Physics Tutor Doing the Experiment - 3 Simple Rules for Uncertainty

Welcome to the last post in our series on experimental error! As a physics tutor, I walk you through the experiental process and explore the traps that might lead you down the wrong path. Over the last several posts, we’ve explored the concepts ofaccuracy and precision of a measurement, averaging out the noise inherent in your measurement, and identifying and quantifyingany biases that might be throwing your results off. In this post, let’s put it all together. We’ll return to the experiment mentioned in the very first post and see how all the techniques we have learned enable us to reach our goal: writing down a final result, along with a quantified, rigorous statement of how much certainty we have about that result. The types of skills that these techniques encompass – thinking deeply and analytically about a physics problem, using your physical intuition to brainstorm problems, and applying rigorous analysis methods – will be useful throughout your career, from high school physics classes, through the SAT 2 and AP tests, into college physics courses and GREs, and hopefully beyond. What result do we want? Let’s briefly remind ourselves what we’re trying to measure. In this experiment, we are trying to measure g, the acceleration due to gravity, by dropping a ball from a known height and measuring how long it takes to hit the ground. We can solve for g to find where t is the measured time and h is the measured height from which we drop the ball. Rule 1: Add or subtract two quantities – add absolute errors The height h is the more straightforward quantity. Say we know the top of our table is 1.403Â ± 0.002 m from the floor and we hold the ball 0.540 Â ± 0.010 m above the tabletop. We can measure the table height to a precision of 2 mm but our arms can only hold the ball to within 1 cm of the intended drop height. This brings us to our first rule of propagating errors: When you add two quantities, you add their absolute errors. This makes intuitive sense if you imagine trying to measure a room by laying many cheaply made yardsticks end to end; if each yardstick might be independently off by, say, a tenth of an inch, then all those many tenths of inches will add up to give you the uncertainty in the length of the room. If the total height is given by then the total uncertainty in the height is given by Rule 2: Multiple or divide two quantities – add relative errors Let's step away from the ball-dropping experiment for a moment to introduce rule 2. Say you want to multiply the velocity displayed on your car’s speedometer by the number of hours spent listening to a carefully selected iTunes playlist to find the number of miles covered in your roadtrip. In this case, you need to take another approach to propagating errors. When you multiply or divide two quantities, you add their relative errors. The reasoning behind this rule is also easy to understand. Say you drive for 4 hours at 65 miles an hour, but traffic and rest stops put uncertainties in both your velocity and time: you weren’t doing 65 the entire way (traffic), nor were you on the road for the full 4 hours (rest stops). Because velocity and time are multiplied, the absolute uncertainty in terms of miles caused by your rest stops depends on your average velocity, and the absolute uncertainty caused by traffic depends on your total travel time. Consequently, it’s hard to determine what your total absolute uncertainty should be. If, on the other hand, you say that your travel time is 4 hours plus or minus 10% and your velocity is 65 mph plus or minus 15%, then you can say that the total distance traveled is 260 miles plus or minus 25%, or 260 Â ± 65 miles. More generally, if then the total relative uncertainty is Rule 3: Raise a quantity to a power – multiply relative error Now that we’ve seen rule 2, rule 3 is straightforward to understand. Let’s circle back to our ball-dropping experiment to see it applied. By using the techniques outlined in the previous posts, we can come up with a statistical uncertainty (from our noisy measurements) and a systematic uncertainty (from biases in our experiment) for t. The total uncertainty in t, then, is just the sum of the two: Notice, though, that our expression for g depends on t2, not t. In the same way that raising a number to the nth power is equivalent to multiplying that number by itself n times (i.e. 23=2*2*2=8), when you raise a quantity to the nth power, you multiply its relative uncertainty by n. Bringing it all together Now, we can apply all three rules to figure out the uncertainty we should quote for our final answer. We find and, plugging in, And so concludes our analysis of the ball-dropping experiment! It is a relatively simple experiment, one that most physics students see in the first few weeks of their high school class, but we have hopefully illuminated some of the subtleties that arise when performing even such a straightforward experiment. Keeping these considerations in mind will help you be a stronger physics student, whether experimenting at the lab bench, working through your homework, or sitting for the big exam. If you still have questions about problem solving in physics, I'd be happy to help! ;

Oprah Winfrey - One of the Most Influential Women in the World - Free Essay Example

