# Physics 1

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## Variables

The variables that you change are called the independent variables (or the input variables), while the variable that is measured is called the dependent variable (or output variable), and the things which stay the same are called the control variables.

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Mass--grams (g), kilograms (kg)--top-pan balance

Weight or Force--newtons (N)--spring balance, newton meter

Time--seconds (s)--stopwatch, clock

Length--millimetres (mm), centimetres (cm), metres (m)--ruler, tape measure

Area--square centimetres (cm²), square metres (m²)

Volume--cubic centimetres (cm³), millilitres (ml), litres (l)--measuring cylinder

Temperature--degrees Celsius (˚C)--thermometer

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## Recording data

The results of an experiment should be presented in a table. The independent variables should be in the left-hand columns, and the dependent variable in the right-hand column. Each column should have a heading – the name of the variable and its units. The values should be entered as decimals, not fractions, and the independent variables should be in order of increasing size. Use a ruler and add a title. This rule also applies to graphs.

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If one of the results looks as if it does not fit the pattern or trend of the rest, it is called an anomaly. These should be double checked.

• The results of an experiment are usually displayed on a graph.
• Physicists mostly use line graphs, but if the independent variable is not a number, then use a bar or pie chart.
• The independent variable should nearly always (there are some exceptions!) be on the x-axis, while the dependent variable should nearly always (there are some exceptions!) be on the y-axis.
• The scales should be chosen so that as much of the graph paper as possible is used, and both axes should be labelled with the variable and its unit.
• Points should be plotted carefully, and usually a best fit line should be drawn through the points.

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## A Simple Pendelum

A simple pendulum bob swinging back and forth on a thin string. The time it takes to make one complete swing is called the period. The mass of the bob, the length of the string and the angle of release (all independent or input variables) affect the period (the dependent or output variable).

It turns out that the period:

• depends on the length (the longer the length, the longer the period)
• but does not depend on the mass of the bob or on the angle of release

Galileo is the first person to notice that the period of a pendulum does not depend on the angle of swing, in Pisa Cathedral in the second half on the 16th century. He was celebrated in 2009 because it was 400 years since he first turned the newly invented telescope into the night sky to make discoveries that would change our ideas about the Solar System forever. He discovered that Jupiter had four large moons which orbit around the planet at different rates.

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## Longitude and Latitude

Even as the swings of a pendulum die away and get shorter in length, they take the same time. One use that the pendulum was put to was in the production of clocks. Galileo never got round to making a pendulum clock, but a Dutch scientist called Christiaan Huygens managed it later on in the 17th century.

Clocks became important for other reasons (apart from just telling the time) in the 18th century. It is quite easy to tell how far north or south you are on the surface of the Earth – i.e. to work out what your latitude is – simply by observing how high the Sun rises in the sky during the day, or how high certain stars rise during the night.

But it is very difficult to work out how far east or west you are – i.e. to find out your longitude. It was realised, however, that if a clock could be manufactured that would work reliably at sea (up and down, up and down, ...), that would solve the problem.

The clock could be set to ‘Greenwich time’ as the ship set sail. Further round the world the time on the clock would be compared with the local time (judged by seeing when the Sun as highest in the sky) and the difference in hours noted. The Earth spins once on its axis – i.e. through 360° – in 24 hours, so each hour of time difference is equivalent to 15° east or west of Greenwich.

The man who solved the problem was a carpenter from Lincolnshire called John Harrison. His clocks can still be seen to this day in the Royal Observatory at Greenwich, and his work was celebrated in American writer Dava Sobel’s book ‘Longitude’.

Nowadays of course our mobile phones can tell us where we are with frightening precision – via satellites in orbit around the Earth and the global positioning system (GPS).

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## GPS Global Positioning System

GPS is a space-based satellite navigation system that provides location and time information in all weather, anywhere on or near the Earth, where there is an unobstructed line of sight to four or more of the GPS satellites. It is maintained by the USA and is freely accessible to anyone with a GPS receiver.

A GPS receiver calculates its position by precisely timing signals sent by the GPS satellites above the Earth. The receiver works out the distance to each satellite using the speed of light. The distance to each satellite defines a sphere. The point at which three, or ideally four, of these spheres intersect gives the position of the receiver. A similar method is used to pinpoint the location of an earthquake.

