Chapter 3Chapter 3

Newton’s LawsNewton’s Laws

Every object possesses inertia.Every object possesses inertia.

Inertia is the tendency of a body at rest Inertia is the tendency of a body at rest to remain at rest, and of a body in motion to remain at rest, and of a body in motion to continue moving with unchanged to continue moving with unchanged velocity.velocity.

oror

Inertia is the sluggishness of an object to Inertia is the sluggishness of an object to changes in its state of motion.changes in its state of motion.

MassMass - a measure of the inertia of an - a measure of the inertia of an objectobject

THE MASSTHE MASSTHE MASSTHE MASS

Demo - Inertia rocksDemo - Inertia rocks

Demo – Hoop and chalkDemo – Hoop and chalk

slug..

A slug weighs 32.2 lb. A slug weighs 32.2 lb.

The The standard kilogram is an object whose is an object whose mass is defined to be one kilogram.mass is defined to be one kilogram.

Abbreviation is kg.Abbreviation is kg.

There is an English unit of mass. TheThere is an English unit of mass. The

THE STANDARD KILOGRAMTHE STANDARD KILOGRAMTHE STANDARD KILOGRAMTHE STANDARD KILOGRAM

In general force is the agency of change.In general force is the agency of change.

In mechanics forces cause accelerations.In mechanics forces cause accelerations.

It is a vector.It is a vector.

An external force is one whose source lies An external force is one whose source lies outside of the system being considered.outside of the system being considered.

FORCEFORCEFORCEFORCE

The net external force acting on an object The net external force acting on an object causes the object to accelerate in the causes the object to accelerate in the direction of that force.direction of that force.

THE NET EXTERNAL FORCETHE NET EXTERNAL FORCETHE NET EXTERNAL FORCETHE NET EXTERNAL FORCE

The combination of The combination of forces that act on an forces that act on an object is the net force.object is the net force.

(Only the net force is (Only the net force is shown in the figures on shown in the figures on this slide.)this slide.)

a F

F a

F a

F a

The acceleration of an The acceleration of an object is directly object is directly proportional to the net proportional to the net force.force.

m

m

m

This symbol means proportional to

F am

F a

F a

1a m

The acceleration is The acceleration is inversely proportional inversely proportional to the mass of the to the mass of the object.object.

Consider the same Consider the same net force applied to net force applied to different mass different mass objects.objects.

m

m

m

m

m

The acceleration is proportional to the force The acceleration is proportional to the force and inversely proportional to the mass of the and inversely proportional to the mass of the object.object.

The Newton (N) is the SI unit of force. The Newton (N) is the SI unit of force.

A resultant 1 N force will give a 1 kg mass an A resultant 1 N force will give a 1 kg mass an

acceleration of 1 m/sacceleration of 1 m/s22. .

The pound (lb) is the English (The pound (lb) is the English (US customary) ) unit of force.unit of force.

A resultant 1 lb force will give a 1 sl mass anA resultant 1 lb force will give a 1 sl mass an

acceleration of 1 ft/sacceleration of 1 ft/s22..

THE NEWTONTHE NEWTONTHE NEWTONTHE NEWTON

An object at rest will remain at rest; An object at rest will remain at rest;

an object in motion will continue in motion an object in motion will continue in motion with constant velocity, except insofar as it is with constant velocity, except insofar as it is acted upon by an external force.acted upon by an external force.

““If you leave an object alone, it has constant If you leave an object alone, it has constant velocity.”velocity.”

NEWTON’S FIRST LAWNEWTON’S FIRST LAWNEWTON’S FIRST LAWNEWTON’S FIRST LAW

Newton stated it in terms of momentum.Newton stated it in terms of momentum.

A less rigorous form of the second law will be A less rigorous form of the second law will be used here.used here.

If the net external force acting on an object is If the net external force acting on an object is not zero, then the acceleration of the object is not zero, then the acceleration of the object is directly proportional to the net external force directly proportional to the net external force and inversely proportional to the mass of the and inversely proportional to the mass of the object.object.

