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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.
The amplitude of an oscillation is the maximum displacement of the system from its rest position. There are a number of other oscillations. Mechanical oscillations, for example, are in use everyday. The suspension units on cars and motorcycles are oscillators. They are, however, designed to provide smaller amplitudes as the oscillations continue: they dampen down. A car will bounce up and down only a few times before coming to rest. Once started, oscillations gradually die away. The kinetic energy of the oscillation is transferred to heat through fiction, so that the amplitude gets smaller and smaller.
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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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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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Where : T = Periodic Time (s) K = Spring stiffness G = Acceleration due to gravity (m/s) This means that K is the spring stiffness (or spring constant), F is the weight or force applied to the spring and X is the extension of the spring after the force has been applied. Graphically: B Extension (x) A Load (F) This is the graph that I expect to find from my results as it means that the extension of the spring will increase proportionally to the force that is applied to it. The graph should also curve at the top as this will be the elastic limit and will be unable to return to its original position and shape.
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The more molecules there are the more energy is needed to weaken the bonds. When a load is applied this creates gravitational potential energy(g.p.e). Therefore, materials smaller in width and length need less weight for the elastic limit to be reached. VARIABLES There are several variables which when altered will effect the behaviour of elastic bands and springs. To make a fair procedure their are certain variables that need to be controlled, and others that need to be varied in order conduct the experiment and give a detailed conclusion. The room temperature will effect the experiment, if it drops the particles will vibrate less, and will be drawn closer to each other, meaning the bonds will be harder to break and the material will contract.
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An investigation into the effects of a force applied to a spring and the time for it to complete a set number of oscillations
The temperature for this investigation will be room temperature, approximately 23?C. The same spring will be used. The same displacement for the spring will be used. The same spring will be used because of differences in the spring constant. The number of oscillations the spring hast to complete will always be 10. Scientific knowledge When using springs in an investigation, it helps to revise/research a law called Hooke's Law. This is a formula that states that the force acting on a spring and the spring extension have a constant relationship. Which can be expressed by the simple equation: F=KX Force=constant x extension Using this formula, we can find the constant of
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