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PHYSICS 183 for Spring 2009
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CONCURRENT FORCES
The correct mathematical manipulation of vector quantities (such as forces, velocities , etc.) is a necessary feat for you to learn as we try to resolve the complex behavior of objects into simple actions. Thus, a vector may be resolved into component vectors; or if we wish, vectors may be added together to give a single resultant vector. Vector forces can be easily used and measured on a horizontal circular "force-table". Knowing that forces cancel one another if they have equal magnitudes and act in opposite directions gives a physical requirement for studying how vectors interact. The conditions for a body to be in a state of rest or in a state of uniform motion are known as the conditions for equilibrium. For translational equilibrium, which requires no change in translational speed or no change in the direction of motion, the vector sum of all the forces acting on the body must be zero. Today you will study the case for several forces acting on an object at the same point (concurrent forces). Three strings are attached to the circular ring positioned at the center of the force table. Each string runs over a pulley and attaches to a mass hanger. The magnitude of the force applied to the center ring by each of these is the mass times the acceleration of gravity (as we will learn later). To save time you may record only the mass without calculating the force, but keep in mind that 0.200 kg is not a force (the force is 0.200 kg x 9.82 m/sec2 = 1.96N). Set up the masses and angles given in the Table for Case 1. By trial and error, determine what mass at what angle is required for equilibrium. Once you are close to equilibrium the peg in the center of the force table can be removed so that you can better judge when the ring is centered. It is helpful to give the ring a little "nudge" so that it moves a little. Once in motion it is more likely to come to the true equilibrium position. The ring is in equilibrium when the ring returns to a centered position of the peg (or its hole). Draw the equilibrium arrangement into your notebook. How is this force related to the sum of the first two forces? All measurements of physical quantities involve error. Errors are limitation on accuracy, not mistakes. No measurement is perfect. So when a scientist states a measured value he or she also states the possible range of error. For instance, if I measured a book with a meter stick the result might be 35.2 cm ± 0.05 cm, which means that my best estimate of the length of the book is 35.2 cm, but it might be as small is 35.15 cm or as large as 35.25 cm. While trying to find the angle which would produce equilibrium you probably found that there was a small range of angles over which the forces were balanced rather than just one position. Determine this range of angles by starting at the angle you recorded in the last part, then move the pulley very slowly to the right until the ring is no longer centered. Record this angle and repeat moving to the left. Record your measurement of the angle with error. For instance, if you found that equilibrium could be achieved anywhere between 43o and 47o, your answer should be stated as 45o ± 2o. In order to determine the error in the mass reposition the pulley at the center of the range of angles, then add and subtract mass a little at a time until you have found a range of mass values for which the system is in equilibrium. State the mass with error. Often scientists check their experimental results by calculating what theory predicts the result should be. For each case, calculate the x and y components of the two given forces. Find the magnitude and direction of the sum of these two forces. Now find the magnitude and direction of the force which will balance these two forces. (You can give the magnitude of the force in terms of the mass.) Compare this with your experimental results. Is the theoretical value within the range of values found in the experiment? In other words, do the theoretical and experimental results agree to within the accuracy limits of the experiment? Repeat the procedure for the other two cases given in the table.
(Hint: place all of your data and the results of theoretical calculations in a single table. Each row in the table should be for a given experimental setup. Be sure to include column headings similar to the following.)
MA(kg) AngA(deg) MB(kg) AngB(deg) Exp.Mass(kg) Exp.Angle(deg) Theory M(kg) Theory Ang(deg)
Remember to include a summary about what you have learned in you laboratory notebook!
Comments and suggestions should go to the webmaster: Beverleyy Taylor last modified on October 29, 2001
ForceTable97.doc |