The Relationship Between Centripetal Force And Velocity Environmental Sciences Essay

The Relationship Between Centripetal Force And Velocity Environmental Sciences Essay Investigate the relationship between centripetal force and velocity in circular motion, when a stopper is swung with a string in which different weight hangers are attached to. DATA COLLECTION AND PROCESSING According to Mr. Isaac Newton, an objects natural state of motion is to stay at rest if its already at rest or to continue in linear, uniform motion unless its subjected to a net, external force. This means that if an object is moving at constant velocity (or speed) in a straight line, it will continue to move in a straight line, at that same velocity, unless some outside force changes its motion in some way. So in order for an object to move in a circular path, some force is needed to pull it away from the straight-line trajectory it wants to follow (i.e., its natural state of motion). Some force needs to pull the rotating object in at every single point along its circular path in order for it continue moving in a circular fashion (instead of allowing it to follow its natural state of motion)[1]. If an object moves in a circular path there must be centripetal Force acting on it. In this experiment we will investigate the relationship between centripetal force and velocity. Next we will show how our raw data is going to be manipulated: Initially we will show T for 20 revolutions, at each trial. Subsequently the average for 20 revolutions will be calculated (based on 3 trials). Using this averaged value we will calculate the period of 1 revolution. In this process we will have to divide the uncertainty in time by 20. Details about uncertainty calculation will be added later on. Next we are going to calculate the average linear speed, v, of the stopper for each mass of the weight hanger. We will include a sample calculation. We must remember that we used a fixed radius of 0.5 meters. We have to bear in mind that we will have to add the percentage uncertainty in the radius and the percentage uncertainty on T and add them up when calculating the uncertainty for linear velocity. Theoretically, the centripetal force should be directly proportional to the square of the speed. In order to check this, a column v2 will be added to one of our data tables. When we do that the uncertainties on V must be squared. We will also display a column indicating the centripetal force. We know that the centripetal force is equivalent to weight in this experiment; the weight, in turn, is equal to the tension on the string. When calculating the uncertainty for the resultant force (weight) we took the uncertainty on mass and multiplied it by ten which is the gravity value. In order for us to calculate centripetal force the following formulas will be used: Fc = mv2/ r Fc = W = mg The uncertainties involved with the measurements which have fixed values are: Centimeters: 1cm  ± .05cm Time: 1s  ±0 .005s Mass: 1kg  ± 0.000005kg UNCERTAINTY ON T The uncertainty on T is the same of that on the stopwatch. As we start and stop the stopwatch we must, therefore, double the uncertainty: 2( ±0 .005) =  ±0.01 SAMPLE CALCULATION OF T FOR ONE REVOLUTION OF A MASS OF 0.1 KG Average T for 20 revolutions: 15.3 Average T per revolution: 15.3 / 20 = 0.765 Uncertainty was also divided by 20: ( ±0.01/ 20) =  ±0.0005 As the uncertainty on T was already multiplied by 2 we do not need to double it this time CALCULATING UNCERTAINTY ON VELOCITY FOR 0.1 KG As mentioned earlier now we will have to calculate percentage uncertainties. We will apply the following formula: http://scidiv.bellevuecollege.edu/Physics/measuresigfigs/Measuresigfigseq1.gif Percentage uncertainty in radius: (0.05 / 0.5) x 100=  ±1.0% Percentage uncertainty on T for 1 revolution (calculated above): (0.00025/ 0.765) x 100 =  ±0.0326% By adding p the above uncertainties we get the percentage uncertainty for velocity which is  ±1.0326% in this case. In order to obtain the percentage uncertainty for v2 we simply square the uncertainty on v. SAMPLE CALCULATION OF V FOR 0.1 KG v = 2 pi r/T V= = 4.106  ± 1.0326% In addition we will calculate UNCERTAINTY ON MASS The uncertainty on mass was calculated based on the electronic scale used. The uncertainty on the scale was  ±0.05 grams. Since we need the uncertainty in kg we multiply this value by 1000 and we get:  ±0.00005 Table 1 Showing magnitude of resultant force and averaged results Mass (kg) ( ±0.00005) Centripetal Force (N) ( ±0.000005) T for 20 revolutions ( seconds) ( ±0.01) Trial 1 Trial 2 Trial 3 0.100000 1.000000 15.50 14.81 15.56 0.150000 1.500000 13.69 13.80 13.91 0.200000 2.000000 12.31 12.76 12.43 0.250000 2.500000 11.57 11.55 11.61 0.300000 3.000000 10.40 11.20 10.80 0.350000 3.500000 10.38 10.01 10.21 In table 1 we presented the value obtained in each trial for 20 rotations. In table 2, on the other hand, we are going to present the average value of 1 rotation for each mass. By doing so we believe to have increased the accuracy of the results. In order to calculate the uncertainty for 1 oscillation we divided the uncertainties in 20 rotations by 20; as the left-most column (table 2) shows. In spite of that there were cases where the difference between the highest and lowest value obtained were greater than the uncertainty itself. In the cases where this happened we found the differences between these values (highest and lowest) and use it as the uncertainty. Now we will show these differences between higher and lower values. In the three trials for 0.1 Kg the difference between the highest and lowest value is: 15.56 14.81 = ± 0.75. Hence this value will be used as the uncertainty as it is greater than the