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(numerical value)
Displacement problems will find the
distance from the starting point to the
ending point.
In calculating, you will find the total distance traveled.
*Calculate the total amount traveled
What formula for triangles?
*Here we have to consider the direction…
Bellringer-9/4/14
1. What is the difference between
distance and displacement?
2. Solve for distance and
displacement:
A
7
B 8 C
Motion & Forces
Describing Motion Motion
Speed & Velocity
Acceleration
Newton’s First Law
Newton’s First Law of Motion
An object at rest will remain at
rest and an object in motion
will continue moving at a
constant velocity unless acted
upon by a net force.
motion
constant velocity
net force
A. Motion
Problem:
Is your desk moving?
We need a reference point...
nonmoving point from which
motion is measured
A. Motion
Motion
Change in position in relation to
a reference point.
Reference point
Motion
A. Motion
Problem:
You are a passenger in a car
stopped at a stop sign. Out of the
corner of your eye, you notice a
tree on the side of the road begin
to move forward.
You have mistakenly set yourself
as the reference point.
B. Speed & Velocity
Speed
rate of motion
Speed is the distance traveled per
unit time
If you know the distance an object
traveled in a set time, you can
calculate speed
time
distancespeed
vd
t
B. Speed & Velocity
Instantaneous Speed
speed at a given instant
Average Speed
time total
distance totalspeed avg.
B. Speed & Velocity
Problem:
A storm is 10 km away and is
moving at a speed of 60 km/h.
Should you be worried?
It depends
on the
storm’s
direction!
B. Speed & Velocity
Velocity
speed in a given direction (it is
a vector!)
can change even when the
speed is constant! (storms!)
Speed v. Velocity
1. How are speed and velocity similar?They both measure how fast something is
moving
2. How are speed and velocity different?Velocity includes the direction of motion and
speed does not (the car is moving 5mph East)
3. Is velocity more like distance or displacement? Why?
Displacement, because both are vectors which include an amount and a direction.
C. Acceleration
Acceleration
rate at which velocity changes
change in speed or direction
t
vva
if
a: acceleration
vf: final velocity
vi: initial velocity
t: time
a
vf - vi
t
C. Acceleration
Positive acceleration
“speeding up”
Negative acceleration
“slowing down”
D. Calculations
Your neighbor skates at a speed of 4 m/s.
You can skate 100 m in 20 s. Who skates
faster?
GIVEN:
d = 100 m
t = 20 s
v = ?
WORK:
v = d ÷ t
v = (100 m) ÷ (20 s)
v = 5 m/s
You skate faster!v
d
t
D. Calculations
A roller coaster starts down a hill at 10 m/s.
Three seconds later, its speed is 32 m/s.
What is the roller coaster’s acceleration?
GIVEN:
vi = 10 m/s
t = 3 s
vf = 32 m/s
a = ?
WORK:
a = (vf - vi) ÷ t
a = (32m/s - 10m/s) ÷ (3s)
a = 22 m/s ÷ 3 s
a = 7.3 m/s2a
vf - vi
t
D. Calculations
Sound travels 330 m/s. If a lightning bolt
strikes the ground 1 km away from you,
how long will it take for you to hear it?
GIVEN:
v = 330 m/s
d = 1km = 1000m
t = ?
WORK:
t = d ÷ v
t = (1000 m) ÷ (330 m/s)
t = 3.03 s
v
d
t
D. Calculations
How long will it take a car traveling 30 m/s
to come to a stop if its acceleration is
-3 m/s2?
GIVEN:
t = ?
vi = 30 m/s
vf = 0 m/s
a = -3 m/s2
WORK:
t = (vf - vi) ÷ a
t = (0m/s-30m/s)÷(-3m/s2)
t = -30 m/s ÷ -3m/s2
t = 10 sa
vf - vi
t
E. Graphing Motion
slope =
steeper slope =
straight line =
flat line =
Distance-Time Graph
A
B
faster speed
constant speed
no motion
speed
E. Graphing Motion
Who started out faster?
A (steeper slope)
Who had a constant speed?
A
Describe B from 10-20 min.
B stopped moving
Find their average speeds.
