physics - chapter 2 - one dimensional motion
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Bellaire High School Advanced Physics Chapter 2 - One Dimensional MotionTRANSCRIPT
Lesson 2-1Displacement and Velocity
Displacement Lets say you travel from here to Pittsburgh Many different ways, by boat, by car, by
plane Different methods mean different amounts of
time
Displacement End point is always the same
To describe the results of your motion you need to specify Distance from starting point Direction of travel Direction and distance mean
Displacement is a vector
Back to the Pittsburgh example Displacement is the same no matter what method of travel
or how many stops, starts, or detours
Displacement Displacement is the change in position SI unit is the meter Usually talk about displacement of objects
that move An object at rest has zero displacement
No matter how much time passes, the object will not move
Displacement Displacement is NOT equal to distance
traveled Think of “Something moved around, what is the
shortest distance it could have taken?” Nascar races have zero displacement In football
Offense hopes for positive displacement Defense hopes for negative displacement
Reference Points Coordinate systems are useful to describe
motion Yard markers help on a football field Squares on a chess board
A meter stick is helpful to determine displacement
Reference Points Lets say we have a ball
The ball begins at 15 cm We refer to the starting point as xi
The ball rolls to the 45 cm mark We refer to the ending point as xf
Displacement is found by subtraction Final position – starting position
The Displacement Equation Final position –
starting position Recall Δ means
‘change in’ The displacement
equation is:
x x xf i
Direction of Displacement Displacement may also occur in the vertical
direction A helicopter sits on a heli-pad 30 m above the
ground, it takes off and hovers 200 m above the ground What is the yi? What is the yf? What is the Δy?
yi = 30 m, yf = 200 m, Δy = 170 m
Sign on Displacement Displacement may be positive or negative
From our equation Δx = xf – xi we see Δx is positive if xf > xi
Δx is negative if xf < xi
There is no such thing as a negative distance A –Δx simply tells a direction
Sign on Displacement Coordinate directions
Using ‘right’ as positive and ‘left’ as negative is only by convention That does not mean it is necessarily correct
As long as you remain constant throughout the situation, you may call ‘left’ positive. Thus making ‘right’ negative
Similarly, you may call ‘down’ positive Thus making ‘up’ negative
Displacement Practice
1) xi = 10 cm, xf = 80 cm
2) xi = 3 cm, xf = 12 cm
3) xi = 80 cm, xf = 20 cm
4) xi = 28 cm, xf = 11 cm
70 cm
9 cm
-60 cm
-17 cm
Concept Chall. Pg 41
Velocity Quantity that measures how fast something
moves from one point to another Different than speed, Velocity has direction
Speed is the magnitude part of the velocity vector Velocity has direction and magnitude
Average Velocity To calculate, you must know the time the
object left and arrived Time from initial position to final position Avg. Vel. is displacement divided by total time
vx
t
x x
t tavgf i
f i
Avg. Velocity vs Avg. Speed Main difference
Average Velocity depends on total displacement (direction)
Average speed depends on distance traveled in a specific time interval
Lesson 2-2Acceleration
Acceleration Lets say you are driving at 10 m/s
You approach a stop sign and brake carefully and stop after 6 seconds
Your speed changed from 10 m/s to 0 m/s over that time
Lets say you had to brake suddenly and stopped after 2 seconds
Your speed changed from 10 m/s to 0 m/s over that time
Acceleration What was the main difference between those
two examples? Time
A slow, gradual stop is much more comfortable than a sudden stop
Average Acceleration The quantity that describes the rate of change
of velocity in a given time interval is acceleration
av
t
v v
t tavgf i
f i
Average Acceleration Units of acceleration are length per seconds squared
Analysis:
av
t
m s
sm s s m savg
// / 2
Constant Acceleration As an object moves with constant a, the V
increases by the same amount each interval There is a very specific relationship between
displacement, acceleration, velocity, and time The relationship is used to produce a group of
very important equations
Kinematic Equation #1 Displacement depends
on acceleration, initial velocity and time and
vx
tavg
vv v
avgf i2
x
t
v vf i
2
xv v
tf i
2
x v v tf i 1
2( )Kinematic Equation #1:
Kinematic Equation #2 Final velocity depends
on initial velocity, acceleration and time
av
t
v v
tf i
a t v vf i
v a t vi f
v v a tf i Kinematic Equation #2:
Kinematic Equation #3 We can form another
equation by plugging #2 into #1
x v v ti f 1
2( ) v v a tf i
x v v a t ti i
1
2( ( ))
x v a t ti
1
22( )
x v a t ti( )1
2
Kinematic Equation #3:
x v t a ti ( )1
22
Kinematic Equation #4 So far, all of our Kinematic Equations have
required time interval What if we do not know the time interval We can form one last equation by plugging
equation #1 into #2
Kinematic Equation #4
x v v ti f 1
2( )
LNM
OQP2 2
1
2 x v v ti f( )
2 x v v ti f( )
2
x
v vt
i f( )
v v a tf i
LNMM
OQPPv v a
x
v vf ii f
2( )
LNMM
OQPPv v a
x
v vf ii f
2( )
( )( )v v v v a xf i i f 2
Kinematic Equation #4
( )( )v v v v a xf i i f 2
v v a xf i2 2 2
Kinematic Equation #4: v v a xf i2 2 2
Note: A square root is needed to find the final velocity
Lesson 2-3Falling Objects
Free Fall In a vacuum, with no air, objects will fall at
the same rate Objects will cover the same displacement in the
same amount of time Regardless of mass We cannot demonstrate this because of air
resistance
Gravity Objects in free fall are affected by what?
Gravity A falling ball moves because of gravity
“The force of gravity” Gravity is NOT a force!! Gravity is an acceleration
Gravity as an Acceleration Since acceleration is a vector
Gravity has magnitude and direction Magnitude is -9.81 m/s2 or 32 ft/s2
Direction is toward the center of the Earth Usually straight down
Gravity is denoted as g rather than a Gravity is a special type of acceleration
Always directed down, so the sign should always be negative
-9.81 m/s2 or -32 ft/s2
Path of Free Fall If a ball is thrown up in the air and falls back
down the same path, some interesting things happen At the maximum height, the ball stops
As the ball changes direction, it may seem as V and a are changing
V is constantly changing, a is constant from the beginning a is g throughout
Path of Free Fall At ymax
What is the velocity? 0 m/s
What is the acceleration? g or -9.81 m/s2
Free Fall It may be tough to think of something moving
upward and having a downward acceleration Think of a car stopping at a stop sign
When an object is thrown in the air, it has a +Vi and –a Since the two vectors are opposite each other, the
object is slowing down
Free Fall The velocity decrease until the ball stops and
velocity is 0 It is tough to see the ‘stop’ since it is only for a
split second Even during the stop, a = -9.81 m/s2
What happens after the ball stops at the top of its path?
Free Fall The ball begins to free fall
When the ball begins to move downward It has a negative velocity It has a negative acceleration V and a now in the same direction Ball is speeding up
This is what happens to objects in free fall They fall faster and faster as they head toward
Earth