uncertainty in time. In the three trials for 0.15 Kg the difference between the highest and lowest value is: 13.91 13.69 =  ±0.22. Hence this value will be used as the uncertainty as it is greater than the uncertainty in time. In the three trials for 0.2 Kg the difference between the highest and lowest value is: 12.76 12.31 =  ±0.45. Hence this value will be used as the uncertainty as it is greater than the uncertainty in time. In the three trials for 0.25 Kg the difference between the highest and lowest value is: 11.61 11.55 =  ±0.06. Hence this value will be used as the uncertainty as it is greater than the uncertainty in time. In the three trials for 0.3 Kg the difference between the highest and lowest value is: 10.80 10.20 =  ±0.60. Hence this value will be used as the uncertainty as it is greater than the uncertainty in time. In the three trials for 0.35 Kg the difference between the highest and lowest value is: 10.38 10.01 =  ±0.37. Hence this value will be used as the uncertainty as it is greater than the uncertainty in time. Table 2 Preparing the results for graphical analysis T for one revolution (seconds) ( ±0.0005) Absolute Uncertainties ( ± seconds) Percentage uncertainty on T ( ± %) V (m/s) Percentage uncertainty on V ( ± %) V2 (m2/s2) Percentage uncertainty on V2 ( ± %) 0.76500 0.75 0.000653 4.105 1.000653 16.859 1.001306 0.69209 0.22 0.000722 4.537 1.000722 20.857 1.001445 0.62239 0.45 0.000803 5.045 1.000803 25.457 1.001607 0.57880 0.06 0.000864 5.425 1.000864 29.430 1.001729 0.53970 0.60 0.000926 5.818 1.000926 33.846 1.001853 0.51040 0.37 0.000976 6.152 1.000976 37.850 1.001953 Now we will plot square root of centripetal force against V. We will make use of the percentage uncertainty on V to plot the horizontal error bars and the uncertainty on centripetal force to plot the vertical error bars. The uncertainty on centripetal force is  ±0.000005 and, therefore must be squared to give us the uncertainty on. So we have which is equal to  ±0.002236. Thus we have explained how our error bars were calculated. The graph we came across was the following: Graph 1 Showing correlation between and V Not as we were expecting the graph resembles a parabola. We believe that, in order to obtain a straight line we must square both the centripetal force and velocity. This will give us the proportionality found in the formula: F = mv2/ r. We believe that, by plotting this graph we will be able to prove our prediction that the velocity squared is proportional to centripetal force. By plotting the mentioned correlation we get: Graph 2 Showing correlation between Fc and V2 Even though the best linear fit is not a perfect straight line there are no big discrepancies in our results (such as an outlier). The RSME value or the root means square error tells us how far the linear fit is from the plot points. The value of 0.02 is really low and suggests that the best fit is really close to the original data. Also the difference between the possible maximum value and possible minimum value of the spring is so low: Maximum slope: 0.13 Minimum slope: 0.11 Difference: 0.02 So we have the slope of our straight line being: 0.12  ± 0.02 Because the RSME value is low, we can infer that the value obtained is realistic. In addition due to the fact that the best linear fit touches (including or not the error bars) all the data points we can infer that the graph is accurate and, consequently, so are our results. CONCLUSION AND EVALUATION All in all this investigation led to fairly precise results. We do however think that the experiment can be improved in several ways. The following improvements would increase the reliability of the experimental procedure. Among the difficulties involved in the experiment we found, for instance, speed which we did not manage to keep constant when swirling the mass. Every so often the movement of our body would vary the speed at which the mass was being swung. In addition the swing rotation was not constantly a horizontal line. These factors will cause our results to become less accurate. Furthermore we faced some difficulties when swinging the stopper with constant power and speed; sometimes our hands touched the string which was not supposed to be touched during the rotations. The stopwatch delay and the human reaction time also affected our results to some extent. For example in a time of 5 seconds the human reaction time of 0.7 seconds can be very significant in the result as 1.4 seconds are involved in starting and stopping the stopwatch. Therefore these factors together are the responsible for us not obtaining a perfect parabola and consequently a perfect straight line. Moreover we found really ha rd to determine the initial and final point in relation to which the rotations were being counted. This probably led us to miscount the number of rotations. Therefore in some cases we might have had more or less than 20. Many changes could have been made to the experiment to make it more accurate: Setting up a better method of counting the rotations completed by the bung by using more advanced equipment than merely relying on human reactions. Increase the amount of rotations to ensure greater accuracy.  ·Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   Increase the number of repeats to get a more accurate average.  ·Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Set up computer equipment to time the experiment more accurately. This could be done using a motion sensor connected to a data logger (logger pro 3) to record the information.  ·Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   By doing the experiment outside uncontrollable factors such as wind can increase friction acting upon the bung and alter the time by small amounts which still make the experiment less accurate. Further work as increased number of repeats could be carried out. In addition, different experiments can be done with increased number of rotations and larger radii. If one decides to investigate the effect of another variable such as radii the experiment will keep the same; the only difference will be that the weight hanger will be kept constant and the radii will vary. If we decided to increase the radii being investigated we would conclude that as the radius increases so would the time to complete 20 rotations for the bung, in a proportion directly related to the increase in distance. This is because we know that F = mv2/ r. Where F = force, m = mass, v = velocity and r = radius. So if r is increased then all the other variables increase in direct proportion to the initial increase. Newtons First Law states that an object travels at constant velocity unless acted on by an unbalanced force. The unbalanced force is the weight in our experiment which increases the force making the sp eed increase because more force is being added. Therefore, this explains why the speed increases. Now we will try to explain our results based on our scientific knowledge. If we draw a free body diagram of what is happening during the experiment we will come to the conclusion that the tension in the string (which is equal to the centripetal force) is being produced by the force of gravity which is acting on the load being used. From graph 2 we see that centripetal force increases in a direct proportion to the square of velocity. This relationship is further explained by the formula: F = Since m and r are kept constant and v is our dependent variable we see that force, in fact, should increase as our experiment suggests. Thus our experiment proves the formula for centripetal force. Looking at the experiment we see that fairly good results were obtained. They, despite the uncertainties, allowed us to prove Hooks Law. Due to the fact that the experiment was dynamic, a few sources of errors affected our results. We see that the curve obtained is pretty close to a straight line which is reinforced by the low RSME value. All in all this tells us that the method is reliable and lead to precise results.

Counseling: Meaning of Life and Client Essay

Abstract This paper consists of my ideas on therapy and the roles of therapy. It also involves the ideas of a person’s relationship with Christ, their purpose and meaning in life, and what changes they need in their life for the therapy to work. My ideas on therapy stem from Existentialism and Person Centered Therapy. Personal Theory of Counseling Counseling is the ability to help people with their problems and assist them in finding their purpose in this life. Counseling is also helping people learn how to be open to new experiences, be more independent, and teach why the willingness to grow is important (Corey, 2009, p.169). Change is also a big part of counseling. People have to be willing to change in order for counseling to work. This therapy’s human nature involves trusting people, being positive, allowing for change, having self-understanding, and self-direction (Corey, 2009, p. 139-140). It also includes having self-awareness, being responsible, creating your own identity, knowing your values and goals, finding God, and realizing death will happen (Corey, 2009, p. 139-140). It also includes unconditional positive regard, which is accepting and caring for others (Corey, 2009, p. 174-175). Throughout the beginning of people’s lives they feel fulfilled, and they have self-determination to motivate them (Corey, 2009, p. 139-169). During sessions the client needs to be able to take charge of his or her own desired change. This means the client should be able to state and know what he or she wants out of therapy. The client should also be able to identify what he or she wants to change in their life. The counselor can only help as much as the client wants to be helped. So the client has to be able to make choices and help in their change (Corey, 2009, p. 165-175). Also, during sessions it is important to focus on the positive things in the person’s life. This can be done by allowing the client to think about things that have brought them happiness. Happiness according to Walker (2010) is, â€Å"A sense that life is good and a state of welling-being that outlasts yesterday’s moment of elation, today’s buoyant mood, or tomorrow’s feeling of sadness† (p. 500). These thoughts help the client to understand why they are here in this world, and it helps them find their meaning in life (Corey, 2009, p. 144-146). It is significant the client knows he or she has a meaning in life. If the client does not feel like they have a meaning in life, the counselor should help in this area of their life (Corey, 2009, p. 144-146). This can be done by having the client do an activity involving writing down all the good things of their life. Also, the client needs to understand and know he or she is in charge of their self-understanding and self-direction. This means the client needs to focus of their self-understanding and self-direction (Corey, 2009, p. 139-142). This can be done by having the client do activities that involve discovering their self-understanding and self-direction. Focusing on these areas will help the client through more difficult issues in counseling. This therapy will help target the key problems causing issues in the client’s life. These problems stem from not allowing change and development to take place in their life (Watson & Tharp, 2007, p. 200). An example of this is not fixing problems as soon as they happen in their life. The client has to learn the skills needed to allow