Chapter 3 Section 1Newton’s Second Law

Newton’s First LawLaw of Inertia (first stated by Galileo)

• An object at rest will remain at rest unless it experiences a net external force. An object in motion will continue in motion at the same speed and in the same straight-line direction unless it experiences a net external force.

• Corollary: If either the magnitude or the direction of the velocity of an object changes, someone or something has exerted a net force on the object.

Newton’s 1st LawLaw of Inertia

• The motion of an object changes if and only if an unbalanced force acts on the object.

Newton’s Second Law of Motion

• The acceleration of an object is directly proportional to the net resultant force acting on the object and is inversely proportional to the mass of the object. The direction of the acceleration is in the direction of the net resultant force

F = m a

a α Fm

Acceleration and Force• For a given object (mass) the greater the

force, the greater the acceleration.

Acceleration and Mass• For a given force, the greater the mass, the

smaller the acceleration.

Units• Base Units

– length meter m– mass kilogram kg– time second s

• Derived Units– velocity = distance/time m/s– acceleration= ∆v/∆t = m/s/s– Force= ma = kg m/s2 Newton

in honor of Isaac Newton

Newton

• 1 Newton (1N) is the force needed to accelerate a 1 kilogram (kg) mass at 1 m/s/s.

September 23, 2011

• Read Page 68 and 69• Page 69 Practice Problems 1,2,3,4

Page 69 Practice Problems 1-4• You push a wagon that has a mass of 8 kg. If

the net force on the wagon is 4 N, what is the wagon’s acceleration

• Given• Asked• Formula

Problems• Given:

• Asked:

• Formula:

• Substitute:

• Answer:

September 24

• Read the last paragraph on page 70 and first paragraph on page 71

• Homework Assignment Page 74: 7-8

Schedule• Monday 9/23 Page 68-69 Newton’s 2nd Law

– Page 69:1-4• Tuesday 9/24 Friction

– P74: AM 7,8• Wednesday 9/25 Air Resistance • Thursday 9/26 Friction Lab• Friday 9/27 Gravity• Monday 9/30 Projectile Motion• Tuesday 10/1 Circular Motion, Centripetal Force

– Page 82: 6,7,8

• Wednesday 10/2 Thursday Section 3 Newton’s 3rd Law• Thursday 10/3 Momentum

– Page 86:1-4

• Friday 10/4 Conservation of Momentum– Practice Problems

• Monday 10/1 NTWS Sections 1-2, DRCM 1• Tuesday 10/2 Chapter Review 1-14 and 24,25,28• Wednesday 10/3 Test Section 1-2 Chapter 2

FrictionCause- Microwelds(Figure 4 page 71)

FrictionBox Not Moving

Applied Force

Static Friction

FrictionBox Moving

Applied Force

Kinetic Friction

FrictionRolling

Static Friction

FrictionSliding

Kinetic Friction

• Static Friction- object not moving

• Kinetic friction- object sliding• Rotational

–rolling- static friction–sliding- kinetic friction

• Static Friction > Kinetic Friction

Practical Application• Driving a car• Wheels rolling – Static Friction• Wheels sliding – Kinetic Friction

• Static Friction > Kinetic Friction

• Anti Lock Brakes (ABS)- prevents slamming on the brakes and locking the wheels

Assignment Page 74: 7-8• Given:

• Asked:

• Formula:

• Substitute

• Answer with Units:

Air Resistance

• Without air resistance, all objects would fall with the same acceleration.

• The acceleration of gravity• g =- 9.8 m/s2

• Feather and ball - see page 73

Air resistance

Air Resistance• The amount of air resistance depends on the• Speed• Size • Shape of the object.

• The faster an object falls the greater the air resistance.

Air Resistance (cont)

• An object falling from an air plane starts with zero velocity but it is accelerating at -9.8 m/s2

• The object keeps falling faster and faster but the air resistance increases the faster it falls.

Terminal Velocity

• Finally the force of air resistance becomes equal to the force of gravity and the object no longer accelerates.

• The velocity stays the same.• The object does not stop and float.

