LINEAR MOTION How would you describe the motion of a 100m runner? To illustrate his motion we use a velocity time graph and then using the following equations.

MECHANICS

LINEAR MOTION

How would you describe the motion of a 100m runner? To illustrate his motion we use a velocity time graph and then using the following equations. Graphs

We can calculate speed, velocity and acceleration along with distance and time.

UVAST Equations

We need to understand the meaning of the quantities in the formulae; Speed (v) is the distance travelled per unit timeDisplacement (s) is the distance in a given directionVelocity (v or u), the rate of change of displacement with respect to timeAcceleration (a) is the rate of change of velocity with respect to time

The Physics of sky diving

Sky diving from space

SCALARS AND VECTORS

All quantities can be split into scalars or vectors 

Scalars have magnitude only and no direction; length, area, volume, speed, time

Vectors have magnitude and direction; force, acceleration, velocity, displacement

Head to Head

FORCES

What is the physics behind an accelerating spacecraft?

When a spacecraft is speeding up, slowing down or changing direction it must expel gas in the opposite direction to the acceleration. The momentum of the spacecraft i.e. its mass x velocity is equal to but in the opposite direction to the gas.

Rocket Travel

MASS The Mass of an object

is a measure of how difficult it is to accelerate that object.

The Mass of an object is a measure of its Inertia.

(The inertia of an object in turn is a measure of how difficult it is to accelerate it.)

The unit of mass is the Kilogram (kg).

MOMENTUM

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Tyndall Lecture

Momentum (p) is the product of mass and velocity

Unit = kgms-1

  The total momentum before

an interaction is equal to the total momentum after.

m1u1 + m2u2 = m1v1 + m2v2

  The principle of conservation

of momentum above is applied directly to snooker or pool

Maths Bit

Question:What is the momentum of a rugby player with mass of 110kg traveling east at 8m/s ?

Answer: p=mv =110 x 8 = 880 kgms-1 east

Question:

Two snooker balls of the same mass, moving in opposite directions, collide head on. The pink ball is moving to the right at 5 m/s, the blue is moving at 3m/s. The pink ball is brought to rest by the collision.

a) What is the velocity of the blue ball after the collision?

b) What is the change in momentum of each ball?

Answer:

a) (movement to the right is + ,movement to the left is - )

m1u1 + m2u2 = m1v1 + m2v2

(m)(5)+(m)(-3)=m(0)+(m)(v)

5m- 3m= mv2m =mv2=v

Velocity after in 2m/s to the right

b) Pink ball:Change =after –before

= m(0) –m(5)=-5m

Change in momentum of pink ball is 5 kgms-1 to the left

c) Blue ball:Change =after –before

= m(2) –m(-3)=5m

Change in momentum of blue ball is 5 kgms-1 to the right

FORCE

Force (F) is that which can cause acceleration

F = ma

Acceleration is proportional to forceSony Ad

The Newton

The Newton is the unit of Force.

Def: 1 newton is the force that gives a mass of 1 kg

an acceleration of 1 ms-2

1 N = 1 kgms-2

Weight

The weight of an object is the force of the earth’s gravity acting on it

W = mg (W = weight, m = mass, g = acceleration due to

gravity)

Mass is constant, Weight changes depending on your position.

Newton’s 1st Law

A body will remain at rest or continue moving at constant velocity unless acted upon by an external force.

Newton’s 2nd Law

The rate of change of momentum is proportional to the applied force and takes place in the direction of the force

Newton’s 3rd Law

To every action there is an equal and opposite reaction

To Show that F = ma is a special case of Newton’s Second Law

From Newton II: Force is proportional to the rate of change of momentum

Force rate of change of momentumF (mv – mu)/t

F m(v-u)/tF ma

F = k (ma)F = ma

Friction

Friction is a force that opposes the motion of a body. It allows tyres to grip the road or the soles of your shoes to grip the path.

Terminal Velocity

Diagram Page 96

Initially only force is weight. a>0

As velocity increases air resistance begins to oppose motion. a>0

Eventually speed reached where resistance is equal to force, velocity becomes constant. a=0

MEASUREMENT OF ACCELERATION DUE TO GRAVITY (g) USING THE FREEFALL METHOD

APPARATUS : Millisecond timer, metal ball, trapdoor and electromagnet

TO SHOW THAT ACCELERATION IS PROPORTIONAL TO THE FORCE WHICH CAUSE IT

 APPARATUS Set of weights,

electronic balance, trolley, ticker-tape timer and tape.

DIAGRAM

Density

Density is defined as Mass per unit Volume

The unit of density is the kgm-3

 The symbol for density is (pronounced ‘row’ – same symbol as for momentum – don’t ask!)

= m/V

Phet

Pressure is defined as Force per unit Area.The unit of Pressure is the Pascal (Pa)

1 Pascal =1 newton per square metre

1 Pa = 1 Nm-2

Pressure

Pressure in a liquid at a height h below the surface

P = gh

P= pressure

= density

g = acceleration due to gravity

h = depth in a liquid

1. Pressure increase with depth

2. Pressure acts perpendicular to any surface put in the liquid

3. At a given depth the value of the pressure is the same in all directions

Archimedes’ Principle

When a body is partly or wholly immersed in a fluid it experiences an upthrust equal to the weight of the fluid displaced

(Demonstration)

The law of Flotation

The weight of a floating body is equal to the weight of the fluid it displaces

What is a hydrometer?