A = (2400m) ÷ (30min)
A = 80 m/min
B = (1200m) ÷ (30min)
B = 40 m/min
Distance-Time Graph
A
B
0
100
200
300
400
0 5 10 15 20
Time (s)
Dis
tan
ce
(m
)
Distance-Time Graph
E. Graphing Motion
Acceleration is
indicated by a
curve on a
Distance-Time
graph.
Changing slope =
changing velocity
E. Graphing Motion
0
1
2
3
0 2 4 6 8 10
Time (s)
Sp
ee
d (
m/s
)
Speed-Time Graph
slope =
straight line =
flat line =
acceleration
+ve = speeds up
-ve = slows down
constant accel.
no accel.
(constant velocity)
E. Graphing Motion
0
1
2
3
0 2 4 6 8 10
Time (s)
Sp
ee
d (
m/s
)
Speed-Time Graph
Specify the time period
when the object was...
slowing down
5 to 10 seconds
speeding up
0 to 3 seconds
moving at a constant
speed
3 to 5 seconds
not moving
0 & 10 seconds
Newton’s Second LawGravity
Air Resistance Calculations
Newton’s Second Law of Motion
The acceleration of an object is
directly proportional to the net force
acting on it and inversely
proportional to its mass.
F = ma
F = ma
F: force (N)
m: mass (kg)
a: accel (m/s2)
1 N = 1 kg ·m/s2
am
F
a
F
m
Gravity
force of attraction between any
two objects in the universe
increases as...
mass increases
distance decreases
Who experiences more gravity - the
astronaut or the politician?
less
distance
more
mass
Which exerts more gravity -
the Earth or the moon?
Weight
the force of gravity on an object
MASSalways the same
(kg)
WEIGHTdepends on gravity
(N)
W = mgW: weight (N)
m: mass (kg)
g: acceleration due
to gravity (m/s2)
VS
Would you weigh more on Earth
or Jupiter?
greater gravity
greater weight
greater mass
Jupiter because...
Accel. due to gravity (g)
In the absence of air
resistance, all falling objects
have the same acceleration!
On Earth: g = 9.8 m/s2
mW
g
elephant
m
Fa
featherAnimation from “Multimedia Physics Studios.”
Air Resistance
a.k.a. “fluid friction” or “drag”
force that air exerts on a moving
object to oppose its motion
depends on:
• speed
• surface area
• shape
• density of fluid
Terminal Velocity
maximum velocity reached
by a falling object
reached when…
Fgrav = Fair
Fair
Fgrav
no net force
no acceleration
constant velocity
Terminal Velocity
increasing speed increasing
air resistance until…
Fair = FgravAnimation from “Multimedia Physics Studios.”
Falling with air resistance
Fgrav = Fair
Animation from “Multimedia Physics Studios.”
heavier objects fall faster
because they accelerate to
higher speeds before
reaching terminal velocity
larger Fgrav
need larger Fair
need higher speed
What force would be required to
accelerate a 40 kg mass by 4 m/s2?
GIVEN:
F = ?
m = 40 kg
a = 4 m/s2
WORK:
F = ma
F = (40 kg)(4 m/s2)
F = 160 N
m
F
a
A 4.0 kg shotput is thrown with 30 N of
force. What is its acceleration?
GIVEN:
m = 4.0 kg
F = 30 N
a = ?
WORK:
a = F ÷ m
a = (30 N) ÷ (4.0 kg)
a = 7.5 m/s2
m
F
a
Ms. F. weighs 557 N. What is her
mass?
GIVEN:
F(W) = 557 N
m = ?
a(g) = 9.8 m/s2
WORK:
m = F ÷ a
m = (557 N) ÷ (9.8 m/s2)
m = 56.8 kg
m
F
a
Is the following statement true or false?
An astronaut has less mass on the moon
since the moon exerts a weaker
gravitational force.
False! Mass does not depend on
gravity, weight does. The astronaut has
less weight on the moon.
Do Now
How would you describe how fast an object is moving?
Speed, Velocity, and Acceleration
Goals:
• To investigate what is needed to describe motion completely.
• To compare and contrast speed and velocity.
• To learn about acceleration.
To describe motion accurately and completely, a frame of reference is needed.
An object is in motion if it changes position relative to a reference point.
