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speed (m/s) = distance travelled (m) / time taken (s)

Usually when an object travels from ‘A’ to ‘B’ it’s velocity will vary so a calculation of it’s velocity is really an average velocity.

An instantaneous velocity is the velocity at a given moment.

Distances measured in one direction are positive, and in the other, negative.

A negative velocity means moving in the opposite direction.

9

8

7

6

5

4

3

2

1

0

D i s t a n c e (m)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Time (s)

1. What is the velocity of the object at first ?

9 3 = 3 m/s

2. For how long was the object stationary ?

6 s

3. What is the velocity in the last part ?

9 6 = - 1.5 m/s

1. A ball is thrown and takes 4 seconds for its velocity to steadily increase to 4 m/s and then travels at a constant velocity for 5 seconds. It then hits a wall and rebounds at a constant velocity of 3 m/s for 5 s before it is caught.

5

4

3

2

1

0

-1

-2

-3

-4

-5

Velocity

(m/s)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Time (s)

2. An object moves at a velocity of 2 m/s for 3 seconds and then accelerates at 1 m/s2 for 2 seconds. It then moves at a constant velocity for 3 seconds and then decelerates at 1 m/s2 until it is stationary. It remains stationary for 2 seconds and then accelerates backwards at 2 m/s2 for 1 second. It then takes 2 seconds to steadily decelerate till it stops.

5

4

3

2

1

0

-1

-2

-3

-4

-5

V e l o c i t y (m/s)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Time (s)

A woman walks out onto the road

A car is travelling at 30 km/hr

X

Will she survive ?

8 m

The driver has a reaction time of 1 second

30 km = 30,000 m

1 hr = 3,600 s

In 1 second the car would travel 30,000 3,600 = 8.33 m

The woman is hit BEFORE the driver applies the brakes !!!!

distance

time

For a distance-time graph a steeper gradient means a higher speed

A tachometer continuously measures an objects speed and can be used to make a tachograph.

If the speed of an object is increasing, we say

that it is accelerating.

Acceleration (m/s2) = change of velocity, m/s

time taken for the change (s)

A force arises from an interaction between two objects.

When one object exerts a force on another, it always experiences a force in return (a reaction force).

A force and a reaction force are called an ‘interaction pair’.

The two forces in an interaction pair are equal in size and opposite in direction and they act on different objects.

the box acts downwards on the table due to gravity

the table acts upwards on the box due to the reaction force

the two forces are equal and opposite

gravity

reaction force of friction on acting on the feet

force of the feet acting on the ground

reaction force of the ground acting on the feet

The horizontal motion of objects (like cars and bicycles) can be analysed in terms of a driving force (produced by the engine or the cyclist), and a counter force (due to friction and air resistance).

driving force greater than counter force – speeding up

driving force equal to counter force – stationary

driving force less than counter force – slowing down

A resultant force takes into account all the acting forces.

30N

20N

50N

resultant force = 20N

Friction is the interaction between two surfaces

when they slide over each other

There is a friction force on both objects involved

Friction is caused by the roughness of the sliding surfaces

Friction enables cars and people to get moving

momentum (kg m/s) = mass (kg) × velocity (m/s)

A car has a mass of 5,000 kg and a velocity of 4 m/s.

What is the car’s momentum ?

5,000 x 4 = 20,000 kg m/s

A cyclist cycling at 10 m/s has a momentum of 540 kg m/s.

The cyclist has a mass of 50 kg, what’s the mass of the bike ?

total mass = 540 / 10 = 54 kg mass of bike = 54 – 50 = 4 kg

If a resultant force acts on an object, it causes a change of momentum in the direction of the force

If a resultant force on an object is zero then there is no change of momentum

eg when the driving force = friction

if it is stationary, it stays at rest

if it is already moving, it continues at a steady speed in a straight line

Total momentum before = total momentum afterwards

positive momentum = to the right

negative momentum = to the left

momentum before = m1v1 + m2v2

m1 = m2

v1 = -v2

= m1v1 + -m2v2

= 0

m1

m2

momentum after = m1v1 + m2v2

= -m1v1 + m2v2

= 0

momentum before = m1v1 + m2v2

v2 = 0

= m1v1 + 0

= m1v1

m1

m2

momentum after = m1v1 + m2v2

= 0+ m2v2

= m2v2

therefore m1v1 =m2v2 ie all the momentum of the first ball is transferred to the second ball

