II. Describing Motion Motion

Speed & Velocity Acceleration

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 velocitynet force

Problem:◦ Is your desk moving?

We need a reference point...◦ nonmoving point from which motion is measured

Motion◦ Change in position in relation to a reference point.

Reference point

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.

You can describe the direction of an object in motion with a reference direction.

north, south, east, west, up, or down

Distance Displacement

Distance – the length traveled by an object

Practice – What is the distance?◦Pattie walks 4 km North, then 3 km East◦Joe runs 30 m East, then runs 40 meters

West◦Aaron jogs 4 km East, 4 km North,

4 km West, and 4km South

◦Answers: 7 km ; 70 meters ; 16 km

Distance – length Displacement – distance AND direction of a

movement from the starting point

If an object moves in a single direction, the displacement equals the distance + the direction

start here

4 km total displacement =

4km North

If an object moves in two opposing directions, the displacement is the difference between the two.

start here

3 km4 km

total displacement = 4 km North + -3 km South

= 1 km North (of original starting point)

total distance = 4 + 3 = 7 km

Displacement can be positive or negative. A negative direction can be either the opposite of the original movement, or can follow the sign of a typical graph [North/East vs South/West]

If an object moves in two directions, a triangle will be formed. If the angle is 90º , use a2 + b2 = c2 to solve.

start here

4 km

3 km

displacement

If an object moves in two directions, a triangle will be formed. If the angle is 90º , use a2 + b2 = c2 to solve.

start here

4 km

3 km

5 km

displacement =

42 + 32 = c2

c2 = (16) + (9) = 25

c2 = √(25)

c = 5km

Displacement can be given in:◦units with direction example: x number of meters North

30 meters East + 40 meters West displacement = 10 meters West

Displacement can be given in:◦positive or negative units [like on a graph] positive = North {up} or East {right} negative = South {down} or West {left}

30 meters east + 40 meters west = 30 meters + (-40) meters = -10 meters

Practice – What is the displacement?◦Pattie walks 8km North, then 3 km East 5 km displacement

◦Joe runs 30 m East, then runs 40 meters West 10 meters [or -10] displacement

◦Aaron jogs 4 km East, 4 km North,4 km West, and 4km South 0 meters displacement

go to website!!!!

Draw each scenario and show work.2. Amy runs 2 miles south, then turns around and runs 3 miles north.

a. Distance ___ b. Displacement ___

3. Jermaine runs exactly 2 laps around a 400 meter track.

4. Joe turns around 5 times.

5. Ray runs 30 feet north, 30 feet west, and then 30 feet south.

Speed◦ rate of motion ◦ distance traveled per unit time

time

distancespeed

vd

t

Instantaneous Speed◦ speed at a given instant

Average Speed

time total

distance totalspeed avg.

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!

Velocity◦ speed in a given direction◦ can change even when the speed is constant!

Find the velocity in m/s of a swimmer who swims 110 m toward the shore in 72 s.

v = d t

v = 110m = 1.5 m/s 72 s

Acceleration◦ the rate of change of velocity◦ change in speed or direction

t

vva if

a: acceleration

vf: final velocity

vi: initial velocity

t: time

a

vf - vi

t

Positive acceleration“speeding up”

Negative acceleration

“slowing down”

Your neighbor skates at a speed of 4 m/s towards home. 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!vd

t

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/s2 = 7 m/sa

vf - vi

t

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 = 3 s

vd

t

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

slope =

steeper slope =

straight line =

flat line =

Distance-Time Graph

A

B

faster speed

constant speed

no motion

speed

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

Acceleration is indicated by a curve on a Distance-Time graph.

Changing slope = changing velocity

slope =

straight line =

flat line =0

1

2

3

0 2 4 6 8 10

Time (s)

Sp

ee

d (

m/s

)

Speed-Time Graph

acceleration +ve = speeds up -ve = slows down

constant accel.

no accel. (constant velocity)

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

0

1

2

3

0 2 4 6 8 10

Time (s)

Sp

ee

d (

m/s

)

Speed-Time Graph

III. Defining Force

Force Newton’s First Law

Friction

Force◦a push or pull that one body exerts on another

◦What forces are being exerted on the football?

Fkick

Fgrav

Balanced Forces

◦forces acting on an object that are opposite in direction and equal in size

◦no change in velocity

Unbalanced forces◦unbalanced forces that are not opposite and equal

◦velocity changes (object accelerates)

Ffriction

W

Fpull

Fnet

NN

Net forcethe combination of all the forces acting on an object

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.

Newton’s First Law of Motion◦“Law of Inertia”

Inertia◦tendency of an object to resist any change in its motion

◦increases as mass increases

Since these two forces are of equal magnitude and in opposite directions, they balance each other. The book is said to be at equilibrium. There is no unbalanced force acting upon the book and thus the book maintains its state of motion.

The force of gravity pulling downward and the force of the table pushing upwards on the book are of equal magnitude and opposite directions. These two forces balance each other. Yet there is no force present to balance the force of friction. As the book moves to the right, friction acts to the left to slow the book down.