There are about 30 GPS satellites orbiting the Earth. The idea is that at any location on the Earth at least 6 satellites should be ‘visible’ at any time. The satellites orbit at a distance of about 20,000 km from Earth and travel at a speed of about 4 kilometres per second

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## Mass and Weight

Mass is a measure of how much matter or ‘stuff’ there is in an object. Weight, on the other hand, is a measure of the pull of gravity on an object, so it is a force.
You can use a spring balance to measure the strength of the Earth’s gravitational field. Hang a 1 kg mass on the balance and read off the force: the result – very close to 10 – tells you the gravitational force acting on every kilogram of anything near to the Earth’s surface. So the strength of the Earth’s gravitational field – known as ‘g’ – is about 10 N/kg.
If you have a mass of 60 kg, then your weight on Earth would be: 60 kg × 10 N/kg =600 N.
In general: weight (pull of gravity) = mass × strength of gravitational field.

‘g’ varies a bit over the surface of the Earth – it’s slightly bigger at the poles (because the Earth is squashed, so the poles are closer to the centre), slightly smaller at the equator and smaller the higher up you go (e.g. in Mexico City).
It also varies around the Solar System – on the Moon it’s a sixth of what it is on Earth (1.7 N/kg), on Mars it’s about 3.7 N/kg and on Jupiter about 24.8 N/kg.
If you were able to travel around the Solar System, your mass would stay the same, but your weight would change – because of the different values of g, the local strength of the gravitational field.

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## Density

The density of a substance measures how much mass is contained in a particular volume. Density is defined by the following formula:
density = mass divided by volume, where d stands for density, m for mass and V for volume.

Other variations of this are:​​

Mass = density multiplied by volume...or...volume = mass divided by density

You can measure the density of a regularly shaped solid (like a brick) by measuring the mass and then calculating the volume – e.g. by multiplying the length by the breadth by the width if the solid is a rectangular block.

You can measure the density of a liquid by measuring the mass of a measuring cylinder, filling it with the liquid and measuring the new mass – and then measuring the volume of liquid:

density = {(mass of measuring cylinder + liquid) – (mass of measuring cylinder)} ÷ volume of liquid

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## Archemidies Principle

Anything immersed in water experiences an upthrust, which makes it appear to weigh less. According to Archimedes Principle:
When an object is partially or totally immersed in a liquid, it experiences an upthrust equal to the weight of liquid displaced.
weigh an object in air

• re-weigh it when it is immersed in water
• calculate the upthrust (= weight in air – weight in water)
• measure the volume of water displaced by the object when it is immersed in water by carefully lowering the object into a displacement can (or ‘eureka beaker’) and catching the overflow
• calculate the mass (multiply volume by density) of water displaced
• calculate the weight (multiply mass by 10 N/kg) of water displaced
You should find that the upthrust = the weight of water displaced.
Some things manage to float in water because they experience an upthrust (buoyant force) because they can displace a weight of water equal to their own weight.
Ice is less dense than water so an ice cube/berg will float on water. But because a given weight of ice only has a slightly larger volume that the same weight of water, most of the ice must be underwater in order to displace enough water to balance its weight. In other words, you only see the tip of the iceberg. (Very dangerous!)
Steel ships can float because they are shaped to displace a weight of water equal to their weight; their average density is less than the density is less than that of water, because they are full of empty spaces.
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## The Plimsoll Line

The Plimsoll Line indicates the legal limit to which a ship may be loaded for specific water types and temperatures. To an observer on the ship the water appears to rise or fall against the hull. Temperature affects the level because warm water provides less buoyancy, being less dense than cold water. The saltiness of the water also affects the level, fresh water being less dense than salty seawater.

(Samuel Plimsoll was a British politician and social reformer.)

It turns out that Archimedes principle works in gases as well as liquids – you experience an upthrust just by being in air! But it is very tiny compared to your weight, so you don’t come even close to lifting off.

However, a balloon can float in air if it is filled with a gas which is a lot less dense than air, meaning that the weight of the balloon plus the gas inside it is less than the weight of the air that it displaces. So a balloon filled with helium, hydrogen or even hot air (which is less dense than cold air) can float. Hydrogen balloons aren’t very safe though, as hydrogen burns explosively in air.

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