• Objects that we call stationary—such as a tree, a sign, or a building—make good reference points.
The passenger can use a tree as a reference point to decide if the train is moving. A tree makes a good reference point because it is stationary from the passenger’s point of view.
Describing MotionWhether or not an object is in motion depends on the reference point you choose.
Distance
When an object moves, it goes from point A to point B – that is the DISTANCE it traveled. (SI unit is the meter)
AB
DisplacementKnowing how far something moves is not sufficient. You
must also know in what direction the object moved.
A quantity that has magnitudeand directionis called a…
VECTOR
SpeedCalculating Speed: If you know the distance an
object travels in a certain amount of time, you can calculate the speed of the object.
Speed = Distance/time Average speed = Total distance/Total time
What is instantaneous speed?
Velocity
Velocity is a description of an object’s speed and direction. It is a vector.
As the sailboat’s direction changes, its velocity also changes, even if its speed stays the same. If the sailboat slows down at the same time that it changes direction, how will its velocity be changed?
Speed v. Velocity
1. How are speed and velocity similar?They both measure how fast something is moving
2. How are speed and velocity different?Velocity includes the direction of motion and
speed does not (the car is moving 5mph East)
3. Is velocity more like distance or displacement? Why?
Displacement, because both are vectors which include an amount and a direction.
Graphing Speed
D
I
S
T
A
N
C
E
T I M E
Speed increasing
Object is stopped
Object begins moving at a different speed
The steepness of a line on a graph is called slope.
• The steeper the slope is, the greater the speed.
• A constant slope represents motion at constant speed.
Using the points shown, the rise is 400 meters and the run is 2 minutes. To find the slope, you divide 400 meters by 2 minutes. The slope is 200 meters per minute.
Do Now:
Set up formula triangles to find speed and velocity
Acceleration
Acceleration is the rate at which velocity changes.
Acceleration can result from a change in speed (increase or decrease), a change in direction (back, forth, up, down left, right), or changes in both. Like velocity, acceleration is a vector.
• The pitcher throws. The ball speeds toward the batter. Off the bat it goes. It’s going, going, gone! A home run!
• Before landing, the ball went through several changes in motion. It sped up in the pitcher’s hand, and lost speed as it traveled toward the batter. The ball stopped when it hit the bat, changed direction, sped up again, and eventually slowed down. Most examples of motion involve similar changes. In fact, rarely does any object’s motion stay the same for very long.
1. As the ball falls from the girl’s hand, how does its speed change?
Understanding Acceleration
2. What happens to the speed of the ball as it rises from the ground back to her hand?
3. At what point does the ball have zero velocity?
4. How does the velocity of the ball change when it bounces on the floor?
You can feel acceleration!
If you’re moving at 500mph east without turbulence, there is no acceleration.
But if the plane hits an air pocket and drops 500 feet in 2 seconds, there is a large change in acceleration and you will feel that!
It does not matter whether you speed up or slow down; it is still considered a change in
acceleration.
In science, acceleration refers to increasing speed, decreasing speed, or changing direction.
• A car that begins to move from a stopped position or speeds up to pass another car is accelerating.
• A car decelerates when it stops at a red light. A water skier decelerates when the boat stops pulling.
• A softball accelerates when it changes direction as it is hit.
Calculating Acceleration
Acceleration = Change in velocity
Total time
Change in velocity = final velocity-initial velocity
OR..
= final speed-initial speed
So…Acceleration = (Final speed – Initial speed)
Time
As a roller-coaster car starts down a slope, its speed is 4 m/s. But 3 seconds later, at the
bottom, its speed is 22 m/s. What is its average acceleration?
Calculating Acceleration
What information have you been given?
Initial speed = 4 m/sFinal Speed = 22 m/sTime = 3 s
What quantity are you trying to calculate?
The average acceleration of the roller-coaster car.
What formula contains the given quantities and the
unknown quantity?
Acceleration = (Final speed – Initial speed)/Time
Perform the calculation.
Acceleration = (22 m/s – 4 m/s)/3 s = 18 m/s/3 s
Acceleration = 6 m/s2
The roller-coaster car’s average acceleration is 6 m/s2.
