These notes are a "bare-bones"
summary of the material in the book.
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Speed
The speed of an object is a measure of how fast something is travelling.
speed (m/s) = distance (m) ÷ time (s)
Alternatively the units are kilometres per hour (km/h).
You will also see miles and miles per hour:
1 mile = 1.6 km = 1600 m
1 mph = 0.44 m/s
Despite this country's love of imperial distance measurements, all motorways and many main roads have distance markers in kilometres.
Most modern engineering is done entirely metrically, and has been for many years.
The equation can be rearranged to:
distance = speed × time
or
time taken = distance ÷ time
We can show the movement of objects graphically.
The gradient (slope) gives the speed. The gradient is the rise ÷ run. (The area under the graph means nothing.)
If the gradient is bigger, the speed is bigger. If the graph is curved, it means that the object is accelerating.
The gradient of the graph tells us how the speed is changing:
The steeper the gradient, the greater the acceleration.
If the gradient is negative, that means the car is slowing down. This is called deceleration or negative acceleration.
The area under the graph give us the distance travelled.
The distance is:
area of the rectangle + area of triangle 1 + area of triangle 2
If the graph is not a straight line we then have to count the squares under the graph and convert them.
Acceleration is the rate of change of the speed in a given time. Its units are metres per second squared (m/s2) which means "metres per second every second".
Acceleration (m/s2) = change in speed (m/s)
time (s)
We can rearrange this to:
Change in speed = acceleration × time.
or:
time = change in speed ÷ acceleration
When going round in a circle, the speed remains the same, but there is acceleration. All objects will carry on in a straight line until a force is applied to one side to change the motion. Here we have to use the word velocity, which is NOT a posh word for speed, but:
speed in a given direction.
Force too has a direction. So force and velocity are both called vectors, which have a value and direction. The force makes for a change in velocity towards the centre of the circle. Therefore there is acceleration towards the centre of the circle. This is called centripetal acceleration.
There is no such thing as centrifugal force. You feel that you are
thrown to the outside of a car when you go round a bend. This is because
you are trying to carry on in a straight line. Be a good chap and don't
use it.
Force (N) = mass (kg) × acceleration (m/s2)
In physics code:
F = ma
We can rearrange this to:
a = F/m
or
m = F/a
It is important that the mass is in kilograms and the acceleration is in m/s2.
This relationship is sometimes called Newton's Second Law of Motion.
Forces act in pairs:
The same size.
Opposite directions
If you push on a table, the table pushes against you. The Earth pulls on the Moon, and the Moon pulls on the earth.
This is sometimes called Newton's Third Law of Motion.
A child runs out in front of the car. The driver sees the child and presses the brake pedal hard to stop the car. There are two components to the stopping distance of a car:
The driver seeing and reacting to the emergency. This takes a fraction of a second, but the car is still moving. This is called the thinking distance.
The brakes are applied and the car stops. This is the braking distance.
Stopping distance = thinking distance + braking distance.
The thinking distance can be increased by:
tiredness;
distractions;
effects of drugs (medicinal and recreational) or alcohol.
That is why it's a serious offence to drive with excess alcohol in the blood.
Braking distance is increased by:
Speed of the car. Double the speed, the braking distance goes up four times.
Road conditions - wet or icy;
Poor condition of the tyres. Worn or bald tyres make the car prone to skid.
Worn brake pads. Brake pads press onto a disc and increase the friction. The kinetic energy of the car is turned into heat.
Motorists must take account of the road surfaces and keep their distance from the car in front (even if it's a Toyota).
If we apply a force to move a mass a certain distance, we do a job of work. When we do work, we use energy. Both work and energy are measured in joules (J). Work and force are linked by a simple equation:
Work (J) = force (N) × distance moved in the direction of the force (m)
In Physics code:
W = Fd
Rearrangements:
d = W/F
or
F = W/d
When a car brakes, the kinetic energy of the car is the same as the work done by the pads, so:
braking distance = work done by the brakes ÷ braking force
When we lift things up we do a job of work against gravity. Because of the pull of gravity, any mass is subject to a force called weight. Weight is a force and is measured in newtons.
weight (N) = mass (kg) × acceleration due to gravity (m/s2)
This is the same as Newton's Second Law. There are 10 newtons to a kilogram.
Please do not say that the weight of an object is in
kilograms.
If we lift a load, we do a job of work:
Work done (J) = weight (N) × vertical distance (m).
Power is the rate of doing work. If we do the same job of work in less time, we use more power.
Power is measured in watts (W). Big powers are measured in kilowatts (kW). 1 kW = 1000 W.
Power and energy (work) are linked by the equation:
power (W) = energy (J) ÷ time (s)
In physics code:
P = E/t
Rearranging:
E = Pt
or
t = E/P
At this level we can say that energy and work are the same thing.
When considering buying a car, naturally we want to know about its power and performance. We also need to consider:
fuel consumption (diesel cars are much more economical than petrol cars, although diesel fuel costs slightly more);
heavy cars with big engines obviously use more fuel than lighter cars;
pollution from road vehicles. Modern cars are much cleaner than older cars.
the amount of carbon dioxide give out. Manufacturers have to state how many grams per kilometre is given off. CO2 is a greenhouse gas that causes global warming.
that fossil fuels will run out one day.
boxy cars are not streamlined. There is greater drag, so the fuel consumption is higher.
Fuel for cars comes from crude oil which is a fossil fuel. The chemical energy is converted into kinetic energy to make the car go along the road. Not all the energy is turned into kinetic energy; a lot is lost as heat:
The engine is about 40 % efficient. So 60 % of the chemical energy is lost through the radiator.
Energy is lost to friction. Friction in the car can be reduced by well designed engines, oil, and ball bearings.
