Newton’s First & Second Law

AP Physics C

Facts about FORCE

• Unit is the Newton(N) or pound (lb)• Is by definition a …..

push or a pull• Can exist during physical contact

(Tension, Friction, Applied Force)• Can exist with NO physical contact• called Fundamental Forces

(gravitational, electric, nuclear FIELDS)

Newton’s First Law – The Law of Inertia

INERTIA – the more of it you have, the harder it is to get you moving.

Modern definition: a quantity of matter, also called … MASS. Unit for MASS = kilogram. NOTE: MASS and WEIGHT are NOT the same

thing. MASS never changes when an object moves

to a different planet.

mgW

Weight is a force due to Gravity. It is how your MASS is effected by gravity.

What is the weight of an 85.3-kg person on earth? On Mars=3.2 m/s/s)?

NW

NWmgW

MARS 96.272)2.3)(3.85(

94.835)8.9)(3.85(

Inerte in Galileo’s Italian meant “lazy”

Newton’s First Law is really Galileo’s Law of Inertia

An object in motion remains in motion in a straight line and at a constant speed OR an object at rest remains at rest, UNLESS acted upon by an EXTERNAL (unbalanced) force.

The bottom line: There is NO ACCELERATION (no change in velocity) unless a force acts, but you can have MOTION even if there is NO force acting.

“Common sense” told us the opposite for generations, so inertia was a real intellectual breakthrough.

EQUILIBRIUM is when there are either NO FORCES acting or those that are acting all cancel each other out.

00 Facc

Free Body Diagrams

A pictorial representation of forces complete with labels.

W1,Fg1 or m1g

• Weight(mg) – Always drawn from the center, straight down

• Force Normal(FN) – A surface force always drawn perpendicular to a surface.

• Tension(T or FT) – force in ropes and always drawn AWAY from object.

• Friction(Ff)- Always drawn opposing the motion.

m2g

T

TFN

Ff

It helps if you first circle the object you are analyzing, and labe only the forces acting ON IT. Other than gravity, these forces must involve physical contact.

Free Body Diagrams

mg

FNFf

N.F.L and Equilibrium

Since the Fnet = 0, a system moving at a constant speed or at rest MUST be at EQUILIBRIUM.

TIPS for solving problems• Draw a FBD• Resolve anything at angles into

COMPONENTS• Write equations of equilibrium• Solve for unknowns

ExampleA 10-kg box is being pulled across the table to the

right at a constant speed with a force of 50N.a) Calculate the Force of Friction

b) Calculate the Force Normal

mg

FNFa

Ff

NFF fa 50

NFmg n 98)8.9)(10(

ExampleSuppose the same box is now pulled at an angle of 30

degrees above the horizontal.a) Calculate the Force of Friction

b) Calculate the Force Normal

mg

FN Fa

Ff30

NFF

NFF

axf

aax

3.43

3.4330cos50cos

Fax

Fay

NF

FmgF

mgFF

mgF

N

ayN

ayN

N

73

30sin50)8.9)(10(

!

What if it is NOT at Equilibrium?

If an object is NOT at rest or moving at a constant speed, that means the FORCES are UNBALANCED. One force(s) in a certain direction overpowers the others.

THEN THE OBJECT WILL…..

ACCELERATE.

Newton’s Second Law

The acceleration of an object is directly proportional to the NET FORCE and inversely proportional to the mass.

maFm

Fa

maFa

NETNET

NET

1 FFNET

Tips:• Draw an FBD• Resolve vectors into components• Write equations of motion by adding

and subtracting vectors to find the NET FORCE. Always write larger force – smaller force.

• Solve for any unknowns

ExampleA 10-kg box is being pulled across the table to

the right by a rope with an applied force of 50N. Calculate the acceleration of the box if a 12 N frictional force acts upon it.

mg

FNFa

Ff

2/8.3

101250

sma

a

maFF

maF

fa

Net

In which

direction, is this object accelerating?

The X direction!

So N.S.L. is worked out using the forces in the “x” direction only

Example

m1g

m2g

T

TFN

A mass, m1 = 3.00kg, is resting on a frictionless horizontal table is connected to a cable that passes over a pulley and then is fastened to a hanging mass, m2 = 11.0 kg as shown below. Find the acceleration of each mass and the tension in the cable.

amT

amTgm

maFNet

1

22

2

21

2

122

122

212

/7.714

)8.9)(11(

)(

smmm

gma

mmagm

amamgm

amamgm

Now that we know a we can find F

amT

amTgm

maFNet

1

22

NT 1.23)7.7)(3(

Run

RiseSlope

ma

FmaF NET

Net

Where does the calculus fit in?

dt

xdm

dt

dvmamF

2

First derivative

Second derivative

DON’T WORRY ABOUT THE STUFF ON THIS SLIDE OR THE NEXT FOR NOW.

Where does the calculus fit in?

dt

xdm

dt

dvmamF

2

220.03)( tttv

There could be situations where you are given a displacement function or velocity function. The derivative will need to be taken once or twice in order to get the acceleration. Here is an example.

You are standing on a bathroom scale in an elevator in a tall building. Your mass is 72-kg. The elevator starts from rest and travels upward with a speed that varies with time according to:

When t = 4.0s , what is the reading on the bathroom scale (a.k.a. Force Normal)?

)4(40.03)4(

40.03)20.03( 2

a

tdt

ttd

dt

dva

4.6 m/s/s

)6.4)(72()8.9)(72(N

NN

net

F

mgmaFmamgF

maF

1036.8 N

DON’T WORRY ABOUT THE STUFF ON THIS SLIDE UNTIL NOVEMBER

m1g

m2g

T

TFN

A mass, m1 = 3.00kg, is resting on a frictionless horizontal table is connected to a cable that passes over a pulley and then is fastened to a hanging mass, m2 = 11.0 kg as shown below. Find the acceleration of each mass and the tension in the cable.