for change and development. This will include working on problem solving skills and developing a better understanding on how to address their daily issues. The client also needs to learn how to take responsibility and handle their problems. Another problem is focusing on past experiences rather than the present. During therapy the client will learn how to focus on the here and now, not focus so much on the past (Watson & Tharp, 2007, p. 205). This will be done by having the client think about past experiences that still bother them. After thinking about the experiences the client will work on letting those issues go through role playing. The therapeutic process of this therapy has a set of goals for the counselor to use to help the client during the sessions (Watson & Tharp, 2007, p.210). These goals help the client learn how to be more independent and self-aware of the changes they need in their life. The point of this therapy is helping the client realize being independent and self-ware of the changes in their lives is very important and can lead to positive results. The first goal of the therapeutic process is allowing the client to be in charge of the change they want to accomplish (Corey, 2009, p. 170-171). An example of this is allowing the client to decide what change they want to master first. Through this goal the counselor and client can build a more trustworthy and deeper relationship. This also leaves room for a more positive and realistic change. The second goal includes working on the needs of the client (Corey, 2009, p. 170-171). This involves teaching the client how to identify their identity, learn self-awareness, and what their purpose is in life (Corey, 2009, p. 139-146). This goal also helps the client develop the skills needed to meet their needs. An example of how this will be done is using role playing and journaling. Another goal is allowing the client to be free in choosing their therapy topics. This means to some degree allowing the client to choose what he or she wants to talk about. Letting the client choose the topics helps make them more comfortable in talking about the more touchy subjects needed to reach the root of the problem. The next goal is opening doors in the client’s life to figure out where God is in their life. This includes showing the client the love of God and what God can and will do in their life. Also, this goal will give the client the opportunity to develop a relationship with God. The last goal is allowing the client to establish goals they want out of the sessions (Corey, 2009, p. 170). An example of this is allowing the client to explore what goals they want. The goal also includes letting the client decide whether the goal is working or not. If the goal is not working, the counselor should allow the client to drop the goal if they want to. It is very important the client feels like they have a say in their therapy. The client will be more willing to be open and honest if they have a say in their therapy. The relationship between the counselor and client should be friendly and trustworthy. The client needs to be able to trust and depend on the counselor. The relationship should develop over time and be positive to the client. Even though the relationship is friendly, there should only be contact during sessions or on the phone. The client needs to understand this is a concrete rule because of ethical standards. Also, the client needs to know that you are just his or her counselor and not a close friend. This is also because of ethical standards. The client needs to be aware that experiences during sessions will be comfortable, but they should also understand the sessions will not always be easy. The hard parts, though, are necessary for their desired change. During the sessions there will be no assessment, because it is not needed for this type of therapy. This is because the client will be choosing their desired change and what they want out of therapy. A normal session will involve the client being in a comfortable chair and feeling free to say what is on their mind. Even though they are free to speak what they are feeling, there will still be general topics for each session. During each session there will be a planned topic, but the topic may not get covered until later if the client needs attention on other topics. The first few sessions will involve the client and the counselor getting to know each other. This will include the client sharing about their life and what brought them to this point in their life. Also, these sessions will involve a few techniques to help the client feel more comfortable around the counselor. These techniques will include saying words that describe who they are as a person. Another technique will be having the client write down thoughts they are having about the counseling sessions. The next few sessions will cover the client’s self-awareness, his or her identity in this world, the client’s goals and values, and their relationship with God (Corey, 2009, p.139-147). During these sessions the client will work on building up his or her self-awareness through writing down their feeling. Also, the client will work on their self-awareness by thinking about what makes them who they are as a person (Corey, 2009, p. 139-140). The client will also work on figuring out their identity in this world (Corey, 2009, p. 139-140). They will do this through writing down and thinking about what they are doing in the world to make a difference. They will also journal their thoughts on their identity in the world and what makes it their identity. During the sessions the client will also work their goals and values. This will include the client making a list of their current goals and values