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Chapter 3: LINEAR MOTION
• Here we'll consider only the simplest
form of motion—that along a
straight-line path—linear motion.
• Linear Motion
• (Motion in a straight line,
such as falling straight
downward)
• Speed and Velocity
• Acceleration
• Relationships among
distance, velocity, and
acceleration.
• Falling motion.
Motion can be described by
• Sentence • Mathematical • Graph
• Motion Diagrams/ Pictures
• Images of a moving object that records its
position after equal time intervals
• If the distance between is equal= constant
• If different distances= acceleration
• Operational definitions- describe motion
(speeding up, slowing down, at rest &
constant speed)
A Motion diagram
• Shows a series of images of an
object that records its position
after equal time intervals
Coordinate System
• based on where to put the measuring tape & when to start the stopwatch
• tells zero point of variable & direction the values of variable should increase
• origen- zero pt/beginning
• Position vector- gives direction & amount
Linear Motion
• Straight line
• Is relative to other objects or reference points
• Distance vs. displacement
• Point of origin /reference point
Force • Push or pull
• Causes acceleration
• Net Force is the combination and sum of all forces
• Net force ~ acceleration; directly proportional – Double one…
• Friction – In opposite directions of
movement
– You increase a force- you increase the friction
Motion Is Relative
• Everything moves.
• Even things that appear at rest move. They move relative to the
sun and stars.
• You're moving at about 107,000 km/hr relative to the sun. And
even faster relative to the center of our galaxy.
• When we discuss the motion of something, we describe motion
relative to something else.
Motion Is Relative
• When walking down the aisle of a moving bus, your speed is
relative to the floor of the bus – which is likely quite different from
your speed relative to the road.
• a racing car with a speed of 300 km/hr is relative to the track.
• Unless stated otherwise, when we discuss the speeds of things in
our environment we mean relative to the surface of the Earth.
Motion • A change in position • Need a reference point
• Compare the motion of a person sitting on the bus to the bus
• Compare to a Boy riding his bike on a sidewalk
• Being observed by kid on another bus traveling at 20 km/hr
• Also observed by lady standing at corner
• What is the speed?
Position • separation between
that object & a reference point.
• Needs both distance & direction
• Symbol- d
Distance vs Displacement
Distance Displacement
• the shortest distance of
the object from point O
in a specific direction.
Unit: metre (m)
Type of Quantity: Vector
quantity
The total length that is
traveled by that object.
Unit: metre (m)
Type of Quantity: Scalar
quantity
• Distance traveled =
• 200 m
• Distance is a scalar
quantity
• Displacement = 120 m, in
the direction of Northeast
• Displacement is a vector
quantity
Speed
• Speed is a measure of how fast
something moves, measured by
a unit of distance divided by a
unit of time
• Any combination of distance and
time units is legitimate for
measuring speed;
• for motor vehicles (or long
distances) the units kilometers
per hour (km/h) or miles per
hour (mi/h or mph) are
commonly used.
• shorter distances, meters per
second (m/s) are often useful
units.
Instantaneous Speed
• Cars vary in speed on a trip
• You can tell the speed of the car at any instant by looking at its speedometer.
• The speed at any instant is the instantaneous speed.
Average Speed
• Average speed is defined as:
• the whole distance covered divided by the total time of travel
• it doesn't indicate the different speeds and variations that may have taken place during shorter time intervals.
Velocity
• Speed = distance /
time
• Velocity =
distance/time +
direction
• The car on the circular track may have a constant speed, but its velocity is changing every instant. Why?
Velocity
• Constant velocity
and constant speed,
however, can be very
different
• Constant velocity
means constant
speed with no change
in direction.
• A car that rounds a
curve at a constant
speed does not have
a constant velocity—
its velocity changes
as its direction
changes
For objects traveling in a straight line, speed & velocity will be the same.
Average velocity = total distance
time interval
v = ∆ d
∆ t
Calculating Speed
• Skater A skates at 4 m/s • You skate for 100 m for 20
seconds. • Who skates faster? • V = d/t • V = 100 m/20 s = 5 m/sec • You are faster
Graphing Speed
• Independent variable = time
• Dependent variable = distance Velocity- • vertical separation of 2
points time interval- • horizontal separation
ratio of displacement to time interval is average velocity
Instantaneous Velocity
• May use a position-time graph to determine
• the slope at different times.
