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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.
You can alter the length of the card, the compression of the spring and the distance that the trolley travels. To make this test a fair one, when the light gate is used, we will keep the same trolley with the same spring throughout the whole experiment. The only variable that we will change at any time during the experiment is the compression of the spring, this is for obvious reasons. For example, on the computer simulation, the weight of the trolley will be kept the same.
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What does the behaviour of P and S waves tell geologists about the structure of the Earth's interior?
This fracture can occur in several different directions: Apart from each other, together or past each other-called a shearing movement. When the rocks eventually do fracture, a large amount of energy is released, most notably in the form of P and S waves, sound waves and the movement of the rocks releases movement (kinetic) energy. After an earthquake, P waves are always detected at seismic stations well in advance of the S waves. From this we can make the assumption that P waves travel faster than S waves.
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Investigate the way in which springs arranged in parallel (i.e. side by side) behave when a fixed load (force) is applied to them. Explain how the increasing the number of springs affect the behaviour.
It will no longer follow Hooke's Law. Preliminary Work: I have already done work about forces and acquired enough knowledge in order to conduct this investigation. However, before I begin, there are two variables that I need to determine how to control and use: the weight of the load and the number of springs. I will conduct two tests to find out the number of springs that will give me the most reliable results and the most adequate weight of the load. Test for the number of springs I will start with two springs and work my way to a greater number.
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If you leave a very large weight hanging on the string, it will gradually get longer and longer until it breaks. In this state the wire is behaving as if it were a fluid instead of a solid. If too large a force is applied to the spring two things happen. 1. The length of the spring increases by a far greater amount for each extra newton of force added. Hooke's law is no longer obeyed - the line on the graph curves upwards: Plan & Prediction: Apparatus: Stand, Hook, Metre rule, a rubber band, small 30cm ruler.
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To do this I added weights to the spring until it did not return to its original shape. This occurred at 12N and so I set a limit of weight to 10N for my experiments. The reason why 11N was not used is that 10 experiments is a more standard number and also that the limit of proportionality is slightly less than the elastic limit of the spring, therefore using 10N ensure I do not exceed the proportional or elastic limit of the spring.
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* Hanger * 1N weights (5) * Metre ruler * Safety glasses Diagram Method 1. Set up equipment as shown 2. Put on safety glasses in case any springs snap 3. Measure the original length of one spring and hanger 4. Add a 1N weight and measure the new length 5. Repeat this until the total weight on the spring is 5N 6. Take the original length from the new length and record the extension 7. Move the metre ruler to change the scale from which you are measuring from 8.
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Moreover, according to Newton's second law, the equation of motion: Fnet = ma ? Fnet = ma = -kx, then a = - (k/m)x = -w2x ? = As the mass m executes simple harmonic motion (SHM), the period of oscillation is defined as ? T2 = 4?2() Therefore, a graph with T2 as the y-axis and m as the x-axis has a slope of which should be a straight line passing through the origin. However, as the mass of the spring will affect T. T should be equal to where me is the effective mass of the spring.
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Observe and analyze the characteristics of the different types of waves and their behavior towards changes in variables.
Another way that step III can be done in case that it fails, is by placing the spring on the ground, and create a horizontal wave, meaning that the person holding the string less end, will give it a whip like movement parallel to the ground. V. Observe how the wave moves, how it returns, position, direction, etc and record the observations. 3rd Part: I. Draw a table (See picture 3.1) of six columns: Median, Distance, Tension, Amplitude, Time and Velocity.
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Before carrying out my experiment I had to find out the elastics limit of the spring (where too much weight has been added and the spring cannot return to its original shape) so that I could find a suitable range of results. I found that the elastic limit of the spring is 90g so to make sure that I don't exceed the elastic limit. I also hope to carry out the experiment 3 times and also take an average to increase the reliability of my results.
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* Factors that affect resistance: Heat (temperature) Area Material Length * Which of these variables is the best variable to measure in the experiment? Length is the best variable because * Materials to consider to use for the experiment: Copper Con Plan * The apparatus will be collected as follows: Clamp stand 3 springs Metre rule 100g weights Set square * Then experiment will be set up with the apparatus with the spring attached to the clamp. * 100g weights will be added to the spring. The extension will be measured and recorded each time a 100g weight is added.
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x b = elastic limit - deformed permanently c = Energy stored this can be worked out by using:- E = 0.5Fx ==> Area of a right angled As the extension increases from the load being pulled down by gravity it gains energy, (Gravitational potential energy) this is converted into elastic energy in the spring, when the load is removed this energy is released, the spring snaps back to its original form. Demonstrating elastic deformation. Beyond this point, the elastic limit, there is plastic deformation.
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Planning Equipment 1 x crane 1 x spring 4 x 100g weights 1 x stop clock 1 x weight holder with 1 x 100g weight The method for doing this practical is as follows. First I would set up the equipment and below I have drawn I diagram to represent their layout. First of all I would adjust the claw to a considerable height and then place on the spring by putting the claw through one of its coil ends and then tightening it.
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This was especially designed for people that wanted to learn to surf but couldn't get the hang of it. He tried a lot of different shapes and finally prevailed with a type of rectangular shape made from a piece of plywood. At first of all when he started to make these boards and sell them not very many people were interested, but as the word spread people started wondering what this strange board is like to ride so the bought them to try them out and they had loads of fun. After that it really started to take off and Tom opened up a proper business and called it Morey Boogie Boards.