momentum before = m1v1 + m2v2

v2 = 0

= m1v1 + 0

= m1v1

m2

m1

momentum after = m1v1 + m2v2

= -m1v1 + m2v2

m1 rebounds of m2 and transfers some of it’s momentum to m2

m1 > m2

v2 = 0

= 0+ 0

v1 = 0

m2 pushes off m1

m1

m2

momentum after = m1v1 + m2v2

= -m1v1 + m2v2

= 0

therefore m1v1 = m2v2

When a force is applied to an object, its velocity increases

The longer the force is applied, the greater the change in velocity

The greater the force applied, the greater the change in velocity

momentum

= mass x

velocity

increasing the velocity increases momentum

When a force is applied to an object, its momentum increases

The longer the force is applied, the greater the change in momentum

The greater the force applied, the greater the change in momentum

change of momentum = resultant force x time during which it acts

=

resultant force

x

time for which it acts

Increasing the time it takes for a change in momentum

reduces the force that causes the change in momentum

If the time from impact to the velocity becoming zero is increased

then the impact force is reduced

which means less injury

Seat belts, air bags, crumple zones, cycle helmets etc increase the time during impact and therefore reduce the impact force.

crumple zone

The energy of a moving object is called kinetic energy

When a force moves an object, work is done

work done (J) = force (N) × distance moved (m)

A braking force of 1000N is applied by a driver to stop his car. The car covered 50m before it stopped. How much work did the brakes do ?

1,000 x 50 = 50,000 J

When an object is lifted to a higher position above the ground, work is done by the lifting force against the gravitational force acting on the object (its weight)

As an object falls, its gravitational potential energy decreases as it is transferred into kinetic energy and heat (friction with the air)

When an object is lifted this increases the object’s gravitational potential energy (GPE)

change in GPE (J) = weight (N) × height difference (m)

A crane is lifting a 50kg load up into the air with a constant speed. If the load is raised by 20m how much work has the crane done ?

remember that 1 kg has a weight of 10 N (on Earth)

50 kg = 500 N

work done = 500 x 20 = 10,000 J

kinetic energy (J) = ½ × mass (kg) × [velocity]2 (m/s2)

E = ½ m v2

A 70 kg boy runs at 10m/s. What is his kinetic energy ?

kinetic energy = ½ x 70 x 102 = ½ x 70 x 100 = 3,500 J

What is the kinetic energy of a 100g tennis ball being thrown at a speed of 5m/s ?

100g = 0.1 kg

kinetic energy = ½ x 0.1 x 52 = ½ x 0.1 x 25 = 1.25 J

A parachutist with a total mass of 70 kg jumps from a helicopter at a height of 1,500 m. He pulls the cord of the parachute when he is 1,000 m above the ground.

(a) Ignoring air resistance, what is the speed of the parachutist just as he pulls the cord ?

You will need to use the formula E = ½ m v2. You are given the mass (70kg) in the question and you can work out E (energy) by using GPE = weight x height. Remember that 70kg = 700N.

GPE = weight x difference in height

GPE = 700 x (1,500 – 1,000) = 700 x 500 = 350,000 J

E = ½ m v2

700,000 / 70 = v2

{divided both sides by 70}

350,000 = ½ m v2

v2 = 10,000

{replacing E with 350,000}

700,000 = m v2

v = √10,000

{multiplied both sides by 2}

{getting the square root}

700,000 = 70 x v2

v = 100 m/s

{replacing m with 70}

(b) Why doesn’t the parachutist actually reach the speed calculated in part (a) ? [2 marks]

because of air resistance [1], some of the gravitational potential energy is dissipated as heat [1]

(c) The parachutist actually reached the velocity of 40 m/s before the using the parachute. How much energy was dissipated ?

total energy = 350,000 J

velocity (without taking air resistance into account) = 100 m/s

velocity (taking air resistance into account) = 40 m/s = 40%

therefore 60% of the energy is dissipated

350,000 x 60 / 100 = 21,000 J

(d) What principle is used to calculate part (c) ?

the conservation of energy (all of the energy is accounted for)

Electric charge – objects become charged when

electrons are transferred to or from them, for

example, by rubbing

Two types of charge are positive and negative (these

names are just labels)

Two objects with the same charge repel each other

Two objects with different charges attract each other

current =

resistance

Metal wire

Normally the free electrons in a metal move around slowly at random.

metal ions

+

electrons

potential difference

The potential difference (voltage) provides energy which makes the electrons move through the metal ie it generates a current.

