centripetal

# Centripetal - 27 Experiment III Centripetal Force Goals • Learn the procedure for determining the exponents in a power law • Experimentally

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27 Experiment III: Centripetal Force Goals Learn the procedure for determining the exponents in a power law Experimentally determine the relationship between the centripetal force and the mass, radius, and speed for an object in uniform circular motion Introduction and Background Centripetal Force : Those of you who have tied an object to a string and whirled it in a horizontal circle no doubt have noticed that you have to pull on the string, and therefore, on the object in a direction toward the center of the circle in order to keep the object in the circular path. If you do not pull on the string, the object will simply fly off. This pull or force, as you learned in class, is called a centripetal force. You may also have noticed that you have to pull harder if the mass increases, or the speed increases, or the radius decreases, which is consistent with theoretical relationship between centripetal force (F) and the mass (M), speed (V), and radius (R) you have learned in class. In this lab, however, we will pretend that we know nothing about the relationship and try to determine it through some designed experiments. Determination of a Power Law : A power law is a functional form as shown below: n x C y × = (3-1) where C is a constant and n is the exponent; namely, y is proportional to the n th power of x . We can take the logarithmic of both sides of Equation 3-1: C x n y log log log + × = (3-2) Therefore, a plot of log y versus log x should be a straight line whose slope is the exponent n . Many relationships in physics take some form of a power law and very often we need to determine the exponents in these power laws. To do this experimentally we would generate a set of data points of (y, x) and plot log( y ) versus log( x ) on linear scales to determine the slope and thus the exponent. In case multiple variables are involved, ie c b a x x x C y 3 2 1 × × × = (3-3) we would determine the exponents one at a time. For example, to determine b , we would keep x 1 and x 2 constant in the experiment and we would have ) log( log log 3 1 2 c a x x C x b y × × + × = (3-4) where the last term is just a constant and the slope of log y versus log x 2 yields the exponent b . Exponents in Centripetal Force

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## This note was uploaded on 11/10/2011 for the course PHY 2053 taught by Professor Lind during the Fall '09 term at FSU.

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Centripetal - 27 Experiment III Centripetal Force Goals • Learn the procedure for determining the exponents in a power law • Experimentally

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