NEWTON’S SECOND LAWNEWTON’S SECOND LAWNEWTON’S SECOND LAWNEWTON’S SECOND LAW

The force in each of these equations The force in each of these equations represents the vector sum of all of the represents the vector sum of all of the forces acting on the object of mass m.forces acting on the object of mass m.

F ma

Fa m

or

This vector equation can be written out as This vector equation can be written out as three separate scalar equations.three separate scalar equations.

F ma

x xF ma y yF ma z zF ma

Forces represent interactions between Forces represent interactions between one piece of matter and another.one piece of matter and another.Therefore, forces come in pairs.Therefore, forces come in pairs.For each force exerted on one body, For each force exerted on one body, there is an equal, but oppositely directed, there is an equal, but oppositely directed, force on some other body interacting with force on some other body interacting with it.it.““You cannot touch without being You cannot touch without being touched.” Paul Hewitttouched.” Paul HewittThis is often called the Law of Action and This is often called the Law of Action and Reaction.Reaction.

NEWTON’S THIRD LAWNEWTON’S THIRD LAWNEWTON’S THIRD LAWNEWTON’S THIRD LAW

THE LAW OF UNIVERSAL THE LAW OF UNIVERSAL GRAVITATIONGRAVITATION

THE LAW OF UNIVERSAL THE LAW OF UNIVERSAL GRAVITATIONGRAVITATION

1 22

m mF

r

r

m1 m2

1 22

m mF G

r

11 2 26.67 10 /G x N m kg

Gravity is the most dominant force in Gravity is the most dominant force in

nature.nature.

Yet it is the weakest.Yet it is the weakest.

1 unit2 units

3 units4 units

Let’s look at the inverse-Let’s look at the inverse-square nature for the force of square nature for the force of gravity.gravity.

The weight of an object is the The weight of an object is the gravitational force acting downward on gravitational force acting downward on the object.the object.

Because the Earth is not a perfect Because the Earth is not a perfect uniform sphere, and because it is uniform sphere, and because it is spinning, the weight measured by a spinning, the weight measured by a scale (often called the effective weight) scale (often called the effective weight) will be very slightly different from that will be very slightly different from that defined here.defined here.

THE WEIGHTTHE WEIGHTTHE WEIGHTTHE WEIGHT

Look at the force of gravity on a freely Look at the force of gravity on a freely falling object.falling object.

We call that the weight of the object.We call that the weight of the object.

A 1 kg object would weigh 9.81 N A 1 kg object would weigh 9.81 N

or 2.20 lb.or 2.20 lb.

RELATIONSHIP BETWEEN RELATIONSHIP BETWEEN MASS AND WEIGHTMASS AND WEIGHT

RELATIONSHIP BETWEEN RELATIONSHIP BETWEEN MASS AND WEIGHTMASS AND WEIGHT

F ma

W mg

It is an applied force that tends to It is an applied force that tends to stretch things. stretch things.

It’s magnitude is called the tension.It’s magnitude is called the tension.

THE TENSILE FORCETHE TENSILE FORCETHE TENSILE FORCETHE TENSILE FORCE

It is a tangential force acting on an It is a tangential force acting on an object that opposes the sliding of that object that opposes the sliding of that object on an adjacent surface with object on an adjacent surface with which it is in contact. which it is in contact. The friction force is parallel to the The friction force is parallel to the surface and opposite to the direction of surface and opposite to the direction of motion or of impending motion. motion or of impending motion. Only when the applied force exceeds Only when the applied force exceeds the maximum static friction force will an the maximum static friction force will an object begin to slide.object begin to slide.

THE FRICTION FORCETHE FRICTION FORCETHE FRICTION FORCETHE FRICTION FORCE

The normal force is a part of the contact The normal force is a part of the contact force between surfaces in contact.force between surfaces in contact.

The normal force is perpendicular to the The normal force is perpendicular to the surfaces in contact.surfaces in contact.

The frictional force is parallel to the The frictional force is parallel to the surfaces in contact. surfaces in contact.

