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Material Type: Lab; Class: Physical Science Course Observations and Investigations: Matter (GL); Subject: Physical Science; University: Harford Community College; Term: Unknown 2007;
Typology: Lab Reports
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Harford Community College Physical Science 106 Period of a Simple Pendulum Lab Introduction In order to understand the motion of a pendulum, one must analyze the forces involved as we do using Newton's Laws of Motion. For the simple pendulum, the forces depend on the angle of inclination of the mass attached to a light string attached to a support as pictured below. Forces on a simple pendulum. In the diagram, the force of gravity m g acts vertically downward. This force may be broken down into 2 forces, one parallel to the string and the other perpendicular. The parallel force mgcos simply pulls the string tight, and no motion occurs due to this force. Discussion Questions
To Investigate further the nature of this dependence, we shall consider the dependence of the log of the variables. We begin by taking the log 10 of the lengths and the periods from your previous table. Then, plot the log values below. Length (cm) log 10 (length) Deflection (cm) Period (sec) log 10 (period) 100.0 2.00 5.0 (brass) 85.0 5.0 (brass) 70.0 5.0 (brass) 55.0 5.0 (brass) 40.0 1.60 5.0 (brass) 25.0 5.0 (brass) 1.3 1.5 1.7 1.9 2. log(length) in cm Log(period) in seconds vs. log(length) of a Simple Pendulum 0.
Now, the period of a simple pendulum has a complicated mathematical form, but for small deflections it reduces to a simple expression, g L T 2 which may be rewritten as (^2) L a L 0. 5 g T then, taking the log of both sides and using the usual rules for logs [ e.g. log(ab)=log(a) + log(b) and log(a b ) = b log(a)] we have log( T )log( a L^0.^5 )log( a )log( L^0.^5 )log( a ) 0. 5 log( L ) now, this is of the form y = b + mx, an equation of a straight line, where m=0.5 is the slope of the line. So a plot of this equation should yield a straight line with a slope of 0.5. This is a power law relationship, very common in nature. Measure the slope of a straight line joining the points in your previous plot. The slope is simply the rise/run which is measureable from your plot. Show all work below. Slope = ______________. Discussion/Google Questions