• Is the tangent to a curve on a position-time graph
Calculating Time from Speed
• Sound travels at 330 m/s. If lightning hits 1 km from you, how long will it take the sound to reach you?
• V = d/t same as t = d/v • T = 1 km/330 m/s • = 1000m/330m/s • =3.03 s
Plate tectonics
• Pieces of Earth’s solid crust floats on a molten mantle.
• Causes “plates” continents are on to move
Measuring speeds of tectonic movements
• Because it is slow- we measure in units of year
• San Andreas Fault moves 2 cm/yr
• Australian plate moves 17 cm/yr
What speed units would you use for
• Running a race
• Drive between Denver and Laramie
• The speed of a slug
14-Feb-12 Physics 1 (Garcia) SJSU
Changes in Velocity Velocity changes if speed or direction of motion change.
25 m/s, downward
10 m/s, downward
25 meters per second, 45 degrees upward
25 meters per second, 45 degrees downward
Velocity changes in both these cases.
• The best way to imagine a situation with several physical quantities is by drawing a graph.
• To picture the behavior of the speed of an object, we plot the distance on the vertical axis and the time on the horizontal axis.
Here, the total distance travelled ( y) divided by the time taken ( x) is the gradient of the slope. This is also equal to
the average speed of the object - remembering that
In this case, the speed is constant as the slope of the distance-time graph is constant.
By re-arranging the equation we can plot slopes of either distance, or time, on a graph to find their values. For example, we can see how to
find the distance from a speed-time graph by rearranging to get:
• We then plot a speed-time graph as shown below:
The blue rectangle has an
area equal to the speed
multiplied by the time.
We can see from the
equation above, that this
is equal to the distance
travelled.
• The speedometer of a car moving to the east
reads 100 km/h. It passes another car that
moves to the west at 100 km/h. Do both cars
have the same speed? Do they have the same
velocity?
• During a certain period of time, the
speedometer of a car reads a constant 60
km/h. Does this indicate a constant speed? A
constant velocity?
Acceleration
• We can change the velocity of something by changing its speed, by changing its direction, or by changing both its speed and its direction.
14-Feb-12 Physics 1 (Garcia) SJSU
Acceleration
Define acceleration as,
(ACCELERATION) = (Change in Velocity)
(Time interval)
Note: An object accelerates anytime its velocity changes. Examples include: Object speeds up. Object slows down (speed decreases). Object speed constant but direction changes (curved path)
Best example of acceleration is objects in free fall
Acceleration
• it is a rate of a rate
• Acceleration is not
velocity, nor is it even a
change in velocity.
Acceleration is the rate
at which velocity itself
changes
Uniform or constant Acceleration
• Does not change
• velocity-time graph = straight line
• initial velocity- when the clock reading is zero
acceleration
measured in m/s/s or m/s2
• Acc.= final veloc.-initial veloc. time needed to change veloc.
• A = vf-vi = Δv t t • Make sure your final & initial acceleration are identified
so that you can ID it is positive or negative (speeding up or slowing down)
• Speed = distance /time • Velocity = distance /time + direction
– You may have constant speed & velocity is going straight
– If you are changing direction they are not the same
– Constant velocity – Instantaneous velocity – Average velocity
Force Causes Acceleration
• Consider a hockey puck at rest on ice. Apply a force, and it starts to move—it accelerates.
• When a force is no longer pushing the puck- it moves at constant velocity.
• Apply another force by striking the puck again, and again the motion changes.
• Applied force produces acceleration.
Crash Safety
• During a crash, your body continues to move at the same rate of speed.
• An abrupt stop at 50 m/hr would have you hitting the steering wheel/windshield at that speed.
• Things that slow the time of impact can save your life.
Crash Safety
• The force needed to slow a person from 50 km/h to zero in 0.1 sec is equal to 14 X the body weight.
• Seat belts allows your body to slow at the same rate as the seat
• Seatbelt • Air bags • ?
