Calculating the Young Modulus of Constanton Essay Example for Free

Calculating the Young Modulus of Constanton Essay Introduction Constanton is a copper-nickel alloy mainly used in the for its electrical resistance properties. It has a high resistance which is constant over a wide range of temperatures. I am going to find out the Youngs modulus of this wire and observe its behaviour. Apparatus * Constanton Wire * G-Clamp x2 * Pulley * Hanging weights * Ruler * Micrometer * Small marker flag * Wooden end blocks * Sponge Blocks Underlying Theory When a sample is deformed by a force, the deformation is proportional to the magnitude of the force. This is shown by Hookes Law where: Force is equal to a stiffness constant (k) times the extension (e).The force is proportional to the extension. For a sample we can also calculate stress and strain: Where stress is equal to force (F) divided by area (A) and strain is equal to extension (e) divided by original length (l). When you plot these on a Stress-strain graph it proves Hookes law when it is straight line but as soon as the graph curves, the sample is showing plastic deformation as it is past the elastic limit. Using this graph we can work out the Youngs Modulus of a sample which is: This is also measured in Nm-2 or Pascals (Pa). It can also be calculated by working out the gradient on the stress-strain graph. When a wire obeys Hookes Law it deforms elastically. This means that when the load is removed, the wire returns back to its initial length. The atoms in the wire move small distances from their equilibrium positions but then return. After the elastic limit the wire starts to deform plastically. The atoms move within the structure so they cannot return when the load is removed. Measurements Throughout the experiment these measurements will need to be taken and observed: * Stress Force and surface area * Strain Initial length and the extension * Youngs modulus * Percentage error error of each piece of equipment * Hookes law (F=ke) Method To measure the Youngs modulus of constanton I will: 1) Set up the equipment as shown. 2) Choose a suitable section of wire from the real that doesnt appear bent, twisted or deformed. Measure the diameter of the wire with a micrometer before attaching it to the weights. 3) Attach a marker flag so the extension can be measured. 4) Start the experiment by measuring the initial length of wire and adding the 100g weights and measuring the new length each time. 5) Record your results in a table and plot a stress-strain graph using these results. Weight (g) Mass (N) Length (mm) Stress (Nm-2/Pa) Strain 6) Repeat the experiment three times or until you get a set of similar results. Results Experiment 1 In the first attempt at calculating the youngs modulus of constanton i used 0.44mm diameter wire with an initial length of 500mm. I measured both in millimetres because this would avoid converting units when calculating the strain of the wire (e/l). The wire only extended by 1mm when 1700g were added to it so I abandoned the experiment and changed my method slightly to get more extension for mass. Experiment 2 I changed the diameter of wire used to 0.23mm which is almost half the thickness than before. By using thinner wire we should see more extension for the amount of weight added so we can measure it with a ruler more easily. The initial length of wire was also 500mm. When i carried out the experiment the wire proved to be too thin because as only 500g was added the wire started to show rapid plastic deformation and continued to extend by roughly 6% (30mm) of its original length before the wire broke. Experiment 3 I changed the diameter again so I could record more conclusive results. I used a diameter of wire in between the diameters of the first two experiment (0.31mm) and an initial length of 500mm. I still couldnt record too accurate results as the wire didnt extend enough so I could only plot three points on a graph before it showed plastic behaviour. Further experimental changes were needed. Experiment 4 This time I changed the initial length of wire used to 800mm from 500mm. This would amplify the extension so I could measure it with the ruler