Newton’s First & Second Law

AP Physics C

Facts about FORCE

• Unit is the NEWTON(N)• Is by definition a push or a pull• Can exist during physical

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

called FIELD FORCES ( gravitational, electric, etc)

Newton’s First Law – The Law of Inertia

INERTIA – a quantity of matter, also called MASS. Italian for “LAZY”. Unit for MASS = kilogram.

Weight or Force due to Gravity is how your MASS is effected by gravity. mgW

NOTE: MASS and WEIGHT are NOT the same thing. MASS never changesWhen an object moves to a different planet.

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(

Example Problem

Sam weighs 270 N on Mercury, and Andy weighs 530 N on Venus. Who has a larger mass? The acceleration due to gravity on Mercury is 3.59 m/s2 and the acceleration due to gravity for Venus is 8.87 m/s2.

Newton’s First LawAn 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.

There are TWO conditions here and one constraint.

Condition #1 – The object CAN move but must be at a CONSTANT SPEEDCondition #2 – The object is at RESTConstraint – As long as the forces are BALANCED!!!!! And if all the forces are balanced the SUM of all the forces is ZERO.

The bottom line: There is NO ACCELERATION in this case AND the object must be at EQILIBRIUM ( All the forces cancel out).

00 Facc

Explain Inertia in each of the following situations:

Crash Dummy http://www.cleanvideosearch.com/media/action/yt/watch?videoId=d7iYZPp2zYY

Football /Ref http://www.youtube.com/watch?v=qLp6qH1Izxw Cat http://www.youtube.com/watch?v=xlcL-n-6U-o Cheetah http://www.youtube.com/watch?v=pWWtngjd4oI Working in Space and Inertia http://www.sciencewithmrnoon.com/physics/unit03.htm Straw in Plywood http://www.physics.umd.edu/lecdem/services/demos/demosc3/c3-12.htm Masses on String http://www.physics.umd.edu/lecdem/services/demos/demosc3/c3-03.htm

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

Free Body Diagrams

mg

FNFf

Normal force

The force that keeps one object from invading another object is called the normal force

“Normal” means “perpendicular” You can determine the normal force by

considering all forces that have components perpendicular to a surface

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(

!

Tension A pulling force. Generally exists in a rope, string, or

cable. Arises at the molecular level, when a

rope, string, or cable resists being pulled apart.

Tension (static 2D)

The sum of the horizontal and vertical components of the tension are equal to zero if the system is not accelerating.

15 kg

30o 45o

32 1

Problem: Determine the tension in all three ropes.

15 kg

30o 45o

32 1

T1 = 131 NT2 = 107 NT3 = 147 N

Friction Friction is a force that exists between

two surfaces that opposes a sliding motion

Fs: Static friction exists before sliding occurs, it prevents movement

Fk: Kinetic friction exists after sliding occurs, it opposes motion once objects are moving

• Ff is directly proportional to Fn

(normal force):

• Coefficient of friction ():– Determined by the nature of the

two surfaces – s is for static friction.– k is for kinetic friction.– s > k

μ

f nF F f

n

F

F

Typical Coefficients of Friction

Values for have no units and are approximate

A block pulled to the right on a rough horizontal surface

Two blocks in contact with each other, pushed to the right on a frictionless surface

Two blocks connected by a cord, one is on top of the table, the other is hanging off the side. The table surface is rough, the pulley is frictionless

A block pulled up a rough incline

Now Try These Phun Phree Body Diagrams

Fn

Fa

Fg

Fk

Fn Fa

Fg

Fk

Fn

Fa

Fg

P’

Fn

P

Fg

T

Fg

Fn

T

Fg

Fk

What is the Frictional force in this situation? EXPLAIN

Mass of the block is 500 g Force applied is 3 N. = 0.75 The Block is stationary

Classroom Practice Problem

Sample problem: A 1.00 kg book is held against a wall by pressing it against the wall with a force of 50.00 N. What must be the minimum coefficient of friction between the book and the wall, such that the book does not slide down the wall?

Fμs = .196

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 into COMPONENTS• Write equations of equilibrium• Solve for unknowns

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 over power the others.

THE OBJECT WILL THEN 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.

• Solve for any unknowns

Newton’s 2nd Law

A 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

Problem: A hockey puck has an initial velocity of 20 m/s. If the puck slide 115m before coming to a stop, what is the coefficient of kinetic friction between the puck and the ice?

μk = .196

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

Example

amT

amTgm

maFNet

1

22

NT 1.23)7.7)(3(

Run

RiseSlope

ma

FmaF NET

Net

Non-constant Forces

Up until this time, we have mainly dealt with forces that are constant. These produce a uniform, constant acceleration.

Kinematic equations can be used with these forces.

However, not all forces are constant.• Forces can vary with time, velocity, and with

position.

Calculus Concepts forForces That Vary With Time

The Derivative• The derivative yields tangent lines and slopes• We use the derivative to go from

• position -> velocity -> acceleration

The Integral• The integral yields the area under a curve• Use the integral to go from

• acceleration -> velocity -> position

In these two approaches, F = ma, so methods for determining or using acceleration are also used to find force

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

Sample problem: Consider a force that is a function of time:

◦ F(t) = (3.0 t – 0.5 t2)N If this force acts upon a 0.2 kg particle at rest for 3.0 seconds,

what is the resulting velocity and position of the particle?

vf = 45 m/sxf = 50.6 m

Sample problem: Consider a force that is a function of time:

F(t) = (16 t2 – 8 t + 4)N If this force acts upon a 4 kg particle at rest for 1.0 seconds, what is

the resulting change in velocity of the particle?

Δv = 1.33 m/s