The electrons experience resistance when they flow through the metal.

The symbol for voltage is V

The symbol for current is I

The symbol for resistance is R

r2

R

=

+

SERIES

V

I

i2

v1

v2

i1

I = i1 = i2

The current is the same everywhere

The sum of the voltages across each component equals the supply voltage

V = v1 + v2

Resistance

PARALLEL

I

I3

i4

i1

i2

i5

I = I3

I1 = I4

I2 = I5

I = I1 + I2

Total current = the sum of the currents through each component

Current does not get used up

V

v1

v2

Voltage = energy per unit of charge

V = v1 = v2

The voltage across each component is the same as the supply voltage.

If more bulbs are added in parallel to a circuit then they will all be as bright as normal and more current is drawn from the power supply

The potential difference is largest across the component with the greatest resistance, because more energy is transferred by the charge flowing through a large resistance than through a small one

The current is smallest through the component with the largest resistance, because the same battery voltage causes more current through a smaller resistance than a bigger one

Current is a flow of electrons

Electrons have charge (negative)

So current is a flow of charge

How do we quantify current ?

Current is the amount of charge flowing in a particular amount of time

Voltage provides energy to the electrons

Electrons have charge (negative)

So Voltage provides energy to the charge

How do we quantify voltage ?

Voltage is the amount of energy a particular amount of charge has

All components will offer resistance to a flow of electrons

How do we quantify resistance ?

If a current of 1A flows through a component when the voltage across it is 1V then the component is said to have a resistance of 1 ohm [ 1 W ]

I

=

R

V I R

=

I

I

V

V

=

R

R

=

I

I

V

I

=

R

Multiply both sides by R

R x

x R

R I = V

Or V = I R

Take

V = I R

and divide both sides by I

or

I

=

R

V = I R

V = I R

V

V

R

=

I

I

R

current = voltage / resistance

voltage = current x resistance

resistance = voltage / current

Q. A current of 4 A flows through a circuit with resistance 3 W. What is the voltage ?

use

V = 4 x 3

Voltage = 12

V

10

R =

I =

2

5

V

V

V

I

R

=

=

I

R

I

R

Q. A current of 5 A flows through a circuit with voltage 10 V. What is the resistance ?

use

resistance = 2

W

Q. A circuit with voltage of 6 V has a resistance of 2 W . What current should flow ?

use

current = 3

A

I

=

R

8

12

V = I R

V = I R

I =

R =

4

2

V

V

V

V

R

I

R

=

=

=

R

I

I

I

R

Q. A current of 4 A flows through a circuit with voltage 12 V. What is the resistance ?

use

resistance = 3

W

Q. A circuit with voltage of 8 V has a resistance of 2 W . What current should flow ?

use

current = 4

A

Q. A current of 60 A flows through a circuit with resistance 4 W. What is the voltage ?

use

V = 60 x 4

Voltage = 240

V

I

=

R

16

V = I R

V = I R

R =

2

230

I =

5

V

V

V

V

I

R

R

=

=

=

R

I

I

I

R

Q. A current of 2 A flows through a circuit with voltage 16 V. What is the resistance ?

use

resistance = 8

W

Q. A circuit with voltage of 230 V has a resistance of 5 W . What current should flow ?

use

current = 46

A

Q. A current of 25 A flows through a circuit with resistance 3 W. What is the voltage ?

use

V = 25 x 3

Voltage = 75

V

The higher the temperature the lower the resistance

The greater the light intensity the lower the resistance

Resistors are used in circuits to control the size

of the current

Two resistors in series have a larger resistance than

one on its own.