She is a known television personality, actress, producer, and a philanthropist. Although she has done various works in the media, Oprah is popular because of her show, The Oprah Winfrey Show. She has won many awards and is one of the wealthiest African-American individuals in the United States (Peck, 2010). Her wealth came after years of living in poverty and enduring abuse. Winfrey was born to a poor teenage girl in 1954 (Peck, 2010). She stayed with her grandmother during the first few years of her life. During that period, Winfrey was subjected to physical abuse. After a few years, she joined her mother who lived in a poor and dangerous neighborhood. Winfreys mother did not have enough time to supervise and protect her child, and in turn, Oprah was sexually assaulted by different men. Some of the men who abused her were family members whom she trusted (Illouz, 2003). Winfreys first abuse happened when she was nine years old, and by the time she was 14 years she became pregnant (Illouz, 2003). Unfortunately, her baby died during infancy. After a few years, Winfrey was sent to stay at her fathers house. During her time there, she focused on her life and began performing better in school. That was the beginning of her story. Winfrey held several jobs before starting The Oprah Winfrey Show. She also started acting and later on, became a producer. She has also authored several books during her time. Depression Oprah Winfrey has openly discussed her struggle with depression in 1998 (McKenzie, 2017). Her depression was caused by the failure of her movie, Beloved, which had been produced in the same year. Winfrey had expected the movie to perform well at the box office, but things did not go as she had hoped (McKenzie, 2017). She had dedicated a lot of effort in the movies and could not believe that things did not turn out as planned. As a result, Winfrey started having negative thoughts and feelings about herself. The fact that she was already a successful person did not stop her from falling into depression. She felt like a failure at that moment. During that period, Oprah sought solace in food. She would eat to suppress her emotions (McKenzie, 2017). At some point, Oprah began purchasing tickets to enhance the numbers at the box office. However, her efforts were fruitless thus resulting in more negative thoughts. Winfrey also suffered from sleep disturbances, lack of energy, and the desire to stay alone (McKenzie, 2017). Just like many people who become depressed, she found something that could take away her pain. In her case, food was the only thing that could make her feel better. How Oprah Winfrey Overcame her Depression In most cases, mental health problems require medication. It is usually appropriate to seek medical assistance from healthcare practitioners (Segal, Williams, Teasdale, 2018). However, some people possess certain unique strengths that can help them in overcoming their mental illness. Oprah Winfrey was one of these individuals. One of her strengths was that she was able to realize that she was not well. Realization enables people to start working towards finding a solution to their problems (Park et al., 2018). After realizing that she was unwell, she began taking care of herself. She would focus on more positive things she had in life (McKenzie, 2017). Oprah started disregarding any negative thoughts and feelings she had about herself and instead appreciated herself. She began focusing more on the things she had instead of those she hoped to have. Oprah also controlled her eating habits, and within six weeks she was able to overcome her depression. Oprah once said she learned never to put all her hopes and expectations in one basket (McKenzie, 2017). She learned always to appreciate whatever she had instead of what she did not have. Oprah was fortunate to have overcome her mental illness through self-care methods. What I Learn from Oprahs Experience Oprah Winfreys experience shows that mental disorders can affect any individual no matter their social status. Winfrey became depressed even though she was very successful and rich. She had been working on her popular show, The Oprah Winfrey Show, for many years and had become very famous. From her experience, it is clear that anyone can be depressed when they are under extreme stress. On normal occasions, stress is a good thing, and it helps keep human beings alert and motivated (Needham et al., 2015). However, too much stress is harmful and can lead to episodes of depression. In addition to that, Oprahs experience shows that every person has their way of dealing with their depression. Some people prefer staying indoors while others start drinking excessively. People suffering from depression use such methods to feel better about themselves (Midgley et al., 2017). However, such habits can be harmful to an individuals health. For instance, people who become excessive drinkers during their depression can suffer from alcohol-related diseases. On the other hand, people who seek comfort from food risk suffering from obesity-related illnesses. Therefore, suffering from depression can indirectly lead to other diseases or physical discomforts. Additionally, Oprahs experience shows that high self-evaluation is important when dealing with depression. The moment she realized she had a mental disorder she decided to start appreciating all the things she had and stop stressing over those that she wished she did. Her experience shows that positive thoughts and optimism can cure depression. A person suffering from the illness can practice this method on their own or seek the help from a medical practitioner (Sobrinho, Campos, Holden, 2016). One can also engage in positive activities like being kind to others, being grateful, meditating, and many others. Through such behaviors, a depressed individual will start feeling better about himself or herself (Sobrinho, Campos, Holden, 2016). Consequently, such an individual will be able to come out of depression. Lastly, Oprahs experience shows that people should learn to diversify economically, socially, and emotionally. Diversifying ensures that an individual will not be too attached to a specific item. As a result, such a person will not be overly disappointed if one of the important items in their lives fails to work as anticipated (Sobrinho, Campos, Holden, 2016). The level of stress will be low thus protecting him or her from mental illness. Conclusion Oprah Winfrey managed to become very successful despite her poor background. In 1998, she was depressed for six weeks and was able to overcome her situation through positive thinking. Her experience shows anyone gets depressed and that positive thinking can get them out of their situation.