Dimensional Analysis in Physics Problems

Dimensional Analysis in Physics Problems Dimensional analysis is a method of using the known units in a problem to help deduce the process of arriving at a solution. These tips will help you apply dimensional analysis to a problem. How Dimensional Analysis Can Help In science, units such as meter, second, and degree Celsius represent quantified physical properties of space, time, and/or matter. The International System of Measurement (SI) units that we use in science consist of seven base units, from which all other units are derived. This means that a good knowledge of the units youre using for a problem can help you figure out how to approach a science problem, especially early on when the equations are simple and the biggest hurdle is memorization. If you look at the units provided within the problem, you can figure out some ways that those units relate to each other and, in turn, this might give you a hint as to what you need to do to solve the problem. This process is known as dimensional analysis. A Basic Example Consider a basic problem that a student might get right after starting physics. Youre given a distance and a time and you have to find the average velocity, but youre completely blanking on the equation you need to do it. Dont panic. If you know your units, you can figure out what the problem should generally look like. Velocity is measured in SI units of m/s. This means that there is a length divided by a time. You have a length and you have a time, so youre good to go. A Not That was an incredibly simple example of a concept that students are introduced to very early in science, well before they actually begin a course in physics. Consider a bit later, however, when youve been introduced to all kinds of complex issues, such as Newtons Laws of Motion and Gravitation. Youre still relatively new to physics, and the equations are still giving you some trouble. You get a problem where you have to calculate the gravitational potential energy of an object. You can remember the equations for force, but the equation for potential energy is slipping away. You know its kind of like force, but slightly different. What are you going to do? Again, a knowledge of units can help. You remember that the equation for gravitational force on an object in Earths gravity and the following terms and units: Fg G * m * mE / r2 Fg is the force of gravity - newtons (N) or kg * m / s2G is the gravitational constant and your teacher kindly provided you with the value of G, which is measured in N * m2 / kg2m mE are mass of the object and Earth, respectively - kgr is the distance between the center of gravity of the objects - m  We want to know U, the potential energy, and we know that energy is measured in Joules (J) or newtons * meter  We also remember that the potential energy equation looks a lot like the force equation, using the same variables in a slightly different way In this case, we actually know a lot more than we need to figure it out. We want the energy, U, which is in J or N * m. The entire force equation is in units of newtons, so to get it in terms of N * m you will need to multiply the entire equation a length measurement. Well, only one length measurement is involved - r - so thats easy. And multiplying the equation by r would just negate an r from the denominator, so the formula we end up with would be: Fg G * m * mE / r We know the units we get will be in terms of N*m, or Joules. And, fortunately, we did study, so it jogs our memory and we bang ourselves on the head and say, Duh, because we should have remembered that. But we didnt. It happens. Fortunately, because we had a good grasp on the units we were able to figure out the relationship between them to get to the formula that we needed. A Tool, Not a Solution As part of your pre-test studying, you should include a bit of time to make sure youre familiar with the units relevant to the section youre working on, especially those that were introduced in that section. It is one other tool to help provide physical intuition about how the concepts youre studying are related. This added level of intuition can be helpful, but it shouldnt be a replacement for studying the rest of the material. Obviously, learning the difference between gravitational force and gravitational energy equations is far better than having to re-derive it haphazardly in the middle of a test. The gravity example was chosen because the force and potential energy equations are so closely related, but that isnt always the case and just multiplying numbers to get the right units, without understanding the underlying equations and relationships, will lead to more errors than solutions.

Brutal Treatment of Women Suffragists at Occoquan

Brutal Treatment of Women Suffragists at Occoquan An email has been circulating that tells of the brutal treatment in 1917 at Occoquan, Virginia, prison, of women who had picketed the White House as part of the campaign to win the vote for women. The point of the email: it took a lot of sacrifice to win the vote for women, and so women today should honor their sacrifice by taking our right to vote seriously, and actually getting to the polls. The author of the article in the email, though the emails usually omit the credit, is Connie Schultz of The Plain Dealer, Cleveland. Is the email true? a reader asks or is it an urban legend? It sure sounds exaggerated but its not. Alice Paul led the more radical wing of those who were working for womens suffrage in 1917. Paul had taken part in more militant suffrage activity in England, including hunger strikes that were met with imprisonment and brutal force-feeding methods. She believed that by bringing such militant tactics to America, the publics sympathy would be turned towards those who protested for woman suffrage, and the vote for women would be won, finally, after seven decades of activism. And so, Alice Paul, Lucy Burns, and others separated in America from the National American Woman Suffrage Association (NAWSA), headed by Carrie Chapman Catt, and formed the Congressional Union for Woman Suffrage (CU) which in 1917 transformed itself into the National Womans Party (NWP). While many of the activists in the NAWSA turned during World War I either to pacifism or to support of Americas war effort, the National Womans Party continued to focus on winning the vote for women. During wartime, they planned and carried out a campaign to picket the White House in Washington, DC. The reaction was, as in Britain, strong and swift: arrest of the picketers and their imprisonment. Some were transferred to an abandoned workhouse located at Occoquan, Virginia. There, the women staged hunger strikes, and, as in Britain, were force-fed brutally and otherwise treated violently. Ive referred to this part of woman suffrage history in other articles, notably when describing the history of the suffragist split over strategy in the last decade of activism before the vote was finally won. Feminist Sonia Pressman Fuentes documents this history in her article on Alice Paul. She includes this re-telling of the story of Occoquan Workhouses Night of Terror, November 15, 1917: Under orders from W. H. Whittaker, superintendent of the Occoquan Workhouse, as many as forty guards with clubs went on a rampage, brutalizing thirty-three jailed suffragists. They beat Lucy Burns, chained her hands to the cell bars above her head, and left her there for the night. They hurled Dora Lewis into a dark cell, smashed her head against an iron bed, and knocked her out cold. Her cellmate Alice Cosu, who believed Mrs. Lewis to be dead, suffered a heart attack. According to affidavits, other women were grabbed, dragged, beaten, choked, slammed, pinched, twisted, and kicked. (source: Barbara Leaming, Katherine Hepburn (New York: Crown Publishers, 1995), 182.) Related Resources: An image of Emmeline Pankhurst, who led the militant British woman suffragists, including hunger strike tactics, which inspired Alice Paul  and the National Womans PartyA firsthand account of this is in Doris Stevens Jailed for Freedom (New York: Liveright Publishing, 1920. (Gutenberg text)The movie Iron Jawed Angels focuses on this period of the woman suffrage movement.Sewall-Belmont House, home of the National Womans Party, is now a museum which includes many archives of these events.The Library of Congress presents some photos of women suffrage prisoners: Suffrage Prisoners