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.

Vector & Scalars

• Scalar quantity- gives only magnitude

• vector- gives magnitude and direction.

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)

Particle Model

• Uses of dots instead of pictures to represent movement.

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

What is happening?

Speed is the rate of change in distance.

• Type of quantity: Scalar 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.

Approximate Speeds in Different 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 is the rate of change in displacement

• Vector quantity

• m/s/s or • m/s2

Velocity changes when you speed up, slow down or change direction.

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

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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.

Acceleration Video Why things fall

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.

How does the earth's pull on Dr. J's craft compare to that on Tripod's?

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

vertical motion

• The relationship between time up or down and vertical height is given by

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

Time of Fall (seconds) Distance Fallen (meters)

0 0 1 5 2 20 3 45 4 80 5 125

t ½ 10 t 2

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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!

Graphing Acceleration

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

EOC

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.

Non-Horizontally Launched Projectiles

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?

The Plane and The Package

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

Terminal Velocity

•

Terminal Velocity

Free Fall Table 3.2 shows the instantaneous speed of a

freely falling object at 1-second intervals

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.

Time of Fall (seconds) Distance Fallen (meters)

0 0 1 5 2 20 3 45 4 80 5 125

t ½ 10 t 2