because the rate of extension would increase and also the amount of extension would increase. By increasing the initial length of wire it would also decrease the percentage error in the measurement of the wire with the ruler. The percentage error goes from 0.1% to 0.063%. Experiment 5 This was a repeat to check the accuracy of experiment 4. In this experiment i encountered a few problems. The knot holding the weight hangers on kept slipping and the results found did not match the pervious pattern. Experiment 6 This was my third repeat of experiment 4. This gave me a fairly similar set of results to experiment 4. Due to time restrictions, no more experiments could be carried out to do a third repeat. Calculations * Using the diameter to work out the surface area. Let x = diameter X 10-3 = to change from millimetres to metres 2 = to change diameter into radius Then substitute it into the formula for the area of a circle. * Change grams into Newtons for force. Which is equivalent to 10 * Changing Pascals (Pa) into Megapascals (MPa) * Working out gradient to find the Youngs Modulus. Graphs To plot the graphs i only plotted points where the wire extended by a millimetre because the wire was extending between those points but I could not take sensitive enough measurements with a ruler. To plot the graphs i also changed Stress from Pascals (Pa) to Megapascals (MPa) to make it easier to plot on the graph. I also used the graphs to work out the Youngs Modulus of the Constanton by finding the gradient of the graph before it reached the elastic limit. Inaccuracies Here are some factors that may have caused some inaccuracies in my measurements: * The wire may contain impurities that change the way the wire behaves. This cannot be helped. * By attaching a pointer you can affect the sample by restricting the way it behaves. To avoid causing too many inaccuracies use as thin a pointer as possible so there is as little as possible touching the sample. * The pulley wheel may cause friction but this is the most sensible way of converting horizontal movement into vertical. * There also may be bends or variation in cross sectional area in the wire. To minimise the risk of this, dont use the first few metres of wire until you find a section that looks roughly undamaged. Percentage Errors The main source of percentage error is in the measurement of the diameter taken by the micrometer even though the micrometer is accurate to 0.005mm and the ruler is only accurate to 0.5mm. In experiments 4, 5, and 6: % error of diameter = [ 0.005 / 0.31] x 100 = 1.6% % error of length = [ 0.5 / 800 ] x 100 = 0.06% Other sources of percentage error are: Diameter of the wire which is an example of uncertainty in the measurements. Actual mass of the weights which is an example of systematic error. Conclusion Using experiments 4 and 6 I was able to work out my youngs modulus of Constanton by finding the gradient of the initial straight part of my graph. Experiment 4 = 280GPa Experiment 6 = 240GPa The real value of the youngs modulus is 162GPa so I am out by approximately a factor of two. This is not too far away from the true value considering the huge uncertainties involved with my measurement technique. To improve my accuracy I would either have to improve my measurement techniques or change my method completely. In conclusion, the method was affective for demonstrating the affects of Hookes law but not for measuring accurately the youngs modulus of constanton. Modifications in the Method * Attaching the pointer to the pulley stops the pointer coming into contact with the sample of wire which could obstruct deformation but if the wire extends more than the pulley can measure then the experiment will not work. * Illuminate the pointer to produce a magnified shadow of the movement. This makes it easier to see movement and allows for more accurate measurement however you need to calculate and calibrate magnification. * Use wire that isnt wound round a real because it distorted the start point of my curve. A typical youngs modulus curve starts at the origin but mine doesnt because first few hundred grams was used to apply tension to the wire to bend out the curves.