3.4 Connecting Motion w Forces
• Force
• A push or a pull
• Can change the motion of objects
• Balanced forces- equal & opposite
• Unbalanced-
Force
• The sum of forces is
called the net force.
• If the net force is not
zero, the applied
forces are
unbalanced.
• If the net forces are
zero, the applied
forces are balanced
and cancel each other
out. The object is in
equilibrium.
What is meant by unbalanced force?
If the forces on an object are equal and opposite, they are said to be balanced, and the object experiences no change in
motion. If they are not equal and opposite, then the forces are unbalanced and the motion of the object changes.
Some Examples from Real Life
Two teams are playing tug of war. They are both
exerting equal force on the rope in opposite directions. This balanced force results in no change of motion.
A soccer ball is sitting at rest. It takes an unbalanced force of a kick to change its motion.
Velocity acquired in free fall, from rest; v = gt (where g = 10 m/s2 or 9.8 m/s2)
• 1. Calculate the instantaneous speed of an apple that falls freely from a rest position and accelerates at 10 m/s2 for 1.5 seconds.
• • 2. An object is dropped from rest and falls freely. After 7 seconds,
calculate its instantaneous speed. • • 3. A skydiver steps from a high-flying helicopter. In the absence of
air resistance, how fast would she be falling at the end of a 12-second jump?
• • 4. On a distant planet, a freely falling object has an acceleration of
20 m/s2. Calculate the speed that an object dropped from rest on this planet acquires in 1.5 seconds
LAW OF UNIVERSAL GRAVITATION
Every object attracts every other object with a force that is directly related to the mass of each object
It is inversely proportional to the square of the distance between their centers.
The force on Timex's craft is only 1/4 of that on Tripod's because Timex is 2x as far from the earth's center.
Law of Universal
Gravitation
The force of gravitational attraction between the
earth & each spaceship can be found using the
frmula abve
where G is the universal constant of gravitation
(6.67 x 10-11 N-m2/kg2).
Forces • gravitational force- weakest force
• attractive force that exists
between all objects
• electromagnetic
force- give materials
their strength, ability
to bend
• strong nuclear force-
strongest- holds the
particles in the
nucleus together
• weak force- involved
in radioactive decay
Gravity depends on
• The size of the mass
• The distance between objects
• Distance is more important than mass
• gravitational force of an object • proportional to its mass • measured in newtons
Weight
• The measure of the force of gravity on the object
• Depends on location
• The greater the mass, the greater the attraction (gravity)
• 9.8 m/s2 on Earth
Falling Objects
• Falling objects fall with the same acceleration- regardless of mass
• A larger mass has a greater inertia, requiring a greater force to change its velocity
• A smaller mass has less inertia, requiring less force to affect its velocity
•
• About falling things
14-Feb-12 Physics 1 (Garcia) SJSU
Demo: String of Falling Balls
Falling objects accelerate (speed increases).
Listen for the sound as balls hit the ground.
Time between “clicks” gets shorter & shorter (falling faster & faster).
String does not pull; no tension while falling.
14-Feb-12 Physics 1 (Garcia) SJSU
Velocity in Free Fall (Down)
How fast do objects go when they fall?
Acceleration of gravity is 10 meters per second per second.
With each second of fall, speed increases by 10 meters/second
Zero meters per sec.
10 meters per sec.
20 meters per sec.
30 meters per sec.
40 meters per sec.
Release 1 second
2 seconds
3 seconds
4 seconds
14-Feb-12 Physics 1 (Garcia) SJSU
Velocity in Free Fall (Up & Down)
Moving upward, with each second the speed decreases by 10 meters/second.
Going back down the motion exactly reverses itself.
Zero meters per sec. 10 meters per sec.
20 meters per sec.
30 meters per sec.
40 meters per sec.
14-Feb-12 Physics 1 (Garcia) SJSU
Position in Free Fall
How far do objects go when they fall?
More complicated because speed is increasing.
There’s a pattern & Galileo figured it out.
But it wasn’t easy.
5 meters
20 meters
45 meters
Release 1 second
2 seconds
3 seconds
4 seconds 80 meters
Higher than King library
Higher than this ceiling
How about an object thrown straight upward?
• Once released, it continues to move upward
for a while and then comes back down.