and what they want their new goals and values to be. Also during these sessions the client will work their relationship with God. This will include going over who God is, what His son done for them on the cross, and how they can have a relationship with God if they want to. After those sessions the counselor will cover the client’s goals for therapy and the issues the client may be facing. This will include the client stating what goals they want out of therapy and how they want to achieve them. After the client decides on what goals they want to work toward, the counselor and client will work together on techniques to help the client. Throughout this process the client can move on and work toward fixing their problems. During the sessions it is significant to cover important topics about life and death (Corey, 2009, p. 147-148). This will include using the Word of God and other resources to reveal what life and death are. After the sessions are complete the client should have an understanding of their self-awareness, his or her identity in this world, their goals and values, their relationship with God, and what death is. Also, they should have a basic plan to help them through future problems and issues Overall, this therapy can help people who have the desire and drive to make it work. People can benefit from this therapy by getting the help they need. This therapy is set up to motivate and help people learn about themselves and how to solve their problems. It is also designed to help people reach their desired change and help them learn their meaning and purpose in life. This therapy can aid people in building a better life and future. References Corey, G. (2009). Theory and practice of counseling and psychotherapy (8th ed. ). Australia: Thomson/Brooks/Cole. Walker, V. (2010). Becoming aware: A text/workbook for human relations and personal adjustment (11th ed. ). Dubuque, IA: Kendall Hunt Pub. Co.. Watson, D. L. , & Tharp, R. G. (2007). Self-directed behavior: Self-modification for personal adjustment (9th ed. ). Australia: Wadsworth/Thomson Learning.

How and Why the Nazis Rose to Power

In this essay I will explain how and why the Nazis rose to power, elaborating on the circumstances of the great depression, the Weimar republic, Adolf Hitler and the Nazi party. Hitler and the Nazis were not prosperous in gaining power from up to 1928, this is because people thought all Nazis were brutes and believed that Hitler was a big joke. Nobody was interested in the Nazi ideas or plans and plus, Germany wasn’t quite ready for them. But Hitler soon came into power in many different ways. He promised to undo the Versailles Treaty which Germany had to reparation to England and France.He also promised to restore hope and to deal with the depression. Hitler also blamed the Jews for inflicting tragedy to Germany. Everyone soon agreed to the Nazi plans for getting rid of democracy and started to follow his ways. In 1929, the American stock exchange collapsed and caused an economic depression. America called in all its foreign loans, which destroyed Weimar Germany. Unemployment in Germany rose to 6 million. The German companies collapsed, the unemployment rate was extremely high, everyone resulted to violence and farming was a crisis because of the low food prices.The government didn’t know what to do so in July 1930 the chancellor cut wages and unemployment pay which had to be the worst thing to do during the depression. The anger and bitterness helped the Nazis to gain more support; in 1928, the Nazis had only 12 seats in the Reichstag and by July 1932 they had 230 seats and were the largest party. The Weimar Republic was after WWI when Germany became a democratic republic after the Kaiser fled. German citizens were allowed to vote, hold meeting for trade unions and would only be arrested if they broke the law which was all fair.There were many problems with the Weimar Republic which was the high unemployment, hunger, poverty; hyperinflation and the leaders were blamed for signing the hated Treaty of Versailles. The Weimar Republic lasted until 1 945, when the German government was finally dissolved because of the Second World War. The main reason why he became chancellor was because of the great depression advantage he had but Hitler was also a great speaker, with the power to make people support him. The depression of 1929 created poverty and unemployment, which made people angry with the Weimar government.People lost confidence in the democratic system and turned towards the extremist political parties such as the Communists and Nazis during the depression. The SA also attacked the Nazis opponents. The Nazis were clearly all Fascists because they all had very extreme right wing views which were racist and nationalistic (e. g. getting rid of Jews/ perfect race). There are many reasons why Hitler had come to power. Germany had just been through a war and had lost. The Treaty of Versailles made a contract for Germany which made living in Germany very hard.The people of Germany were poor and where upset with the Treaty. They wanted someone to help them out of the hole they were in. So Hitler offered them everything they wanted, the people of Germany were brain washed with posters, radio, newspapers and leaflets. Hitler's speeches where strong and effective, the Germans liked the idea of having one strong leader. The Nazis were organised and smart, people liked that; in 1930 The Nazis pulled 6,500,000 votes. Hitler was appointed Chancellor of Germany by President Hindenburg on 30th January 1933 which was 1/3 of the total votes an outstanding 13,500,000.

Health Promotion Is The Process Of Enabling People...

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