Calculating Acceleration
Graphing acceleration
S
P
E
E
D
T i m e
Object accele-rates
Object moves at constant speed
Object decelerates
The slanted, straight line on this speed-versus-time graph tells you that the cyclist is accelerating at a constant rate. The slope of a speed-
versus-time graph tells you the object’s acceleration. Predicting How would the slope of the graph change if the cyclist were accelerating at a
greater rate? At a lesser rate?
Since the slope is increasing, you can conclude that the speed is also increasing. You are accelerating.
Distance-Versus-Time Graph The curved line on this distance-versus-time graph tells you that the cyclist is accelerating.
Projectile Motion
Circular Motion
Free-fall
Projectileany object thrown in the air
acted upon only by gravity
follows a
parabolic path
called a trajectory
has horizontal and vertical velocitiesPROJECTILE MINI-LAB
Projectile Velocities
Horizontal and vertical velocities are
independent of each other!
Horizontal Velocity
depends on inertia
remains constant
Vertical Velocity
depends on gravity
accelerates downward at 9.8 m/s2
A moving truck launches a ball vertically (relative to the truck). If the truck maintains a constant horizontal velocity after the launch, where will the ball land (ignore air resistance)?
A) In front of the truck
B) Behind the truck
C) In the truck
C) In the truck. The
horizontal velocity of the
ball remains constant
and is unaffected by its
vertical motion. Animation from “Multimedia Physics Studios.”
Centripetal Acceleration
acceleration toward the center of a
circular path
caused by centripetal force
B-BALL DEMO
PLATE DEMO
On the ground... friction provides centripetal force
(Centripetal force is a force that makes a body follow a curved path)
In orbit...
gravity provides centripetal force
ROUND LAB
In orbit...
Which satellites travel faster?
Near-Earth Satellites Geostationary Satellites
Free-Fall
when an object is influenced only by
the force of gravity
Has a constant acceleration
Weightlessness
sensation produced when an object
and its surroundings are in free-fall
(no force of support on your body)
object is not weightless!
CUP DEMO
Weightlessness
surroundings are falling at the same
rate so they don’t exert a force on
the object
Go
to N
AS
A.
Go t
o C
NN
.com
.
Go t
o S
pac
e S
ettl
emen
t V
ideo
Lib
rary
.Space Shuttle Missions
TRUE or FALSE:
An astronaut on the Space Shuttle
feels weightless because there is no
gravity in space.
FALSE!
There is gravity which is causing the
Shuttle to free-fall towards the Earth.
She feels weightless because she’s
free-falling at the same rate.
Describe the path of a marble as it
leaves the spiral tube shown below.
It will travel in a straight line since the
tube is no longer exerting a net force
on it.
Solve:
1. If Ms. Farris walks 3 blocks east, 5 blocks south,
and 3 blocks west, what distance has she
traveled?
2. If Ms. Farris walks 3 blocks east, 5 blocks south,
and 3 blocks west, what is her displacement?
3. What is the momentum of a 3 kg toy truck that
moves at 30 m/s? (2 points)
How do we cite articles in APA format?
http://www.nbcnews.com/science/space/surpris
e-giant-black-hole-discovered-dwarf-galaxy-
n205896
http://www.sciencedaily.com/releases/2014/09/
140917131824.htm
https://owl.english.purdue.edu/owl/resource/56
0/01/
1 paragraph should be a summary of your
article; second paragraph should be your
reaction (5-7 sentences)
An object at rest will remain at rest and an object
in motion will continue moving at a constant
velocity unless acted upon by a net force.
The acceleration of an object is directly
proportional to the net force acting on it and
inversely proportional to its mass.
F=MA
What do those variables stand for?
When one object exerts force on a second object,
the second one exerts a force on the first that is
equal in strength and opposite in direction
Define the following on a sheet of paper in your own words
InertiaForceVelocitySpeedTerminal VelocityMassWeight
Force-The push or pull exerted on an object
Inertia-tendency of an object to resist motion
Speed-Rate of motion; Rate of change in an objects position
Velocity-Speed of object + it’s direction
Terminal Velocity-Largest velocity reached by falling object; point where gravity equals force
Mass-amount of matter in an object; does not change
Weight-changes based on gravity