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Period of a Simple Pendulum Lab | SCI 106, Lab Reports of Physics

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

Pre 2010

Uploaded on 08/16/2009

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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 mg 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
1. What forces cancel and why?
2. Which force (refer to the diagram) moves the pendulum bob?
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pf4
pf5

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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

  1. What forces cancel and why?
  2. Which force (refer to the diagram) moves the pendulum bob?
  1. Does the time to complete one swing depend on the string length? Why or why not?
  2. Does this time depend on the mass? Why or why not? Lab Exercises Set up a simple pendulum using the stand, string, support bar and brass weight provided. Measure the mass of the weights. The initial length should be 1 meter. Set a meter stick below the pendulum to measure the initial deflection. For each measurement of time, allow 10 swings then divide the time by 10. Deflection (cm) Period (sec) Mass (g) 5.0 (brass) 10.0 (brass) 10.0 (steel) 15.0 (brass) 20.0 (brass)
  3. What can you conclude based on this data? Now change the length of the string and use the brass weight. You have already obtained data for a 1 meter string length and 5 cm deflection. Continue by changing the length in increments of 15 cm. Fill in the data table then plot the results below.

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( aL^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

  1. What is the significance of your measurement of the slope?
  2. Power law expressions frequently arise in nature. Discuss their significance and cite several examples of power laws in nature.