Free-body diagrams are diagrams used to show the relative magnitude (strength) and direction of all forces acting upon an object in a given situation.

The size of the arrow in a free-body diagram is shows the magnitude of the force. The direction of the arrow reveals the direction in which the force acts.

It is customary in a free-body diagram to represent the object by a box or a small circle and to draw the force arrow from the center of the box or circle in an outward direction.

F = force Fnorm = normal forceFfrict = friction Fapp = applied forceFgrav = gravity

Object lies motionless on a surface.

A rightward force is applied to a book in order to move it across a desk at constant velocity. Consider frictional forces. Neglect air resistance.

Object slows due to friction (rough surface).

An object is suspended from the ceiling.A new force is tension.

A flying squirrel is gliding (no wing flaps) from a tree to the ground at constant velocity. Consider air resistance.

A new force is air resistance. It pushes an object up.

http://www.mrwaynesclass.com/freebodies/reading/index01.html

Free body diagrams with movement

A stationary object remains stationary if the sum of the forces acting upon it - resultant force - is zero.

A moving object with a zero resultant force keeps moving at the same speed and in the same direction.

If the resultant force acting on an object is not zero, a stationary object begins to accelerate in the same direction as the force. A moving object speeds up, slows down or changes direction.

Add forces going in the same direction.

Subtract forces going in opposite directions.

2N

2N

Resultant Forces

http://physicsnet.co.uk/gcse-physics/the-effects-of-forces-resultant-force-and-motion/

TRUE or FALSE?

The object shown in the diagram must be at rest since there is no net force acting on it.

FALSE! A net force does not cause motion. A net force causes a change in motion, or acceleration.

Taken from “The Physics Classroom” © Tom Henderson, 1996-2001.

https://www.youtube.com/watch?v=VutAx3RDFbI

You are a passenger in a car and not wearing your seat belt.

Without increasing or decreasing its speed, the car makes a sharp left turn, and you find yourself colliding with the right-hand door.

Which is the correct analysis of the situation? ...

1. Before and after the collision, there is a rightward force pushing you into the door.

2. Starting at the time of collision, the door exerts a leftward force on you.

3. both of the above

4. neither of the above2. Starting at the time of collision, the door exerts a leftward force on you.

Friction◦force that opposes motion between 2 surfaces

◦depends on the: types of surfaces force between the surfaces

Friction is greater...◦between rough surfaces

◦when there’s a greater force between the surfaces (e.g. more weight)

Pros and Cons?

Static Friction: friction between surfaces that are stationary

Kinetic Friction: friction between moving surfaces

The force necessary to make a stationary object start moving is usually greater than the force needed to keep it moving.

Sliding friction : when objects slide past each other

Rolling friction: If a round object rolls over a flat surface

Fluid friction: an object moving through a fluid such as air (car moving hits air molecules)

How can a car minimize its fluid friction?

smooth surface – wax car surfaceshape of the car -streamlining

http://www.mrwaynesclass.com/freebodies/reading/index01.html

Free body diagrams with movement

IV. Force & Acceleration

Newton’s Second Law

Gravity 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 = maF: force (N)m: mass (kg)a: accel (m/s2)

1 N = 1 kg ·m/s2

am

F

a

Fm

Gravity ◦force of attraction between any two objects in the universe

◦increases as...mass increasesdistance 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)

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

Wg

featherAnimation from “Multimedia Physics Studios.”

http://www.animations.physics.unsw.edu.au/jw/Newton.htm#Newton2

Go to the astronaut’s, David Scott, demonstration

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

F = 200 Nm

F

a

A 4.0 kg shotput is thrown with 30 N of force. What is its acceleration?

GIVEN:

m = 4.0 kg

F = 3.0 N

a = ?

WORK:

a = F ÷ m

a = (30 N) ÷ (4.0 kg)

a = 7.5 m/s2

m

F

a

Mrs. J. 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 = 57 kgm

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.

VI. Action and Reaction

Newton’s Third Law

Momentum Conservation of

Momentum

Newton’s Third Law of Motion◦ When one object exerts a force on a second

object, the second object exerts an equal but opposite force on the first.

Problem:

How can a horse pull a cart if the cart is pulling back on the horse with an equal but opposite force?

NO!!!

Aren’t these “balanced forces” resulting in no acceleration?

◦forces are equal and opposite but act on different objects

◦they are not “balanced forces”

◦the movement of the horse depends on the forces acting on the horse

Explanation:

Action-Reaction Pairs

The hammer exerts a force on the nail to the right.

The nail exerts an equal but opposite force on the hammer to the left.

Action-Reaction Pairs

The rocket exerts a downward force on the exhaust gases.

The gases exert an equal but opposite upward force on the rocket.

FG

FR

Action-Reaction PairsBoth objects accelerate.The amount of acceleration

depends on the mass of the object.

a Fm

Small mass more accelerationLarge mass less acceleration

I. Newton’s Laws of Motion “If I have seen far, it is because I have

stood on the shoulders of giants.”- Sir Isaac Newton (referring to Galileo)

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.

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

Newton’s Third Law of Motion◦ When one object exerts a force on a second

object, the second object exerts an equal but opposite force on the first.