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AS and A Level: Waves & Cosmology
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- 1 When a source of waves is moving relative to an observer (either towards or away) the received waves have a different wavelength to the wavelength transmitted. This is known as the Doppler Effect and we can use it to calculate the speed of a galaxy relative to Earth.
- 2 Almost all galaxies show redshift, meaning that the wavelength received on Earth is longer than it was when transmitted. It’s called redshift because the wavelength received has moved towards tor even beyond the red end of the spectrum . Redshift implies that the galaxy is moving away from Earth.
- 3 Blueshift can be observed from ‘nearby’ stars and galaxies.
- 1 Using redshift data from a number of galaxies, Hubble plotted a graph of recession velocity, v, against distance to the galaxy, d. This graph continues to be updated and it shows that v = Hod which is known as Hubble’s law. This means that the speed of recession is directly proportional to the distance to the galaxy.
- 2 Ho is the Hubble constant and it has a value of about 70 km s-1 Mpc-1, which is equivalent to 2.3x10-18 s-1. 1/Ho= 4.4 x1017 s = 1.4 x 1010 years! This is the age of the universe, about 14 billion years.
- 3 We can also find an estimate for the size of the (visible) universe, assuming that the maximum expansion speed is the speed of light. Using Hubble law, c = Hod so d = c/Ho = 14 billion light years.
- 4 The uncertainty over the value of The Hubble constant is becoming smaller as measurements of distance to galaxies improve
- 5 Since redshift is seen in every direction, the conclusion is that the universe is expanding.
Fate of the universe
- 1 The fate of the universe is closely linked to CRITICAL DENSITY. This is a theoretical density that would have enough mass in the universe to keep the expansion of space slowing down forever. The critical density is given by o= 3H2/8 . The universe would be FLAT. An accurate value for H is important, if we want an accurate value for the critical density. Note: H2 means that the percentage uncertainty in H has to be doubled.
- 2 If the actual density is greater than the critical density, then the universe will stop expanding at some point and then collapse. The universe is then CLOSED. This outcome is known as the Big Crunch.
- 3 If the actual density is less than the critical density, there is not enough mass to stop the expansion and the universe will continue to expand forever. The universe is OPEN.
- 4 Determining the actual density is difficult because there seems to be dark matter which we cannot yet detect directly but which can be inferred by the gravitational effects it has. e.g the rotation of galaxies is not consistent with observable mass but with increased mass that may be explained by the presence of dark matter.
I will explain the results using Hooke's Law. He found that extension is proportional to the downward force acting on the spring. Hooke's Law: F=ke F = Force (Newtons) k = spring constant e = Extension in (Meters) Apparatus The equipment I used was: Retort Stand 2x Boss Clamps Ruler= 30cm Weights (7x50g) Spring Method In order to carry out an experiment that is both safe and fair the following precautions were taken: each part of the apparatus was checked before the practical was set up.
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An Investigation into Hooke's Law - The aim of this experiment is to find out if the amount of weight applied to an elastic or stretchable object is proportional to the amount the object's length increases by when the weight is applied.
Elastic materials include metals and rubber. However, all materials have some degree of elasticity. This was taken from the text book issued to me from my school: " The extension is directly proportional to the load. This is called Hooke's Law. This law also applies to the stretching of metal wires and bars. From your results, plot a graph of extension against load. A straight line through the origin of the graph confirms that the extension is directly proportional to the stretching force.
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My aim in this experiment is to investigate how the compression of a spring affects the amount of kinetic energy transferred to the trolley that it is attached to.
This allowed me to observe the way that my experiment should be carried out and also allowed me to obtain some preliminary results. These results will aid me with my prediction, indicating the type of trend my own results should present. Although the computer simulation is very accurate in its measurements and readings, it is impossible for us to make up the exact same experiment that is shown on the screen, therefore our results will be very different. In this experiment, the trolley had a mass of 500g (the nearest to that of the trolley we will be using)
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However, if I do not exceed the elastic limit the formula F = kx will be applicable. I predict that a system of springs in series will have a different spring constant to a system of springs in parallel. I can use F = kx to show the different spring constants of spring systems in parallel and series. Then I can examine these results to show a relationship between them. To achieve this I must plan an experiment that shows the stiffness of different numbers of springs in series and I parallel. To find the spring constant of a spring I can place different masses onto a spring and measure the length of the extension of the spring.
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Young's Modulus When stress is applied to a material, strain is produced in the material. The strain is proportional to the stress, provided the stress does not exceed a limit known simply as the 'limit of proportionality'. Within this limit, the value of is a constant for that material, and is known as the Young Modulus for the material. The Young Modulus (E) = Provided the limit of proportionality is not exceeded. Before we can work out the Young Modulus we need to know about stress and strain. Stress is defined as the tension (force)
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To investigate the relationship between the extension and the force added, whether they are linked through proportionality.