• Terminal Velocity

Review

• Newton’s 1st Law – law of inertia• Newton’s 2nd Law - F= ma• Unit of Force: kg m/s2 called a newton• Friction

– Static, Kinetic (sliding), Rolling– Static > kinetic

• Air Resistance– Size, Shape, Speed

Chapter 3Section 2 Gravity

Page 75-82

Gravity• A fundamental characteristic of all matter.• Einstein would say it is a fundamental characteristic of

space and time.• Anything that has mass is attracted by the force of gravity.• Anything that has mass attracts other things that have

mass.• Newton found the formula for finding the force of gravity.

FG = G m1m2

d2

G =6.67 X 10 -11N m2/kg2

Gravity

Fundamental Forces• Electromagnetic force

– Attracts or repels

• Strong Nuclear force• Weak Nuclear force• Nuclear forces only over very short distances.

• Gravitational Force– Always attraction– Long distance

Earth’s GravityThe earth exerts a force of attraction on every object. At the same time that object exerts a

force of attraction on the earth.

Fg = m g

g = -9.8 m/s2

W = m g = m *-9.8 m/s2

W = m g = kg*m/s2 = newtons

Weight Varies

Weight vs Mass

• Weight and mass are not the same• Mass is a measure of the inertia of an object,

how much the object resists a change in velocity.

• Mass is a measure of the amount of substance• Weight is a force• Weight is the force of attraction between an

object and the earth

Weightlessness

• If you are in an elevator that is in free fall (being accelerated toward the ground with the acceleration of g) then you would be weightless, but not massless.

• See Figure 15, Page 79

• Elevators don’t free-fall !

Projectile motion

• Projectile- anything that is thrown or shot through the air.

• Projectile- an object moving in the horizontal direction at a constant velocity and under the influence of gravity in the vertical direction.

• The object (projectile) follows a curved path, in fact the curve has a name- parabolic motion.

Projectile MotionPage 80

Projectile MotionParabolic Motion

Time

Constant horizontal velocityAccelerating vertical velocity

Both balls hit ground at same time!

Tuesday October 1

• Read Page 81 and 82

Motion in a Circle (p81)Velocity is constantly changing

Changing Velocity

• Velocity is constantly changing• Changing velocity = acceleration• Acceleration toward the center of the circle• Acceleration means Force• Force toward the center of the circle

Motion in a CircleCentripetal Force/Acceleration

v1

v2Fcenter

Fc = mV2

r

Motion in a CircleCentrifugal Force/Acceleration

v1

v2Fcenter

Foutward

Centrifugal Force is a “made up” force that is really the inertia of the object.

Centrifugal Force

• Fugitive- some one fleeing the law• Centrifugal Force – the force fleeing the center

• Experience going around a curve in a car- “thrown” to the outside.

• Centrifugal force is not a real force but is inertia of the body trying to stay moving in a straight line while the car is turning.

Source of Centripetal Force

• What provides the force that causes the moon to go around a curve rather than following inertia to keep going in a straight line?

Source of Centripetal ForceGravity

Source of Centripetal Force

• What provides the force that causes a car to go around a curve rather than following inertia to keep going in a straight line?

Chapter 3 Assignments• Page 69: 1-4• Page 74: 7,8• Page 82: 6-8 • Lab/Demonstration - Friday• Note Taking Worksheet - Turn in Monday• Chapter Review (Page94-95) 1-14, 24-28

Tuesday• Test- Wednesday

Chapter 3 Section 3Newton’s 3rd Law of Motion

Page 83-88

Newton’s 3rd Law• When one object exerts a force on a second

object, the second object exerts a force on the first object that is equal in strength and opposite in direction.

• For every action force there is an equal and opposite reaction force.

• The ladder law- if you jump off of a ladder the ladder exerts a force that moves you but you also exert a force on the ladder that may move the ladder.

Examples of 3rd Law• When you push on a wall, the wall pushes back on

you.• A skater exerts a force on a second skater and the

second skater exerts an equal force on the first skater.

• When you swim, you push the water back but the water pushes the swimmer forward.

• A rocket engine exerts a force that pushes hot gases out the back of the rocket, but the hot gases exert a force that propels the rocket forward.

Why don’t these opposite forces cancel each other?

• Because the action force acts on one object and the reaction force acts on another object.– Force on wall - force on you– Force on you - force on ladder– Force on water - force on swimmer– Force on #1 skater - force on #2 skater– Force on gases - force on rocket

Momentum (p86)

• The Momentum is a property of a moving object that is related to the force that is needed to change the motion of the object.

• Momentum is the product of the mass and the velocity of an object.

