c. below the plane and ahead of it

Lesson 2c
: Describing

Projectiles with Numbers

Use your understanding of projectiles to answer the following questions. Then click the button to view the answers.

1. Anna Litical drops a ball from rest from the top of 78.4
-
meter high cliff. How much ti
me will it take for the ball to reach the
ground and at what height will the ball be after each second of motion?

2. A cannonball is launched horizontally from the top of an 78.4
-
meter high cliff. How much time will it take for the ball to reach the
gro
und and at what height will the ball be after each second of travel?

3. Fill in the table below indicating the value of the horizontal and vertical components of velocity and acceleration for a
projectile.

4. The diagram below shows the trajectory fo
r a projectile launched non
-
horizontally from an elevated position on top of a cliff. The
initial horizontal and vertical components of the velocity are 8 m/s and 19.6 m/s respectively. Positions of the object at 1
-
second
intervals are shown. Determine the

horizontal and vertical velocities at each instant shown in the diagram.

Lesso
n 2f:
Horizontally Launched Projectiles
-

Problem
-
Solving

A soccer ball
is kicked horizontally off a 22.0
-
meter high hill and lands a distance of 35.0 meters from the edge of the hill.
Determine the initial horizontal velocity of the soccer ball.

Lesso
n 2g
:
Non
-
Horizontally Launched Projectiles
-

Problem
-
Solving

Your Turn to Try It!

Use the
Range of an Angle
-
Launched Projectile

widget

to practice a projectile problem (or two) (or three). Using the given
launch velocity and launch angle, determine the expected horizontal displacement (d
x
). After completing your calculation, use the
Submit

button to check your answer. Find it on the webs
ite!

Lesson 3c: Equilibrium and Statics

Recognize these problems from a previous test.

1. The following picture is hanging on a wall. Use trigonometric functions to determine the weight of the picture.

2. The sign below hangs outside the physics classroom, advertising the most important truth to be found inside. The sign is
supported by a diagonal cable a
nd a rigid horizontal bar. If the sign has a mass of 50 kg, then determine the tension in the
diagonal cable that supports its weight.

3. The following sig
n can be found in Glenview. The sign has a mass of 50 kg. Determine the tension in the cables.

4. After its most recent delivery, the infamous stork
announces the good news. If the sign has a mass of 10 kg, then what is the
tensional force in each cable? Use trigonometric functions and a sketch to assist in the solution.

5. Suppose that a student pulls with two large forces (F
1

and F
2
) in order to lift a 1
-
kg book by two cables. If the cables make a 1
-
degree angle with the horizontal, then what is the tension in the cable?

Lesson 3d: Net Force Problems Revisited

The following problems provide plenty of practice with F
net
= m • a problems involving forces at angles. Try each problem

and then
click the button to view the answers.

1. A 50
-
N applied force (30 degrees to the horizontal) accelerates a box across a horizontal sheet of ice (see diagram). Glen Brook,
Olive N. Glenveau, and Warren Peace are discussing the problem. Glen sugg
ests that the normal force is 50 N; Olive suggests that
the normal force in the diagram is 75 N; and Warren suggests that the normal force is 100 N. While all three answers may seem

reasonable, only one is correct. Indicate which two answers are wrong and
explain why they are wrong.

2. A box is pulled at a constant speed of 0.40 m/s across a frictional surface. Perform an extensive analysis of the
diagram below to determine the values for the blanks.

3. Use your understanding of force relationships and vector components to fill in the blanks in the following diagram
and

to
determine the net force and acceleration of the object. (F
net

= m•a; F
frict

= μ•F
norm
; F
grav

= m•g)

4. The 5
-
kg mass below is moving with a constant spe
ed of 4 m/s to the right. Use your understanding of force relationships and
vector components to fill in the blanks in the following diagram
and

to determine the net force and acceleration of the object. (F
net

= m•a; F
frict

= μ•F
norm
; F
grav

= m•g)

5. The following object is being pulled at a constant speed of 2.5 m/s. Use your understanding of force relationships and vec
tor
components to fill in the blanks in

the following diagram
and

to determine the net force and acceleration of the object. (F
net

= m•a;
F
frict

= μ•F
norm
; F
grav

= m•g)

6. Use your understanding
of force relationships and vector components to fill in the blanks in the following diagram
and

to
determine the net force and acceleration of the object. (F
net

= m•a; F
frict

= μ•F
norm
; F
grav

= m•g)

7. Study the diagram below and determine the acceleration of the box and its velocity after being pulled by the applied force

for
2.0 seconds.

8. A student pulls a 2
-
kg backpack across the ice (assume friction
-
free) by pulling at a 30
-
degree angle to the horizontal. The
velocity
-
time graph for
the motion is shown. Perform a careful analysis of the situation and determine the applied force.

9. The following object is moving to the right and encou
ntering the following forces. Use your understanding of force relationships
and vector components to fill in the blanks in the following diagram
and

to determine the net force and acceleration of the object.
(F
net

= m•a; F
frict

= μ•F
norm
; F
grav

= m•g)

10. The 10
-
kg object is being pulled to the left at a constant speed of 2.5 m/s. Use your understanding of force relationships and
vector components to fill i
n the blanks in the following diagram. (F
net

= m•a; F
frict

= μ•F
norm
; F
grav

= m•g)

11. Use your understanding of force relationships and vector components

to fill in the blanks in the following diagram
and

to
determine the net force and acceleration of the object. (F
net

= m•a; F
frict

= μ•F
norm
; F
grav

= m•g)

Lesson 3e: Inclines Planes

More Practice

Use the
widget

provided in the tutorial
to investigate other inclined plane situations. Simply enter the mass, the incline angle and
the coefficient of friction (use 0 for frictionless situations). Then click the
Sub
mit

button to view the acceleration. Find it on the
website!

Circular Motion and Satellite Motion
-

Chapter Outline

Lesson 1: Motion Characteristics for Circular Motion

a.

Speed and Velocity

b.

Acceleration

c.

The Centripetal Force Requirement

d.

The Forbidden F
-
Word

e.

Mathematics of Circular Motion

Lesson 2: Applications

of Circular Motion

a.

Newton's Second law
-

Revisited

b.

Amusement Park Physics

c.

Athletics

Lesson 3: Universal Gravitation

a.

Gravity is More than a Name

b.

The

Apple, the Moon, and the Inverse Square Law

c.

Newton's Law of Universal Gravitation

d.

Cavendish and the Value of
G

e.

The Value of g

Momentum and Its Conservation
-

Chapter Outline

Lesson 1: The Impulse
-
Momentum Change Theorem

a.

Momentum

b.

Momentum and Impulse Connection

c.

Real
-
World Applications

Lesson 2: The Law of Momentum Conservation

a.

The Law of Action
-
Reaction (Revisited)

b.

Momentum Conservation Principle

c.

Isolated Systems

d.

Momentum Conservation in Collisions

1.

Using Equations as a "Recipe" for Algebraic Problem
-
Solving

2.

Using Equations as a Guide to Thinking

e.

Momentum Conservation in Explosions

1.

2.

Using Equations as a Guide to Thinking

b.

Momentum Conservation in Explosions

HW:

Due on exam day. Previously
distributed in class.

All were
present to receive them!

I put
them on the website in case you
lost them!

1)

Circular Motion and
Satellite Motion, Lesson 3.

2)

Momentum an It’s
Conservation, Lesson 1

Completing these worksheets will
be your review for the concepts
listed on this
page.