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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.
For this investigation I have been asked to find out how different masses on a spring effect the extension when the springs are in parallel, series and on a single spring.
If two springs are placed in series, I believe that the extension of the springs will be double the extension of a single spring with the same load (therefore will have half the spring constant of a single spring); and similarly if two springs are placed in parallel then the load will be spread evenly across the two springs so it will require twice the load to produce the same extension of only one spring (and have twice the spring constant of a single spring).
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This gives me 2.2, 2.0 and 2.5 as 2 is the average round number I will use this. To make the experiment a fair test I will do the experiment three times to gain a fair average. Each of these times I will also use the same type of rubber band as a different type of rubber could effect how far the band will stretch and therefore my results. I will also try to add the weights gently so that the force of it being applied to the band does not affect my results.
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He is appealing to the reader's imagination of what could have been by describing the fallen kingdom that is. He is looking back on time that has passed. In contrast, in Spring and Fall, Hopkins is talking of time that is currently passing, rather than looking back on time that has gone already. Unlike Shelley, Hopkins is talking to a certain person, rather than just any audience who happens to be reading the poem. Spring and Fall is a very personal account of the passage of time, and though less foreign, it is also less familiar in the reader's mind.
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Also you can see how the line goes through the origin, which should be so. This line of best fit allowed me to calculate the speed of the sound waves in the air. This is because the gradient of this line equals the speed. The gradient for a straight line is found by dividing the change in Y by the change in X. Gradient = Change in Y Change in X However, in this case the gradient will be the speed.
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My aim is to investigate what factors affect the period of a Baby Bouncer. The factor that I will be varying will be the mass on the end of the spring.
I am using this prediction due to what is stated in Hooke's law. Equipment Used * Spring * Clamp Stand * Stopwatch * Weights * Ruler Method * Equipment will be set up as in diagram above. * The weights will be dropped from the top of the spring. The stopwatch will be started when the weights are dropped. * We will count 5 oscillations. When the fifth oscillation has been recorded, the stopwatch will be stopped. * This will be repeated 5 times for each mass, and we will be using weights from 100grams to 1000grams, increasing each time by 100grams.
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Weak springs are very sensitive and can be used for measuring small forces. Strong springs can withstand larger forces. Preliminary To help me come up with an initial theory I will carry out a preliminary experiment. For my preliminary I will investigate how mass affects the extension of a spring. The apparatus I will use is a 25mm spring, a clamp to hold the spring, 100g masses and a ruler to measure the length of the spring. The variable I will change is the mass. All the other apparatus remained constant. My method is to connect the spring to the clamp, attach the mass to the bottom of the spring and measure it by holding a ruler to the side of it.
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So we are looking for 10 results and that should enough to draw a suitable graph. We shall then be able to measure the sag, which is caused by the mass on the main beam using a ruler; we shall measure the sag from its lowest point to the floor (fig.3). We shall repeat the experiment for the same weight times so we have an accurate reading, if the measurements are not all the same then we shall take the resulting average.
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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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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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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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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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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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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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Firstly I will make sure that an equal amount of mass (100g each time) is added each time. Then I will make sure that the readings are taken accurately, by using a splint to measure and mark the exact millimetre on the ruler. I will also make sure the spring is as close to the ruler as possible and also hanging off the table if the weights exceed past it to, make sure I get an accurate reading. As if it leans on the desk it could effect the extension and the deformation of the spring.
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I also counted 10 complete bounces of the spring and divided it by 10 so that the time of one bounce would be more precise. I made sure that I started the stop clock as accurately as I could so that my three individual tests would be very similar and this was shown in my results. The variable I am using is the amount of springs used and in what order, this is the only thing I am changing so that my test is fair.
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Prediction Based on my scientific knowledge of Hookes law (extension is directly proportional to the stretching force) and my oscillation of a pendulum experiment which proved Hookes law I predict that the weight I put on the bottom of the spring will be directly proportional to the time taken for one oscillation. Therefore, when I double the weight on the bottom, I will be doubling the time taken for the spring to oscillate. However, based on class discussion and my previous experiment I also predict this rule will not apply after the spring has passed its elastic limits (approx.
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To investigate the relationship between the extension of a compact steel spring and the force producing that extension and to determine the elastic limit and force constant of the spring
After the elastic limit has been reached, the spring stops obeying Hooke's law. Point A is an example of where the mass is removed and the extension remains. This is called the yield point. The extension that remains is the measurement OS that is recorded at the base of the graph. The force constant of a spring is the force needed to cause unit extension. If force (F) produces extension (e) then this can be shown as: Hypothesis From the theory I expect to find that I will get a constant extension with every 100g added to the spring.
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Hook the 20swg spring onto the clamp stand. . Move the metre stick to line up an easy figure with the bottom of the spring e.g., 200mm to make the results easier to record. . Add a 10g mass and record the extension each time until the spring won't return to its normal position. . Do the above for each spring making sure you record it to the nearest millimetre. Measurements I will be using, 10g masses to extend the springs, a 1metre stick to record the extension, and 5 nichrome springs with a gauge of 20swg, 24swg, 28swg, 32swg, and 36swg to extend.
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These values will allow us to plot a graph from which we can clearly analyse the results. The results will be measured in the following table: Distance (in cm) Voltmeter reading (in volts) Voltmeter reading 2 (in volts) Voltmeter reading 3 (in volts) Average reading (in volts) 0 10 20 30 40 50 60 70 80 90 100 Background light will also be measured and taken into account as the experiment is conducted. Background light is light from sources other than our own; these include other experiments being conducted, and natural daylight, which could interfere with our results.
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Up to this point, a spring can return back to its original shape and size, however beyond this point, the spring will become permanently stretched and deformed. Now I am going to investigate the factors, which affect the extension of an elastic cord, instead of a spring. The factors, which affect the extension of elastic, are; * The amount of force applied * The thickness of the cord * The length of the cord * The width of the cord * The temperature of the cord The elastic cord is made of rubber, rubber is a special type of molecule called polymer.
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no block, and so the lateral displacement grows as well, so that when the dragging away is doubled, so will the lateral displacement. Because of this, I think my results will be directly proportionate. Measurements, Fair Test and How to be accurate The measurements of the block are 2cm x 6 cm x 11 cm, and I will be using two blocks. The blocks will be put together, so that I can get more than three results. The Sizes of the amount of glass that the ray passes through will be 2cm, 4cm, 6cm, 8 cm, 11 cm, 12 cm, 13 cm, 17 cm and 22 cm.
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The gradient will in turn the Young's modulus. The initial gradient in the elastic gradient will be calculated to find the Young's modulus. As mentioned, I will compare the difference in Young's Modulus between a pure metal (copper) and one of its alloys (Constantan). I will find the difference in stiffness and consider whether it affects any other physical properties such as tensile strength and ductility. The data book suggests that the Young's modulus of Copper and Constantan are 12*1010 Pascal and 11*1010 Pascal respectively.
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Finding the Spring Constant (k) and Gravity (g) using Hooke’s Law and the Laws of Simple Harmonic Motion
Clamp and Stand 2. 10gram weights 3. Ruler - accurate ? 0.5mm 4. Stopwatch - accurate ? 0.005 seconds 5. Digital scientific scales - accurate ? 0.005g 6. Spring 7. Marker 8. Safety Glasses 9. Gloves Procedure 1. Set up the equipment as below: 2. Safety - Put on safety glasses and gloves as the spring could snap as we put more weight onto it. 3. Place first weight on scales and record mass in the table under mass. (mass must be in kilograms. All results should be recorded to 3 d.p.) 4. Place mass on end of spring 5.
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