THE NORMAL FORCETHE NORMAL FORCETHE NORMAL FORCETHE NORMAL FORCE

For surfaces in contact that are sliding For surfaces in contact that are sliding with respect to each other, the with respect to each other, the coefficient of kinetic friction is the ratio coefficient of kinetic friction is the ratio of the friction force to the normal force.of the friction force to the normal force.

THE COEFFICIENT OF KINETIC THE COEFFICIENT OF KINETIC FRICTIONFRICTION

THE COEFFICIENT OF KINETIC THE COEFFICIENT OF KINETIC FRICTIONFRICTION

k

friction force

normal force

N

F

For surfaces in contact on the verge of For surfaces in contact on the verge of sliding with respect to each other the sliding with respect to each other the coefficient of static friction is the ratio of coefficient of static friction is the ratio of the maximum static friction force to the the maximum static friction force to the normal force.normal force.

THE COEFFICIENT OF STATIC THE COEFFICIENT OF STATIC FRICTIONFRICTION

THE COEFFICIENT OF STATIC THE COEFFICIENT OF STATIC FRICTIONFRICTION

s

maximum static friction force

normal force s max

N

F

FRICTIONFRICTION

Friction opposes the motion between surfaces in Friction opposes the motion between surfaces in contact with one another.contact with one another.

When there is a tendency for movement When there is a tendency for movement between two surfaces and yet there is no between two surfaces and yet there is no motion, the friction is static friction.motion, the friction is static friction.

Static friction has an upper limit.Static friction has an upper limit.

When there is motion between the two surfaces, When there is motion between the two surfaces, the friction is kinetic (sliding) friction.the friction is kinetic (sliding) friction.

FAFA

On the verge of slipping

Maximum Static Friction

Applied Force, FA

Friction, F

Kinetic (sliding) Friction

Sliding

FFFFAFA F FA

DIMENSIONAL ANALYSIS:DIMENSIONAL ANALYSIS:

Fundamental DimensionsFundamental Dimensions

Length - LLength - L

Mass - mMass - m

Time - tTime - t

Derived dimensions are combinations of Derived dimensions are combinations of the fundamental dimensions. the fundamental dimensions.

For example: length/timeFor example: length/time22

Remember that you can only add or Remember that you can only add or subtract things that are alike.subtract things that are alike.

For example velocity plus velocityFor example velocity plus velocity

212ox v t at

22

L LL t t

t t

MATHEMATICAL OPERATIONS MATHEMATICAL OPERATIONS WITH UNITS:WITH UNITS:

When numbers are placed into equations, When numbers are placed into equations, their units must appear with them.their units must appear with them.

Units undergo the same mathematical Units undergo the same mathematical operation as the numbers do.operation as the numbers do.

Conversion from one form of the unit to Conversion from one form of the unit to another may be necessary.another may be necessary.

For example meters to centimeters.For example meters to centimeters.

See examples in text, page 30.See examples in text, page 30.

Free Body Diagrams (FBD)Free Body Diagrams (FBD)

This is a diagram showing some object and This is a diagram showing some object and the forces applied to it.the forces applied to it.

It contains only forces and coordinate It contains only forces and coordinate information, nothing else.information, nothing else.

There are only two kinds of forces to be There are only two kinds of forces to be considered in mechanics:considered in mechanics:

Force of gravityForce of gravity

Contact forcesContact forces

Example FBDExample FBDA car of mass m rests on a 30A car of mass m rests on a 3000 incline. incline.

mg

N

F

x

y

FBD

yma

sinmg

Newton’s Second LawNewton’s Second LawNSLNSL

A car of mass m rests on a 30A car of mass m rests on a 3000 incline. incline.

mg

N

F

NSL

x xF ma

y yF ma

x

y

F xma

N cosmg

What if friction is smaller?

FBD

Newton’s Second LawNewton’s Second LawNSLNSL

A car of mass m rests on a 30A car of mass m rests on a 3000 incline. incline.

mg

N

F

NSL

x xF ma sin xmg ma F

y yF ma

cos yN mg ma oops

x

y

FBD