Factors, which I have to take into consideration, are things like the length and thickness of the rubber bands. I must also make sure to use a new rubber band so it won't be worn out or damaged as not to get wrong results. To overcome this problem I'll use one average sized and thickness rubber band throughout the whole experiment. I must not put to much weight on the rubber band or it will reach its 'elastic point' and be permanently damaged. For this experiment to be a fair test I will keep everything the same and only the controlled variable, the weights, will change.
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This is done by setting up a stand and a clamp. Hanging off the clamp will be the spring. Then a weight carrier will be hung off the spring, and this is where the different masses will be placed. The spring has a restrain force but this shouldn't affect the experiment because it will be extended by the weight carrier. Diagram: The masses will make the spring oscillate and we will count 10 oscillations and record the time with a stopwatch, then you divide the time by 10 and you will get a time for just one oscillation.
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The opposite of this happens when the springs are in series. When springs are in series, they are extended as normal as if they were single springs, so two single results will result in an extension that will be double what it would be with just one single spring. Hooke's law supports this as it suggests that the extension and the mass are in direct proportionality therefore double the load, double the extension, so this must mean half the stiffness. So, when the spring combinations are set up, the mass will be pulled down so that it oscillates.
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I will repeat this five times for each spring combination. I will do the same operation for each of the spring combination. Now for deciding the mass that I will use in the experiment and also work out the stiffness of the spring combination that I will use I did some preliminary work that made me decide that approx. 300g is the mass that I am going to use in this experiment. The following are the spring stiffness that I obtained using the equation Constant (K) = Force (F)/ Extension (in M)
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In this experiment, I am going to find out the relationship between Force and extension using stretchy sweets and then find the stiffness of stretchy sweets using Hookes Law.
cause the stretchy sweet to either expand or contract thereby affecting the extension of the sweet when a load is applied to it. For a fair test, I will use the same length of stretchy sweets each time I repeat the experiment and I will also ensure that the length of stretchy sweet that I use is long enough, because longer sweets gives larger and more measurable extensions. PREDICTION I think that as the load applied to the stretchy sweet is increased, so will the extension and the rate at which it increases will be proportional to the applied load (i.e.
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I know that there will be errors in my experiment and I will try to minimise them by adding precautions in some steps of my plan. I predict that the value I will get for g will be between 9.6 and 10N/Kg. Plan Apparatus Spring (small silver spring 2.1mm in length) Clamp stand Metre rule (marked in mm) Weights (8 x 50g masses) Weight hook (of mass 50g) Large weights (2 x 1Kg) Safety glasses Elastic band Stopwatch (accurate to 1/100 of a second)
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Two springs put into series have a different spring constant than two springs in parallel. I predict that the springs put in series will extend much more than the springs in parallel. This is because springs in series should have a much higher spring constant as they have the properties of a very long spring. If the springs have the same modulus of elasticity then the springs in series' spring constant will be higher than the spring constant of the springs in parallel as the modulus of elasticity will be divided by a much bigger value as the spring acts as a longer spring, thus making the constant a lower value.
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My theory is that if a spring extends further then it will take longer to 'bounce'. I think that this is because when you add weight to the spring, you give it more potential energy. When you let it go it releases kinetic energy. It will travel further, the more potential energy it has. The spring then needs energy to revert back to its original shape. Because it needs energy it takes more time to get back to the original position.
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If the spring has not been permanently strained the reading of the pointer will return to it's original or zero reading when all the weights and the scale pan have been removed. (vii) Finally weigh the scale pan. Actual experiment. (a) Introduction: The aim of this experiment is to find and measure the elastic constant of a spiral spring. (b) Apparatus: (i) Light spiral spring. (ii) A scale pan. (iii) A meter rule. (iv) 2 Clamps and Stands. (v)
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If an elastic band has too many weights on it and has exceeded the limit it will snap. The elastic limit depends on the type of solid used. E.g. a steel bar or wire can be extended elastically by only about 1% of its original length. Where as rubber like materials such as elastic bands can have extensions of up to 1,000%. The elastic limit is in principle different from the proportional limit, which marks the end of the elastic behaviour that can be described as Hooke's law. Which is that 'The load is proportional to the displacement.'
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Double the force, double the stretch, and so on. This is known as a mathematically direct relationship. A graph showing this is similar to the one above. On a graph, since it has a direct relationship, a line is the best representation. A direct relationship can be represented by the generic formula: y = mx + b where m is the slope and b is the y-intercept. More specifically: y = mx + b F = Force in Newtons k = Spring constant Zero x = Extension in Meters F = kx Here, k is called the spring constant.