Aggressive Driving in Massachusetts :: Transportation Aggression Essays

Aggressive Driving in Massachusetts Driving in Massachusetts, doesn’t always get you somewhere. There were 141,675 motor vehicle crashes in Massachusetts in 2003. In response to the problem, Massachusetts law enforcement officials are vowing to get aggressive on aggressive driving, a growing danger in the state. â€Å"We will catch you and there will be consequences, criminal consequences, loss of licenses and even a jail term,† Col. Thomas Robbins, Massachusetts State Police warned aggressive drivers at the launch of ‘Road Respect’, a Spring Mobilization program at the Newton Police headquarters on the morning of April 4. ‘Road Respect’ is an attempt to educate Massachusetts drivers on the dangers of aggressive driving and enforce its decline. The Governor’s Highway Safety Bureau (GHSB), the State Police and over 255 local police departments are participating in the ‘Road Respect’ campaign to make it a success. Over 5,300 people suffered incapacitating injuries and 462 people died from the crashes in Massachusetts in 2003. While there was a decline in traffic accidents nationwide in 2003, Massachusetts experienced an increase of 1.9% from the previous year. â€Å"A friend of mine, Barbara Silva, a nurse at Waltham school was driving to work on Route 128 when another car suddenly cut her off. For some reason the truck ahead of [that car] braked abruptly and [the car] banged into it. She slammed into [the car]. It was a horrible accident. It could have been avoided if [the other car] hadn’t jumped lanes. â€Å"I call it a pinball game that aggressive drivers play when they bounce from one lane to the next. â€Å"It was 8 a.m. in the morning last March when it happened. [The driver] wasn’t drunk or anything and it didn’t have anything to do with the weather conditions,† said Carole Ferguson Page, a Massachusetts resident. The Massachusetts state and local police issued approximately 148,000 aggressive driving citations from 2000 through 2003. 17,950 of these citations involved a crash. The number of aggressive driving citations issued by Massachusetts state and local police increased approximately 3% during this time. Aggressive driving involves failing to yield right of way, making improper and unsafe lane changes, passing on the shoulder, ignoring traffic lights, following too closely (tailgating) and speeding. An aggressive driving citation involves two or more of these violations. Aggressive driving can also result from drunk or drug driving and distracted driving. It is hence densely woven into multiple road dangers. â€Å"Aggressive driving behavior is among our top traffic problems,† said Lt.

Piaget and early childhood

Truss Excelsior College Even though Jean Paging passed over thirty years ago his work is still seen in the classroom today. There are three educational principles that are derived from Piglet's theory that continue to have a major impact on both teacher training and classroom practices, particularly during early childhood. Discovery learning, sensitivity to children's readiness to learn and acceptance of individual differences are the three educational principles that are still impacting the educational atmosphere (Beer, 2010).Discovery learning encourages children to learn through discovery by spontaneous interaction with the environment. Teachers place items in their classroom that students can use for exploration and discovery. Children can explore art supplies, measuring tools, puzzles, table games, building blocks, etc. To enhance learning. Teachers don't readily present verbal knowledge in this setting but encourage discovery by these tactile means (Beer, 2010). Sensitivity to children's readiness to learn is another principle derived from Page's theory.In this environment teachers introduce activities that build on children's current thinking, challenging their incorrect ways of viewing the world and enabling them to practice newly discovered themes. However if the child doesn't not show interest or readiness the teachers will not teach them until they show interest or readiness. Lastly acceptance of individual differences, gives credence to Piglet's theory that children undergo the same stages of development, they Just do it at different rates. For this reason teachers must plan activities for small groups and not the whole class.Evaluations must be related to the child's previous development rather than an average based on normative standards or related to peers in the same age group. This allows for learning tailored to individual differences (Beer, 2010). Although there are three main principles of Piglet's theory still found in the classroom today, her also theorized that there are limitations to early childhood thinking. According to Jean Pigged, egocentrics, conservation, concentration and reversibility and the lack of hierarchical classification, are limitations to early childhood thinking.These limitations are aspects in the operational stage of his cognitive development theory (Beer, 2010). Egocentrics, deals with children's ability to see things form another's point of view. Pigged conducted a three mountains problem, in which a doll was placed behind three distinctive mountains with the larger one facing the doll and the smaller ones facing the child. When asked to identify a picture from the doll's point of view they would only chose the picture that represented what they saw from their point of view.Conservation is explained as physical characteristics of objects remaining the same even when their outward appearances change. In a demonstration a child is shown two glasses with equal amounts of liquid. The child acknow ledges that the two glasses have the same volume of liquid. He then pours the liquid of one glass into a taller glass. Children on the operational phase of thinking will say that the glass that is taller has more liquid even though they didn't see any additional liquid poured to increase volume or any liquid removed to decrease volume.This task also explains two other aspects of his theory, concentration and reversibility. In this experiment the children focus, or center on the height of the glass. They do not process the fact that the changes in height and width are what make the liquid appear taller. This is the premise behind concentration. Irreversibility is also at play here. The children are not able to reverse the process and think that if she pours the taller glass of liquid back into the same glass it was poured out of it would take on the original shape from the original glass..

The Ideological Origins Of The American Revolution Essay

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