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The first thing we did, after setting up the equipment, was to set the spring to its rest point as this was essential for a fair test. We would then pull the spring down a certain length we chose two centimetres. Then as one oscillation would be too fast to measure we would time ten oscillations from being pulled down two centimetre. After we have done this three times with a weight hanging off it, say 100g, we would then add another 100g to the spring and repeat the same process, making sure that the distance we pulled the spring down by was equal to that of before, e.g.
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Prediction/Theory Hooke's Law states that the extension of a spring is directly proportional to the force applied. I expect this to be shown in my results and graphs. A force (F) on a spring is linearly dependent on its extension, ?x. Hooke's law states that to extend a spring by an amount ?x, one needs a force, which is determined by the equation F = k?x. The spring constant, k, is a quality particular to each spring, usually determined by its thickness and the malleability of the metal (the stretchiness of the spring). In this experiment, the force is being applied through the addition of weights; therefore the force will act downwards and be a product of a combination of mass and gravity.
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* When twenty oscillations have completed then stop timing. * Then repeat the method but add on a 100g mass. * Repeat this three times for each measurement of mass, and then find the average of each set of results. Only test masses up to 1kg, as otherwise the spring's elastic limit could be broken, spoiling the spring. Hypothesis: I predict that the time period of the mass-spring system will increase as the mass on the spring increases. Take two masses as an example - a large mass and a small mass.
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Beyond the elastic limit, the applied force separates the molecules to the extent that they are unable to return to their original positions, and the material is permanently deformed or broken apart. SECONDARY EVIDENCE This was an investigation done into springs. The results accumulated were as follows: Force (N) Extension 1(mm) Extension 2(mm) Extension 3(mm) 0 0 0 0 2 20 20 20 4 40 30 30 6 50 50 40 8 60 50 50 10 70 60 60 12 SNAPPED 70 70 14 SNAPPED SNAPPED SNAPPED Fig 1.2 Fig 1.2 represents the results via tabulation and the graph for this information can be found at the back of this investigation, labelled Fig 1.3.
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Investigation of the relationship between extension of a spiral spring material per unit of load applied on it.
This will put the spring a good distanced up to prevent the spring from coming in to contact with the table which it will be on. The spring will be suspended from the stand to allow it enough space to stretch. * Secondly two bosses will be used, one to hold the spiral spring in place and the other to hold the 1 meter ruler firmly in place. The bosses help secure all the apparatus in to place. * Thirdly a weight hanger will be used to put the weights on the spring.
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Variables that could affect T Mass applied to spring; Preliminary experiments should be performed to assess suitable sizes of masses and intervals between different masses used in the experiment. Spring constant; The spring constant will be useful to confirm the relationship. A simple force - extension experiment should be performed to get an accurate value for k which can be compared to the value of k from the final experiment. Amplitude; The amplitude of the oscillations should be kept constant.
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The time for one of this oscillation is called time period. The time period depends on various things. By apply the laws of physics to time period; an equation can be arrived at: For mass on spring where m= mass K is spring stiffness (a constant speed for the spring = 23N/m) This equation is true as long as the elastic limit of the spring is not exceeded My Method * I am going to collect clamp, spring (at constant speed of 23 N/m), some mass and a stopwatch * I am going to set up my experiment on the desk, safely away from other pupils.
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I will have to be careful while working around the light. Because once the light has been switched on and left of a period of time the filament within the light bulb will start to heat up (because of the resistance) and will therefore heat up the glass casing. This will mean I will have to take care not to burn myself. I will also follow the rules of the laboratory and with these precautions I should be safe while carrying out the experiment.
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We are aiming to investigate the effect of force upon a spring. We will also investigate Hooke's law, to see what happens using two springs in parallel and series, and how this effects the spring constant.
When two springs are in series I predict the force will have a separate effect on each, so stretch will increase and the spring constant will decrease. I also predict that if the spring(s) pass their elastic limit, they will not return to their original size. Method: We are going to set up a retort stand and clamp on the edge of a desk with a G - clamp to hold the stand in place. Then we will place a ruler in the retort clamp and attach a spring to the end of the clamp.
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At that point the spring will have reached the point where Hooke's law is no longer accurate. I will do enough experiments to find and exceed the elastic limit. I predict I will need to take about 12 measurements. I will record the spring's extension in mm. I predict the spring's extension will increase in about 40mm each time, until the spring reaches its elastic limit. My predictions are based on Hooke's Law, which basically says if you stretch something with a steadily increasing force, then the length will increase steadily too. I predict the results I gather are going to be reasonably reliable and accurate, also very close to the line of best fit.
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Setting the stage for the environmental protection movement. In addition, Carson disproves her former belief that nature was too great and powerful a thing to ever be effected by humans and their actions. About the author Rachel Carson was born on a farm in Pennsylvania in 1907. She graduated from Pennsylvania College for Women in 1928 and went on to study a Masters in Marine Biology at John Hopkin's University in Baltimore. She continued her academic career teaching at the University of Maryland before finding employment at the US Fish and Wildlife Service.
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Investigate the effects of how springs and elastic bands stretch when weights are hung on them and how springs and elastic bands stretch when the weights are unloaded.
I also predict the more the weight the further the elastic band will go from its starting point. Apparatus: The equipment that I used for this experiment was: * Griffin 100g weights x4 * 1 metre ruler x1 * springs x2 * Clamp stand : * Boss x1 * Clamp x1 Explanation of Hysteresis: Hysteresis represents the history dependence on physical systems. If you push on something, it will yield: when you release, does it spring back completely? If it doesn't, it is showing hysteresis.
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