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the rubber band * Kind of rubber band Method: * Set up the apparatus as above * Assure that the long ruler is exactly straight by lining it up with the setsquare. * Measure the length of the rubber with no weights attached to see what the length of the rubber band is before it is stretched. * Add a 100g weights until the rubber band is unable to stretch anymore, measure the extension or the rubber band every time one 100g weight is added by using the setsq uare to get a more accurate reading.
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I am going to be looking at three plays, they are 'Billy Liar', 'Spring and Port Wine' and, 'Ernie's Incredible Illucinations'. 'Billy Liar' is about a boy with a very vivid imagination.
Ernie imagines things that then become real, and as an audience, we see the effect of his imagination on everyone around him. 'Billy Liar' and 'Spring and Port Wine' show us the inside of the characters imagination. In that way 'Ernie's Incredible Illucinations' show us a reality, the other two plays show us the 'made up' world, so that although the characters think fantasy thoughts, these thoughts do not affect life around them. The cultures of the time were evolving, children were trying to voice their views and make a statement about themselves.
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Bags and coats will be moved out of the way to ensure that no one will trip over them. Whilst loading the elastic band care will be taken to make sure that the elastic band is loading carefully to try and ensure it does not snap. However I will be wearing satfey glasses to prevent injuries to my eyes if the band does snap. I will use some kg masses to stop the retort stand sliding of the desk. Variables Independent Variable: Load (kg) the masses which I am applying to the elastic band. Dependent Variable: Extension (m) to the elastic band I have used the same equipment throughout the experiment (including the same elastic band)
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How does the extension of two or more springs in series or parallel compare with the extension of one spring?
I will keep this a fair test by keeping the length of each spring the same. I will measure in the same units and keep the same conditions for each experiment. Hooke's Law supports my prediction: "The extension is directly proportional to the load" Equipment List: -springs -weights hanger -Newton weights -stand -clamp -boss -meter ruler Please look at the equipment list and set up as shown in the diagram. I would measure the extension of each spring in series and individually. I would record my results in a table. I will measure each extension three times.
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Prediction I think that as the weights are added to the elastic band, the extension will not be proportional to the load. This is because I already know that this applies to springs (Hooke's Law) and I know that springs act in a different way to elastic bands because of the composition of their atoms. Elastic bands' atoms are all tangled up and very random whereas springs' atoms are more regular and coiled. I think that this is an important factor as it shows a quite noticeable difference between the two and it gives me more reason to believe that the band will stretch in a different way to the spring.
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There were little streams, too, with hollow banks and diminutive ponds with narrow dams, hamlets with squat little huts beneath blackened and often half collapsing roofs, and crooked threshing barns with wattled walls and gaping doorways opening on to abandoned threshing floors, and churches, some brick-built with the stucco peeling off in patches, others of wood with crosses awry and churchyards that had gone to wrack and ruin slowly Arkydy's heart sank.
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return to its original shape Elastic - Can be distorted but returns to original shape Stress - When forces are placed on an object Strain - The way stress is reacted to. Plan * I am going to design an experiment to look at the way different materials react to stress. Some of the materials chosen are brittle and some re plastic. The brittle material will simulate the rock needed to produce earthquakes. * I will use the following materials: Wooden Cane Chew stick Bread sticks Chew bar * I plan to add weights to the above objects and record how they bend or deform up to breaking point.
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In this experiment I aim to find a value for the Young's Modulus of a piece of cassette tape. Young's Modulus is a way of expressing how much a certain material is stretched or compressed.
Here is a diagram to illustrate what my experiment will look like: - The apparatus required 1. A clamp Stand 2. Cassette tape (71cm) 3. Set of weights (with intervals of 50g) 4. Weight holder (10g) to attach weights to cassette tape 5. A 200cm rule (made from two metre rules) 6. A Micrometer Method I will set up the experiment as shown in the diagram in order to start my investigation. But first I need to measure the length and cross sectional area of the tape accurately and attach it to the clamp stand. I can then start adding weights:- 1. Measure width and depth of the cassette tape in order to find the cross-sectional area.
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Results Spring We measured the spring before we started to add mass and it was 4.7cm in length. I calculated what 'm' would be for each result. X (cm) 0 0.5 0.8 1.3 1.8 2.3 2.8 4.8 6.6 F (n) 0 0.1 0.2 0.3 0.4 0.5 0.6 1.0 1.5 M 0.2 0.25 0.23 0.22 0.22 0.2 0.2 0.23 See spring graph. Elastic band We measured the elastic band before we started to add mass and it was 8.5cm long. I calculated what 'm' would be for each result. X (cm) 0 0.5 0.8 1.2 1.9 2.7 3.2 4.1 4.9 6.2 F (n)
- Word count: 755