CHAPTER 1MOTION & MOMENTUM

SECTION 1

WHAT IS MOTION?

• All matter is constantly in MOTION

• Motion involves a CHANGE in position.– An object changes position relative to a

REFERENCE POINT.– DISTANCE is the total length of the route

an object travels when it moves.– DISPLACEMENT includes direction of the

stopping point from the starting point.

DISTANCE

A B

Reference point

When going from point A to point B motion occurred because you traveledA distance (10 meters) from your Reference point (A).

D=10 meters

DISPLACEMENT

A

B

D = 40 M

D = 30 MD = 50 M

DISTANCE = 70 METERS (40M + 30M = 70M)DISPLACEMENT = 50 M northeast

N

S

EW

QUESTION:

IS IT POSSIBLE TO HAVE A DISTANCE OF 140 M BUT HAVE A DISPLACEMENT HAVING 0 M?

EXPLAIN YOUR ANSWER.

ATTENTION!!!

• SPEED & VELOCITY ARE ALMOST THE SAME THING

• BOTH TELL YOU HOW FAST YOU ARE GOING

• ONLY DIFFERENCE……• SPEED MEANS HOW FAST• VELOCITY MEANS HOW FAST + A DIRECTION

Velocity is the distance traveled divided by the time taken to travel the distance + a direction

Formula:

VELOCITY = DISTANCETIME

or

V = d t

Mrs. M walked 10 m across the room (that way) in 5 s.Mrs. M traveled at a speed of 2 m/s.

v =10 m5 s

v = 2ms

That way

That way

• The units of velocity are units of distance divided by units of time– V = velocity– d = distance– t = time

• The SI (system international) unit for velocity is meters per second (m/s)

or m s

RULE

• IF VELOCITY DOESN’T GIVE YOU A DIRECTION YOU DON’T HAVE TO INCLUDE ONE….

• IF IT DOES THEN YOU MUST INCLUDE IT.

• SIMPLE….

• An object in motion can change VELOCITY many times as it moves from one point to another:– Speeding up– Slowing down– CHANGING DIRECTION

• AVERAGE VELOCITY is the total distance traveled divided by the total time taken.

• INSTANTANEOUS VELOCITY is the object’s speed at a particular moment in time.

• CONSTANT VELOCITY occurs when an object travels at a steady rate with the same instantaneous speed for some period of time

EXAMPLES

• JOE DROVE 100 MILES IN 2 HOURS– HIS VELOCITY WAS 50 MILES PER HOUR

• MARY DROVE 100 MILES IN 2 HOURS– HER VELOCITY WAS ALSO 50 MILES PER

HOUR

AVERAGE VELOCITY

• ALONG THE WAY JOE HIT TRAFFIC, HE CONTINUALLY WAS SPEEDING UP AND SLOWING DOWN. HE STILL MADE IT TO HIS DESTINATION IN 2 HOURS HIS AVERAGE VELOCITY WAS 50 MILES / HOUR.

INSTANTANEOUS VELOCITY

• WHILE JOE WAS DRIVING HE GOT STUCK BEHIND A TRAFFIC JAM. IN ORDER TO MAKE UP SOME TIME HE HIT THE GAS AND BLEW RIGHT PAST THE STATE POLICEMAN AND WAS PULLED OVER. “SIR, STATED THE POLICEMAN, DO YOU KNOW HOW FAST YOU WERE GOING? I HAD YOU CLOCKED AT 85 MILES / HOUR.

AND THAT CLASS IS AN EXAMPLE OFINSTANTANEOUS VELOCITY. THE MOMENT JOE PASSEDTHE COP HE WAS TRAVELING 85 MILES / HOUR.

CONSTANT VELOCITY

• MARY BEGAN HER JOURNEY. THERE WAS NO TRAFFIC THAT DAY. AS SOON AS SHE STARTED GOING 50 MILES / HOUR SHE POPPED ON THE CRUISE CONTROL AND TRAVELLED MARILY ON HER WAY.

• MOTION can be graphed on a distance-time graph – Time plotted on the horizontal axis (x - axis)– Distance plotted on the vertical axis (y - axis)

distance

time1s 2s 3s 4s 5s 6s

1m

2m

3m4m5m

• The steeper the line on a distance-time graph, the GREATER the VELOCITY

distance

time1s 2s 3s 4s 5s 6s

1m

2m

3m4m5m

fastMuch faster

• A horizontal line on a distance-time graph indicates that no change in position is occurring and the VELOCITY is zero.

distance

time1s 2s 3s 4s 5s 6s

1m

2m

3m4m5m

• Velocity is the speed of an object and its direction of motion.– Velocity changes if either, or both of these

change.