Drag or air resistance. In a boxy vehicle like a lorry, the drag is high. It can be reduced by streamlining the car. Also modern roof boxes are streamlined. Lorries have air deflectors to make them marginally more streamlined.
The car in the foreground of this picture is streamlined. The car reversing in the background is quite boxy.
When the car brakes (as it has to in normal driving) the kinetic energy is turned to heat.
Car fuel consumption can be given in miles per gallon, or litres per hundred kilometres.
1 mpg = 284 litres per 100 km
A diesel hatchback returns an average fuel consumption of 50 mpg = 5.68 litres per 100 km.
Stop-start driving in towns and traffic jams uses a lot more fuel than long runs on the open road. As does the engine just after starting, before it has fully warmed up.
Petrol is more refined than diesel. The petrol engine is also much quieter than a diesel, because the diesel engine ignites the fuel by compressing air in the cylinders, which gets hot. Petrol engines light their fuel with a spark. The reason why diesel cars are more economical than petrol cars is that:
diesel engines are more efficient;
diesel fuel has more energy per litre.
Diesel cars are more expensive to buy and service than petrol cars.
Electric cars are not new. Fast electric cars were invented over one hundred years ago. Most cars then were electric. Electric cars need a large battery that can be recharged from a local supply. The advantages with electric vehicles are:
The fuel (electricity) is much cheaper than diesel or petrol;
They are very quiet;
They cause no local pollution;
Stop-start driving is much easier (There is no need for a clutch or changing gear).
The drawbacks are:
The batteries are much heavier than a tank of petrol;
The motors are not so powerful;
The performance is not good.
The range is limited.
Trams run on rails, so getting a reliable electricity supply is easy.
Kinetic energy is worked out using the formula:
kinetic energy (J) = ½ × mass (kg) × (speed (m/s))2
In physics code:
Ek = ½mv2
If the speed doubles, the kinetic energy goes up four times. The braking distance also goes up four times. It's because of this that the law takes a very dim view of speeding
.
Old fashioned cars were very strong and heavy. They could survive a crash with scarcely a dent. But the people inside would be killed.
Modern cars crumple up more easily. This has the effect of increasing the impact time, thereby reducing forces on the people and the consequent risk of injury is reduced.
Safety measures enable people to walk away from serious impacts:
Seatbelts that restrain the passengers and give a little;
Air bags that prevent people from hitting the steering wheel and the dashboard;
Crumple zones at the front and back that fold up, and push heavy parts like the engine underneath.
Crash barriers on the side of a road that absorbs impact by giving a little;
Safety Cages that stop the passenger compartment being crushed in a roll-over accident;
Escape lanes on steep hills that allow out of control vehicles to pull off the road. The surfaces consist of shingle and there is an incline. This stops the car. It has to be pulled out by a tow truck, but that's better than coming off the road and over the side.
Active safety systems include:
Traction control that stops the wheels spinning;
Anti-lock braking system (ABS) that stops the wheels from locking.
These systems use a computer to monitor the turning rate of the wheels. The computer reduces the power of the engine to stop the wheels spinning. ABS uses the computer to reduce the pressure in the brake callipers when it senses that the wheels are locking.
Falling
An object falls to earth because of the effect of gravity. All objects accelerate towards the Earth at 10 m/s2. We see that heavy objects seem to hit the ground first, but that is due to the air resistance that builds up as the objects travel faster. Two objects of different masses, but similar size and shape will hit the ground at the same time:
When a sky diver leaps from an aeroplane:
The initial acceleration is 10 m/s2. The sky diver's weight is pulling him down, but there is no upwards force.
The acceleration decreases. This is because the air resistance from the air molecules goes up, providing an opposing force.
Eventually the air resistance is the same as the weight. If the weight is 700 N, the drag is 700 N in the opposite direction. The forces are balanced. The speed stays constant at 60 m/s. This is called the terminal speed. If you hit the deck at this speed, it would be pretty terminal as well; you would burst like a water melon.
The kinetic energy at terminal speed is constant.
The parachute increases greatly the surface area, so increasing the drag. This slows the parachutist down.
Eventually the parachutist reaches a new terminal speed, about 4 m/s.
When space probes go to the Moon, they accelerate at 1.6 m/s2, about 1/6th that on earth. However there is no atmosphere, which means that parachutes would not work. They have to slow down with rocket motors, else they will hit the deck at thousands of metres per second...
People pay large sums of money to go on machines (instruments of torture), which are really sophisticated baby-bouncers. Lots of people love being bounced up and down, or swung round in circles.
These machines lift their passengers to a height. The car and its passengers acquire gravitational potential energy.
Gravitational potential energy is worked out with the equation:
GPE (J) = mass (kg) × acceleration due to gravity (m/s2) × vertical height (m)
In Physics code:
Ep = mgDh
The odd looking symbol, D, is "delta", a Greek capital letter 'D', which is the physics code for "change in".
When the car rolls down the roller-coaster, the gravitational potential energy is turned into kinetic energy. Some will be turned into heat or sound. Remember that energy is not created nor is it destroyed. It is turned from one form to another.
gravitational potential energy at the top = kinetic energy at the bottom + energy converted to noise, heat, etc.
In this case:
Ep = Ek
mgDh = 1/2 mv2
If the height is doubled, the kinetic energy is doubled, but the speed only goes up 1.4 times (as the speed is squared - Ö2 = 1.4)
A ball when dropped transfers its GPE to kinetic energy. As it hits the floor that kinetic energy is turned into elastic potential energy. If you take a very fast photograph you can see the ball is squashed. The space hopper is a large bouncy ball.
The elastic potential energy is transferred to kinetic energy as the ball bounces. Some energy is lost as heat as the ball bounces, so it does not achieve the height from which it was dropped.
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