• Momentum is given the symbol “p”• p (momentum) = m (mass) * v (velocity)

Momentum and Forcep = m v F = m a

a = ∆v∆t

vf – vi

∆t=

F = m vf – vi

∆tF = m ( vf – vi )/ ∆t

F ∆t = m ( vf – vi )Impulse = Change in Momentum

Practice Problems Page 86Assignment 1-4

• At the end of a race, a sprinter with a mass of 80.0 kg has a speed of 10.0 m/s. What is the sprinters momentum.

• P = m*v• #1 asks for momentum• #2 asks for speed• #3 asks for mass

Problems• Given:

• Asked: Units:

• Formula:

• Substitute:

• Answer (with units):

Conservation of Momentum

• If there is no outside force acting on an object or a group of objects then F= O so the change in momentum is zero. The momentum before the event is the same as the momentum after the even

F ∆t =0 and m vf – mvi = 0

F ∆t = m vf – mvi

m vf = mvi

Examples of conservation of Momentum

• A pool ball moving at a velocity strikes a group of pool balls at rest. Momentum is transferred from the moving ball to the balls at rest but after the collision, the total momentum must be the same.

• An ice hockey puck moves across the ice and strikes a second puck. The first puck stops but the second puck moves away with the same momentum that the first puck had before the collision.

Review• Newton’s 1st Law – law of inertia• Newton’s 2nd Law - F= ma• Newton’s 3rd Law- Action/Reaction• Unit of Force: kg m/s2 called a newton• Friction

– Static, Kinetic (sliding), Rolling– Static > kinetic

• Air Resistance– Size, Shape, Speed

• Anything that has mass attracts other things that have mass.

FG = G m1m2

d2

G =6.67 X 10 -11N m2/kg2

Fg = m gW = m g = kg*m/s2 = newtons

Weight vs Mass

• Weight and mass are not the same• Mass is a measure of the amount of substance• Weight is the force of attraction between an

object and the earth

Dear TJCA Parents, grades 7-12:

This is an important reminder that any student who has a grade below 70 on midquarter or end of quarter report cards in a core subject area MUST attend the required after school tutoring from 3-4PM on the designated days for the respective courses, listed below, until the end of the next grading period.   PLEASE note that students who do attend mandatory tutoring will be placed in In School Suspension the following day.   We cannot stress enough how important it is to attend these tutoring sessions to help students to bring these grades up.

Mondays:   English, History  (if failing both- teachers will rotate the schedule)Tuesdays:  ScienceThursdays: Math/computerFridays:     Latin, logic, foreign language

We are all making sacrifices to help assure your child's success, so please make sure your child attends these mandatory sessions.

Chapter 3 Assignments• Page 69: 1-4 • Page 74: 7-8• Page 82: 6-8 • Page 86: 1-4 • Note Taking Worksheet/Reinforcement Sheet• Turn in Thursday• Chapter Review (Page94-95) 1-14, 24-28• Test –

Problem 24

• Find your mass if a scale on Earth reads 650N.• Given:

• Asked:• Formula:• Substitute:

• Answer (with units)

Problem 25• You weigh yourself at the top of a high mountain and

the scale reads 720N. If your mass is 75 kg, what is the acceleration of gravity at your location?

• Given:

• Asked:• Formula:• Substitute:

• Answer (with units)

Problem 26 • The 2kg metal ball moving at a speed of 3m/s strikes a

1kg wooden ball that is at rest. After the collision, the speed of the metal ball is 1m/s. Assume momentum is conserved, what is the speed of the wooden ball after the collision?

• Given:

• Asked:• Formula:• Substitute:

• Answer (with units)

Problem 27• Find the mass of a car that has a speed of

30m/s and a momentum of 45,000 kg m/s.• Given:

• Asked:• Formula:• Substitute:

• Answer (with units)

Problem 28• A box being pushed with a force of 85N slides

along the floor at a constant speed. What is t• Given:

• Asked:• Formula:• Substitute:

• Answer (with units) he force of sliding friction on the box?

Tuesday September 27, 2011• Need your book, calculator, Reference Sheet• Turn in all homework with your test• Use the blue (gray) side of scantron• Question 1: a=true, b=false• Show all work on the problems

– Given– Asked– Formula– Substitution– Answer with unit

– After the test– Turn in all homework for chapter 3– Read pages 100-102