2.1 - Newtons Laws

Agenda:

Good Things!

Look at the test?

Begin Forces & Dynamics

 Newton’s Laws

 1st & 2nd Law Worksheet

Our next unit:

We have just finished studying

kinematics – using numbers to describe

motion.

We have only been talking about things

that are in motion, but have not

discussed why they are in motion.

Why does stuff move?

Sir Isaac Newton

“If I have seen further than others, it is by standing upon the shoulders of giants.”

1643 – 1727: (Born the same year Galileo died)

1665 – 1667: Studied at Cambridge (Same time as the great plague in London), co-invented calculus, determined the composition of white light

1687 – Published Principia Mathematica explaining his 3 laws of motion

1696 – 1727: Left Cambridge to live in London, ceased any scientific or mathematical work, was

Newton´s Laws

The First Law

Every object continues

in a state of rest or

uniform motion in a

straight line unless

acted upon by an

Newton’s 1

Law of Motion

Actually, this is a restatement of Galileo’s idea of “inertia”

Every object continues in a

state of rest or uniform motion

in a straight line unless acted

upon by an external force

•

What does that actually

mean

?



Things tend to keep doing whatever

they are currently doing.



You have to apply some kind of force

to make an object change what it is

doing.



Inertia is an object’s resistance to

change.



Mass is the measurement of inertia.

Inertia

Inertia causes stationary objects to stay

stationary.

It causes moving objects to keep moving

in a straight line with constant velocity.

Examples:

 Bowling ball rolling on a hard surface  Hockey puck gliding on ice

 Spacecraft sent out of Earth’s orbit  Satellites (17,000 mph at 150 miles)

Inertia in moving objects

Once something is moving, it requires

no

force to keep moving

 This is counter-intuitive. You see something

moving and think about what made it move.

 Yes, something made it move in the first

place, but once moving, it would require a force to make it STOP.

Equilibrium

If a body is acted upon by a number of coplanar forces and is in equilibrium ( i.e. there is rest (static equilibrium) or unaccelerated motion (dynamic equilibrium)) then the following condition must apply

Newton´s Laws

The Second Law

Newton´s Second Law

1st version

The Physics of Drag Racing:

Let’s say you want to make your car as fast

as possible for a race, what could you do?

 Add more power (increase the force)  Decrease the mass

As force goes up, acceleration goes up.

 These are directly proportional.

As mass goes down, acceleration goes up.

Force, mass, and acceleration:

In physics, we like to capture these

relationships in an equation whenever

possible.

a =

/

m

This is Newton’s 2

Law of Motion

 Usually, it is written as

F

Units for force:

If F = ma



The standard (SI) unit for mass is

kilogram (kg)



Acceleration has units of m/s

.



So, F = kg•m/s



The units for force are kg•m/s

or

How does this relate to gravity?

We have already talked about gravity as a force that causes acceleration.

 Remember the acceleration in the y direction for all of

those fun projectile problems?

Also remember, that we have stated that gravity has a constant acceleration of 9.81 m/s2

Constant acceleration from

gravity

Galileo found that balls of different masses fell at the same rate.

The force of gravity is

stronger for more massive objects.

But it requires more force to accelerate a more

Mass vs. Weight

Mass is how we measure inertia

 It is a measure of the amount of matter in an object.

 It is a scalar quantity, it has just a magnitude.

 It does not depend on gravity and does not change.

Weight is the force of gravity acting on a body.

 It is found by F_w = mg

 It is a vector quantity with magnitude and direction.

Newton´s Second Law

2nd version

The rate of change of

momentum of a body is

proportional to the

resultant force and

occurs in the direction of

the force.

Linear Momentum

The momentum p of a body of constant mass

m moving with velocity v is, by definition mv

Momentum of a body is defined as the mass of the body multiplied by its velocity

Momentum = mass x velocity

p = mv

It is a vector quantity

Its units are kg m s-1 or Ns

Impulse

From Newtons second law

F = mv – mu F = t t

Ft = mv – mu

This quantity Ft is called the impulse of the force on the body and it is equal to the

change in momentum of a body. It is a vector quantity

Law of Conservation of Linear

Momentum

The law can be stated thus

When bodies in a system interact the

total momentum remains constant

Deriving This Law

To derive this law we apply Newton´s 2nd law

to each body and Newton´s 3rd law to the

system

i.e. Imagine 2 bodies A and B interacting

If A has a mass of m_A and B has a mass m_B If

Then the force on A given by Newton 2 is F_A = m_Av_A – m_Au_A t

And the force on B is

F_B = m_Bv_B – m_Bu_B t

Therefore m_Av_A – m_Au_A = -(m_Bv_B – m_Bu_B) t t

Therefore m_Av_A – m_Au_A =

m_Bu_B – m_Bv_B

Rearranging m_Av_A + m_Bv_B

= m_Au_A + m_Bu_B

Newton´s Laws

The Third Law

When two bodies A

and B interact, the

force that A exerts on B

is equal and opposite

Example of Newton´s 3

Q. According to Newton’s third Law

what is the opposite force to your

weight?

A. As your weight is the pull of the

Newton´s 3

Law

The law is stating that forces never occur singularly but always in pairs as a result of the interaction between two bodies.

For example, when you step forward from rest, your foot pushes backwards on the Earth and the Earth exerts an equal and opposite force forward on you.

Important

The equal and

opposite forces

do not act on the

Forces and Free-body

Diagrams

To a physicist a force is recognised by

the effect or effects that it produces

A force is something that can cause an

object to

 Deform (i.e. change its shape)  Speed up

 Slow Down

The last three of these can be

summarised by stating that a force

produces a change in velocity

Free-body Diagrams

A free-body diagram is a diagram in which

the forces acting on the body are represented by lines with arrows.

The length of the lines represent the relative magnitude of the forces.

The lines point in the direction of the force.

The forces act from the centre of mass of the body

Example 1

Normal/Contact Force

Example 2

A car moving with a constant velocity

Normal/Contact Force

Example 3

A plane accelerating horizontally

Upthrust/Lift

Resolving Forces

Q. A force of 50N is applied to a block

on a worktop at an angle of 30

to the

horizontal.

Answer

First we need to draw a free-body diagram

30o

We can then resolve the force into the

2 components

30o

50N Vertical = 50 sin 30o

Therefore

 Vertical = 50 sin 30o = 25N

Determining the Resultant

Force

Two forces act on a body P as shown in

the diagram

Find the resultant force on the body.

30o

50N

Resolve the forces into the vertical and

horizontal componenets (where

applicable)

Solution

30o

50N

30N

50 sin 30o

Add horizontal components and add

vertical components.

50 sin 30o = 25N

Now combine these 2 components

25N

13.3N R

R2 = 252 + 13.32

Finally to Find the Angle

25N

13.3N R



tan  = 25/13.3  = 61.987  = 62o

The answer is therefore 28N at 62o upwards from

Springs

The extension of a spring which obeys Hooke ´s law is directly proportional to the

extending tension

A mass m attached to the end of a spring

exerts a downward tension mg on it and if it is stretched by an amount x, then if k is the tension required to produce unit extension (called the spring constant and measured in Nm-1) the stretching tension is also kx and

so

Spring Diagram