A hydrometer measures the density of liquids. Density is mass per unit volume. The hydrometer is based on the principle of Archimedes. The less dense the liquid the lower the hydrometer will sink.

Uses of Hydrometers

Used to find the percentage alcohol in beers, wines and spirits (alcohol is less dense than water)

The density of sulphuric acid in a lead acid battery and hence determine the charge of the battery.

The percentage of fat in milk, and to check that the milk has not been watered down

The physics of weather

We are surrounded by atmospheric pressure. Pressure is force per unit area. The pressure exerted by the air is roughly 101.3kPa or 1x105 Pa at sea level. Variations in this pressure have an effect on the weather. Low pressure gives us cloudy, wet, windy weather. High pressure results in fine, sunny weather.

Why does water boil at a lower temperature the higher up you go?

The higher you go the less the atmospheric pressure is an the less molecules there are pressing down on the water therefore the water needs less energy to move and will boil at a lower temperature than 100oCBed of Nails

Boyle’s Law

Pressure is inversely proportional to volume for a fixed mass of gas at constant temperature. A good example of Boyle’s law is the use of a syringe.

Exp

Application

If the pressure is doubled the volume is halved

If the pressure is trebled the volume is decreased by 1/3

Graph of p against 1/V is straight line through the origin.

pV =k

For a fixed mass of gas at constant temperature

pV =k

Where k is a constant

P =pressure V=volume K =constant

Newton’s Law of Universal Gravitation

The force of attraction between two point masses is proportional to the product of their masses and inversely proportional to the square of the distance between them. Orders of magnitudeMotion round the earth

Moment

Moment is the force by the perpendicular distance. The further the distance the bigger the moment

A Lever

A lever is a rigid body that is free to rotate about a fixed axisA Couple A couple is a pair of equal and opposite forces whose lines of action don’t coincide.

Equilibrium

If a body is said to be in equilibrium it must satisfy the following; The forces up equal forces down and the forces left equal forces rightThe sum of the clockwise moments equal the sum of the anticlockwise moments

ENERGY

All Energy comes from the sun. We make use of the fusion reactions of the sun for our energy. Fusion is a form of nuclear reaction whereby small nuclei combine to form large nuclei giving a lot of energy.

ENERGY

We define energy as the ability to do work

We define work as the product of force and displacement W = F × s

Forms of Energy

Kinetic Energy is the energy a body has due to its motion

FORMS OF ENERGY

Potential Energy is the energy a body has due to its position

Snowboarding

FORMS OF ENERGY

Heat Energy is the kinetic energy of its internal particles

FORMS OF ENERGY

Sound Energy is the energy of vibrating particles in the medium it travels through

FORMS OF ENERGY

Electrical Energy is the energy as the result of the motion of electric charge

FORMS OF ENERGY

Chemical Energy is the energy stored within the chemical bonds of molecules

FORMS OF ENERGY

Nuclear Energy is the energy stored in the nucleus of an atom

Principle of Conservation of Energy

Energy cannot be created or destroyed but changes from one form to another.

Watt is the unit of Power!! 

All electrical devices have a power rating on them. This allows us to calculate the rate at which work is done or energy is used.The efficiency of the appliance is a measure of how good it is at converting energies without waste.

Elasticity

Many objects change shape when a force is applied to them, e.g. elastic band. When the force is removed the object may return to its original shape, i.e. object is said to be elastic.

Elasticity

If the force applied is too great the object remains permanently strained it has exceeded its elastic limit.

The force trying to pull the object back into its original position is the restoring force. This force is directly proportional to the displacement.

Hooke’s Law

Hooke’s law states that when an object is bent, stretched or compressed by a displacement ‘s’, the restoring force ‘F’ is directly proportional to the displacement-provided the elastic limit is not exceeded.

F = – k s

where k = elastic constant

Experiment App

The equation is known as Hooke’s Law (after Robert Hooke (1635-1703), an inventor, philosopher, architect, ...)

Simple Harmonic Motion

Position O is called the equilibrium

position. If pulled beyond O it vibrates

up and down. When doing this the

particle can be said to be moving in

simple harmonic motion.

Definition: A body is said to be moving

with simple harmonic motion if:

1. Its acceleration is directly

proportional to its distance from a

fixed point on its path.

2. Its acceleration is always directed

towards that point.

CIRCULAR MOTION

Angles in Radians

We usually measure angles in degrees.

360° = 1 rotation

But it's not the most convenient way to measure angles in circular motion.

Radians. The radius of a circle and its circumference are

related by the equation

Circumference = 2πr

360° ≡ 2π radians and 180° ≡ π radians

Formula

s = rθ Where: s = arc length covered r = radius of the circle θ = angle in radians

Angular Velocity Angular Velocity is the

rate of change of angle with respect to time.

Angular Velocity is measured in radians per second, (rad/s).

The symbol for angular velocity is (pronounced“omega”).

Relationship between Linear Speed (v) and Angular Velocity ()

Centripetal Force

The force - acting in towards the centre - required to keep an object moving in a circle is called Centripetal Force.

Centripetal Acceleration

If a body is moving in a circle the acceleration it has towards the centre is called Centripetal Acceleration. 

Circular Satellite Orbits

Geostationary Satellites

These satellites are stationery over one position of the globe

We know that if we want a satellite to remain over a specific spot on the Earth’s surface it must have the same periodic time as the Earth (24 hours).