• At the highest point, when it is changing its
direction of motion from upward to
downward, its instantaneous speed is zero.
• Then it starts downward just as if it had been
dropped from rest at that height.
How about an object thrown straight upward?
• the object slows as it rises. at the rate of 10 meters per
second each second—the same acceleration it experiences
on the way down.
• the instantaneous speed at points of equal elevation in the
path is the same whether the object is moving upward or
downward
• The velocities are opposite, because they are in opposite
directions.
• the downward velocities have a negative sign, indicating
the downward direction
How about an object thrown straight upward?
• Whether moving upward or
downward, the acceleration
is 10 m/s2 the whole time.
• up positive, and down negative.
• B/c the acceleration is the same whether the object is moving up or down, the figure could just as well represent the person at the bottom throwing the ball upward.
• What would be the speed of the ball when it reaches the top? Answer: 0 m/s
14-Feb-12
Lab: Acceleration of Gravity
Record position of falling object using spark timer and paper tape.
• We're talking here of vertical motion.
• How about running jumps? Hang time depends only on the jumper's vertical speed at launch. While airborne, the jumper's horizontal speed remains constant while the vertical speed undergoes acceleration. Interesting physics!
Summary of Terms
• Speed How fast something moves. The distance traveled per unit of time. Velocity The speed of an object and specification of its direction of motion. Acceleration The rate at which velocity changes with time; the change in velocity may be in magnitude or direction or both. Free fall Motion under the influence of gravity only.
Summary of Formulas
• Speed = distance/time • Average speed = total distance covered • time interval • Acceleration = change of velocity • time interval • Acceleration (linear) = change in speed • time interval • Freefall velocity from rest v = gt • Distance fallen in freefall from rest
Acceleration of Gravity Video
• If force = mass X acceleration • And weight is a force, • Then weight = mass x acceleration • Since the acceleration of gravity = 9.8 m/s2
• Weight = mass x 9.8 m/s2
• If an object is thrown down- gravity is no
longer the only force!
Demo: Dropping the Ball
(Distance Fallen) = ½ (Acceleration)(Time)(Time)
How long does it take a ball to fall 3 meters? Using the formula,
Can check that it takes 0.77 seconds since
(3) = ½ (10)(0.77)(0.77)
Beauty of science: Predict, then verify by dropping balls!
14-Feb-12 Physics 1 (Garcia) SJSU
Demo: Reaction Time
Release
Catch
Distance (inches) Time (sec.) 1 0.07 2 0.10 3 0.12 4 0.14 5 0.16 6 0.17 7 0.19 8 0.20 10 0.23 12 0.25 14 0.27 16 0.29 18 0.30
Distance fallen in free fall, from rest; d = 1/2 gt2
• 5. An apple drops from a tree and hits the ground in 1.5 seconds. Calculate how far it falls.
• • 6. Calculate the vertical distance an object dropped
from rest covers in 12 seconds of free fall. • • 7. On a distant planet a freely falling object has an
acceleration of 20 m/s2. Calculate the vertical distance an object dropped from rest on this planet covers in 1.5 seconds.
•
ON WHICH OF THESE HILLS DOES THE BALL ROLL DOWN
WITH INCREASING SPEED AND DECREASING ACCELERATION
ALONG THE PATH?
Air resistance depends on
Objects
• Speed
• Size
• Shape
• Density
• Compare the falling rate of
• Snow
• Sleet
• hail
Air Resistance
• is responsible for different
accelerations
• a feather and a coin in the presence
of air fall with different
accelerations.
• But in a vacuum, the feather and
coin fall with the same acceleration
air resistance
• If all objects fall with the same acceleration, why does a paper wadded up, fall faster than a flat one?
• Air resistance pushes in the opposite direction of movement
• Air resistance pushes up as gravity pulls down.
Air drag depends on the size and the speed of a
falling object
• When acceleration terminates, we say that the
object has reached its terminal speed.
• If we are concerned with direction, down for
falling objects, we say the object has reached its
terminal velocity
As a falling skydiver gains speed, air drag may finally build up until it equals the
weight of the skydiver If and when this happens, the net force becomes zero and the
skydiver no longer accelerates; she has reached her terminal
velocity. For a skydiver, it is about 200 kilometers per hour.