Connecting two resistors in parallel makes a smaller

total resistance

Two resistors in series make a potential divider

Current is less here due to the extra resistance of the heating effect

Current (A)

Current through a filament bulb

Voltage (V)

(watt,W) (ampere, A) (volt, V)

If you know the power, it is easy to calculate how much

work is done (or how much energy is transferred) in a

given period of time:

Work done (or energy transferred) = power x time

(joule, J) (watt, W) (second, s)

Generators produce a voltage by a process called electromagnetic induction

AC generator

AC = alternating current

The size of the induced voltage can be increased by:

• increasing the speed of rotation of the magnet or electromagnet or coil;

• increasing the strength of its magnetic field;

• increasing the number of turns on the coil;

• placing an iron core inside the coil

DC generator

If a magnet is moving out of the coil, or the other pole of the magnet is moving into it, there is a voltage induced in the opposite direction

Number of turns primary coil

=

Voltage across secondary coil

Number of turns secondary coil

Transformer

8 turns

4 turns

Vp / Vs = Np / Ns

Energy = power x time

An atom

proton +

neutron 0

nucleus

orbit / shell

energy level

Animation completed

The nucleus is positively charged

so it attracts the negative electron

How do scientists know about the structure of atoms?

The Rutherford Scattering Experiment

Alpha particles (positive charge)

Thin gold foil

Some particles passed through, some were deflected backwards

Particles passing through the foil indicated atoms have large amounts of space.

The particles that were deflected back indicated the alpha particles had passed

close to something positively charged within the atom (the nucleus)

When an unstable nucleus changes, what can happen ?

alpha radiation

nucleus

beta radiation

gamma radiation

Radioactive isotopes release radiation and the nucleus changes

The behaviour of radioactive materials (radioactive decay) cannot be changed by chemical or physical processes

An isotope is an atom with a different number of neutrons:

A “radioisotope” is simply an isotope that is radioactive – e.g. carbon 14, which is used in carbon dating.

Radioactive changes – some nuclei that are unstable

can become stable by emitting an alpha or beta particle

1) Alpha () – an atom decays into a new atom and emits an alpha particle (2 protons and 2 neutrons – the nucleus of a helium atom)

2) Beta () – an atom decays into a new atom by changing a neutron into a proton and electron. The fast moving, high energy electron is called a beta particle.

3) Gamma – after or decay surplus energy is sometimes emitted. This is called gamma radiation and has a very high frequency with short wavelength. The atom is not changed.

Example

Radium-226 undergoing alpha decay forms Radon-222, an alpha particle and releases energy.

Beta decay

Example

Polonium-218 undergoing beta decay forms Astatine-218, an electron and releases energy.

If a substance is capable of ALWAYS emitting radiation under any conditions we say it is radioactive. There are three types of radiation: ALPHA, BETA and GAMMA.

Sheet of paper

Few mm of aluminium

Few cm of lead

Sources of background radiation

Background radiation

- Radiation dose measures the possible harm the radiation could do to the body. It is measures in millisieverts (mSv).
- The potential harm done depends on
- the amount of radiation
- the type of radiation

Exposure to a radiation source outside your body is

called irradiation

If a radiation source enters your body, or gets on skin

or clothes, it is called contamination

Alpha particles are the most ionising so they are the

most dangerous inside your body

- Employers must ensure that radiation workers receive a
- Radiation dose “as low as reasonably achievable”.
- Precautions taken are
- use protective clothing and screens
- .wear gloves and aprons
- wear special devices to monitor their dose

treating cancer

sterilising equipment

sterilising food

it can kill cancer cells

it can kill microbes without harming the food

it can penetrate the outer casing and kill microbes

Radon gas is harmful because it is radioactive. It

produces ionising radiation that can damage cells.

Medical imaging and treatment

Radioactive materials cane be used to diagnose and

cure many health problems.

Radiotherapy is used to kill cancer cells

= radioisotope

= new atom formed

The HALF-LIFE of an atom is the time taken for HALF of the radioisotopes in a sample to decay…

After 2 half lives another half have decayed (12 altogether)

After 3 half lives another 2 have decayed (14 altogether)

After 1 half life half have decayed (that’s 8)

At start there are 16 radioisotopes

Count

Time

1 half life

A substance is considered safe once its activity drops to the

same level as background radiation.

The energy released can be

calculated from Einstein’s

equation : E = mc²

ENERGY

neutron

U-235

nucleus

neutrons

The fission of one atom can

set off several more causing

a chain reaction

Smaller nucleus

Nuclear waste

High level waste – this is “spent” fuel rods

Intermediate level waste – HLW decays to become ILW

Low level waste – protective clothing and medical equipment

Nuclear fusion – the nuclei of two hydrogen atoms join

together and energy is released.

Protons and neutrons in a nucleus are held together by a

strong nuclear force, which acts against the electrical

repulsive force between protons

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