Speed vs. Velocity

• Speed is how fast an object is traveling

• Velocity is how fast an object is traveling and also the direction!!!

Section 2

Acceleration

• Acceleration - change in velocity divided by the time for the change to occur.– Changes include:

• Speeding up• Slowing down• CHANGING DIRECTION

• Can be calculated if you know the object’s velocity changed during a given time period.

Formula

ACCELERATION = (FINAL VELOCITY – INITIAL VELOCITY)TIME

a = (Vf - Vi)

t

• The unit for acceleration is:– Distance divided by time squared

• The SI unit for acceleration is:– Meters per second squared

m s2

• PHYSICS BOOKS (WHEN YOU ARE IN 11TH GRADE) refer to this as this formula:

a =

Δ – (greek letter delta) means “change in”

this is the equivalent to something – something else.

ADVANCED ONLY!!!

ΔV____t

Example 1

• If you had five apples and ate three…the change would be 2 apples left.

• Therefore Δ apples would be 2 apples.

Example 2

• You were going 10 m/s

• Then slowed down to 6 m/s

• Your change in velocity was 4 m/s

• ΔV = 4 m/s

In PhYsIcS

• There is no speeding up…

• No slowing down…

• Just + (positive)

• And – (negative)

• Remember: you either positively accelerate or negatively accelerate.

• NEVER Decelerate!!!!!! It does not exist

• Acceleration is POSITIVE when an object SPEEDS UP.

• Acceleration is NEGATIVE when an object SLOWS DOWN.

Example #1A dog sat on the sidewalk. The dog saw

his master and ran at 4 meters per second in 2 seconds. What was the dog’s acceleration?

4 t = 2 s

a = (Vf - Vi)

tVf = 4 m

s

Vi = 0 m s

a = (4 - 0 )

2s

m s

m s

a = m s

2 s

a = 2 m s2

Example #2• A dog was walking at a Velocity of 4

meters per second west. The dog came to a stop in 2 seconds. What was the dog’s acceleration?

t = 2 s

a = (vf - Vi)

tsf = 0 m

s

Vi = 4 m s

a = (0 - 4 )

2s

m s

m s

a = m s

2 s

a =-2 m s2

-4

west

west west west

west

west

Velocity - Time graph

• Graphing acceleration:– Velocity on vertical axis (y - axis)– Time on horizontal axis (x - axis)

• An object speeding up will have an upward slope.

velocity ( )

time1s 2s 3s 4s 5s 6s

1

2

345

m s

• An object slowing down has a downward slope.

velocity ( )

time1s 2s 3s 4s 5s 6s

1

2

345

m s

• A horizontal line means NO acceleration or (zero).

Velocity ( )

time1s 2s 3s 4s 5s 6s

1

2

345

m s

momentum

Section 3

• Mass - the amount of matter in the object.– The SI unit for mass is kg.– Weight of an object is related to its mass.– A bowling ball has more mass than a pillow and

weighs more.– However the pillow is larger than a bowling ball. – DO NOT LET SIZE OF AN OBJECT FOOL

YOU!!!

• Inertia - tendency of an object to resist a change in its motion.

• The more mass an object has the harder it is to speed it up, slow it down, or turn it.

• Momentum - a measure of how difficult it is to stop a moving object.– Equals the product of mass and velocity

• We know the faster a bicycle moves, the harder it is to stop.

• If fact by increasing the velocity or increasing its mass will make anything harder to stop.

Momentum

• The symbol used to signify momentum is the letter “p”

• The equation is written as:p = mv

• p - momentum• m - mass• v - velocity

• The SI unit for momentum is:kg . m/s

kilograms multiplied by meters per second

Momentum Equation

m = 14 kg

v = 2 north

p = ?

P = mv

P = (14 kg) x (2 north)

P = 28 kg . north

m s

m s

m s

• Law of conservation of motion - states that the total momentum of objects that collide with each other is the same before and after the collision.

• When playing pool the cue ball moves towards the other balls. When the cue ball collides with the other balls the cue ball slows down and it decreases its momentum. However the other balls speed up and change direction. The other balls are increasing their momentum. The momentum of the cue ball was transferred into the other balls.

• So what slows down the other balls?

• Outside forces such as gravity and friction are almost always acting on objects during a collision.

• These forces are small and can be ignored.

After Collisions

• Objects could – stick together– Collide and bounce off