• A skydiver may vary this speed by varying position.
• Minimum terminal velocity is attained when the parachute
is opened.
Consider a man and woman parachuting together from the same altitude and the man is twice as heavy as the woman , but they are using the same-sized parachutes
The woman will reach her terminal speed when the air drag against her parachute equals her weight. When this occurs, the air drag against the parachute of the man will not yet equal his weight He must fall faster than she does for the air drag to match his greater weight
When Acceleration Is Less Than g—Nonfree Fall
• When weight mg is greater than air
resistance R, the falling sack
accelerates.
• At higher speeds, R increases.
• When R = mg, acceleration reaches
zero, and the chute reaches its
terminal velocity.
Suppose a rescue airplane drops a relief package while it is moving with a constant horizontal speed at an elevated height. Assuming that air resistance is negligible, where will the relief
package land relative to the plane?
Terminal velocity • When the air resistance
balances the pull of gravity • An object reaches terminal
velocity when the drag force has the same magnitude as the accelerating force.
• Why does a piece of paper fall more slowly under gravity than a piece of chalk if the acceleration due to gravity is the same for all objects? (Demonstrate this.)
Skydiving forces
Skydiving is kind of like sticking your head out of the window of a car that is traveling at 100 miles per hour."
Here's a closer look at the physics of skydiving.
Here he is in free fall without a parachute.
At this point the force of gravity is greater than the drag on his body so he is accelerating.
As he accelerates the amount of drag increases, because the faster an object moves through air, the greater the drag.
reached terminal velocity • Eventually drag is equal to
the force of gravity. He is no longer accelerating, but rather moving at a constant speed. He has reached terminal velocity, going as fast as he will go. This is roughly 200 kilometers per hour ( 125 miles per hour).
• Making contact with the ground at that speed would be rather uncomfortable so Philippe opens his parachute.
When drag is more than gravity he slows down
• With the parachute spread out above him rather than folded up tightly on his back, Philippe plus his parachute present a much larger surface area to the air they are moving through, greatly increasing drag.
• Since upward force is now greater than downward force, he suddenly begins to slow down. But as he moves slower and slower, drag decreases until...
Falling at reduced constant velocity
• ...gravity and drag are once again equal and Philippe is again dropping at a constant velocity. But now that velocity is only about 22 kph (14 mph)...
• Then he lands
Free Fall
• During each second of fall, the object gains a
speed of 10 meters per second.
• Free-fall acceleration is approximately equal
to 10 m/s2
freely falling objects use g because the acceleration is due to gravity
• g varies slightly in different locations,
dependent on mass
• Where accuracy is important, the value of 9.8 m/s2 should be used.
Free Fall
• When a falling object is free of all restraints—no friction, air or otherwise, and falls under the influence of gravity alone, the object is in a state of free fall.
• The instantaneous velocity of an object falling from rest can be expressed in shorthand notation as V = gt
• the instantaneous velocity or speed in meters per second is simply the acceleration g = 10 m/s2 multiplied by the time t in seconds.
Acceleration
• it is a rate of a rate
• Acceleration is not
velocity, nor is it even a
change in velocity.
Acceleration is the rate
at which velocity itself
changes
• a falling rock is equipped with a
speedometer.
• In each succeeding second of fall,
you'd find the rock's speed increasing
by the same amount: 10 m/s.
How about an object thrown straight upward?
• Once released, it continues to move upward
for a while and then comes back down.
• At the highest point, when it is changing its
direction of motion from upward to
downward, its instantaneous speed is zero.
• Then it starts downward just as if it had been
dropped from rest at that height.
How about an object thrown straight upward?
• the object slows as it rises. at the rate of 10 meters per
second each second—the same acceleration it experiences
on the way down.
• the instantaneous speed at points of equal elevation in the
path is the same whether the object is moving upward or
downward
• The velocities are opposite, because they are in opposite
directions.
• the downward velocities have a negative sign, indicating
the downward direction
How about an object thrown straight upward?
• Whether moving upward or
downward, the acceleration
is 10 m/s2 the whole time.
• up positive, and down negative.