Newton’s Laws

Mechanics - Study of MotionMechanics - the study of motion

Kinematics - How things move (time line for foundation of kinematics- early 1600's)

work done by Galileo, – Why do all things accelerate at one rate?– How does the earth know to pull on more massive objects with

a proportionally larger force than it pulls on smaller masses? work done by Kepler

– What is the force that emanates from the sun that is responsible for holding planets in elliptical orbits?

Dynamics - Why things move as they do work done by Isaac Newton,

– Work began in 1666– we will see in a later lecture how Newton unified these

two seemingly unrelated fields with one master stroke– His work led to the belief that all one had to do was to

understand the rules governing motion and the world behaved as a machine – producing the same result for the same given input

There are only THREE types of motion that we need to describe: a. objects at rest

b. objects moving with constant velocity c. objects that are accelerating

InertiaAristotelian View of Forces

a. The natural state of an object is to be at rest.b. In order to get an object to move, one must apply a force. (Push a book, etc.)c. However, once the force is taken away, the object once again comes to rest.

Galileo's ramp experiments

Clearly the implication would be that it would continue on with uniform motion forever.

Galileo’s Definition of Inertia: the tendency of an object to resist a change in motion. (the more massive an object, the greater its inertia)

Newton summarizes Aristotelian and Galilean physics by stating in his book Principia his 1st Law of Motion (what we have come to refer to as the Law of Inertia) :

Regardless of the angle of ramp C the ball always seemed to rise to the same height that it had on ramp B. What would happen if he were to remove ramp C?

Law Of InertiaNewton's 1st Law - An object at rest, or in uniform straight line motion, will remain at rest, or

in uniform straight line motion, unless acted upon by a net external force.Another way to state this law might be: If there are no net external forces acting on a body, then it will

continue in it's state of constant velocity (which may be zero).

This is easier to write mathematically.

which translates to: if we add up all of the forces acting on a body from 1 to the nth force and get zero as the resultant, then the body is moving with constant velocity.

n

nn vF

1

constant then ,0 if

Newton’s 2nd LawNewton also explains what happens when the forces do not add up to be zero. Newton's 2nd Law - A net force acting on a body produces on that body, an acceleration

that is directly related to the force impressed upon the body and inversely related to the mass of the body.

An easier way to state it is:

The units of force are directly derived from this formula

units of force = kg m/s2.

This is sufficiently lengthy enough to warrant a short hand version. Thus a unit of force is called a Newton (N) and was made in his honor. Thus, when keeping track of units:

N = kg m/s2

Since acceleration is a vector quantity, force is a vector quantity as well.Caution - a common mistake in solving problems is forgetting to add up all of the forces before applying the second part of Newton's 2nd Law.

n

nnetnetn amFFF

1

then , if

Field versus Contact ForcesFor our purposes we will define a force as a push or a pull on an object.

There are really only four quantified forces in all of nature:Strong interactionWeak interactionElectromagneticGravitation

We will categorize forces into two categories:

Contact forces – forces that result from the physical contact between two objects

Field Forces – forces that arise from the interaction of an object located within a field of influence of another object. E.g., an object in the gravitational field of the earth, or the earth within the gravitational field of the sun, or an electron within the electric field of a proton, or a piece of iron near a magnet, et cetera.

3rd Law, Weight, and Normal ForceNewton's 3rd Law - For every action there is an equal but

opposite reactionor mathematically stated:

Example: Weight - the force with which a gravitational body (such as the earth) pulls on a bodyMathematically it is defined as:Any body that has mass, has weight when it is near to a gravitational body. When a person (mass = 70 kg) is standing on a floor, the force that he exerts on the floor is his weight

It is an observation of Newton that forces naturally occur in pairs

baab FF

€

rW = m

r g

3rd Law, Weight, and Normal ForceThe floor, by Newton's 3rd Law, exerts an equal but opposite force of 686N to

prevent the person from falling through the floor.

This force that acts perpendicular to the floor is referred to as the Normal Force and is another example of a Contact Force that we will encounter frequently.

It is referred to as the normal force, not because it is always there, but because the term normal is a mathematical term that means perpendicular.

Not all surfaces are capable of exerting a force equal in magnitude to the weight of object placed upon them. Thin ice is a good example, but almost any surface can be destroyed, or broken, by placing a sufficiently large mass upon it.

How does this Normal Force Arise?What then, is the nature of this normal force that surfaces seem to exert? How does a wall

know to push back harder when I push with increasing force?

At the most basic level the object placed upon a surface is repelled by electromagnetism.

The outer most electrons that comprise the object are electrically repelled by the electrons that comprise the surface.

The electrons offer a stronger and stronger repulsive force the closer and closer the object is moved to the surface - just as two similar ends of magnets repel any effort to touch them together.

We can break the electric bonds between the atoms that make up the surface if we exert a large enough force.

Hence the more massive an object, the greater gravity tends to pull them onto a surface, and the greater the surface tends to repel the object.

The object will be at rest on the surface (according to Newt's 1st Law) only if the surface is capable of exerting an equal and opposite force to sustain it, otherwise the object crashes through the surface.

Example30N

10kg5kg

What force does the 5kg block exert on the 10 kg block?

2/215/30

)510(30

sma

a

amFnet

NF

F

F

amFFN

on

on

on

neton

10

)2(1030

)2(1030

30

105

105

105

105

Focusing on the 10kg object…

30N F5on10

Focusing on the 5kg object…

F10on5

NF

amF

on

on

102)5(510

510

Look at the two block system as a single object…

(N2L)

(N3L)

Free Body Diagrams

Free Body Diagrams

€

rF BL

€

rF G

x

y

€

rT 1L

€

rT 2L

Free Body Diagrams

€

rF BL

€

rF G

x

y

€

rT 1L

€

rT 2L

θ2θ1

θ2θ1

Train

C1C2C3

Three railroad cars are being pulled with a force of 12,000 N. Car 1 has a mass of 2000kg, car 2 has a mass of 3000 kg, and car 3 has a mass of 5000kg. Neglecting friction, what is the acceleration of the train and what is the force between car 2 and 3?

Solution

2/2.110000/12000

)500030002000(000,12

sma

a

amFnet

Car 3 we already know is accelerating at 1.2 m/s2 so it must have a net force acting on it (provided by Car 2) of:F23= 5000(1.2) = 6000N

C1C2C3

Think of all three cars as a single object whose mass is equivalent to the total masses of the three cars. For now, look at only the horizontal sense.

A free body diagram would indicate only one force if we neglect frictional forces

C1C2C3

A free body diagram of car 3 would indicate only that car 2 is pulling on it

F net

F23

Tug of WarTwo teams are comprised of equal strength players, each capable

of pulling with a force of 400 Newtons. Each team has 4 players each. Each person has a mass of 80 kgs.

In this case, the two forces exerted horizontally add up vectorally to be zero. Does that mean the rope is not moving?

Examples cont.

Now there is a net force of 20 Newtons to the right. This net force is acting upon a total mass of 640 kg (excluding the rope) which produces an acceleration of:

An additional force is exerted by one of the players who becomes psyched. This person now pulls with a force of 420N

€

rF net = m

r a

r a =

r F net

m = 20 N /640 kgr a = 0.03 m/s2