Physics Laboratory Experiments
Physics Laboratory Experiments
8th Edition
ISBN: 9781285738567
Author: Jerry D. Wilson, Cecilia A. Hernández-Hall
Publisher: Cengage Learning
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Chapter 4, Problem 1Q

It was suggested that you measure the time for several periods and determine the average period, rather than timing only one period.

  1. (a) What are the advantages of this method?
  2. (b) How and why would the result be affected if a very large number of periods were timed?
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Use dimensional analysis to determine how the period T of a swinging pendulum (the elapsed time for a complete cycle of motion) depends on some, or all, of these properties: the length L of the pendulum, the mass m of the pendulum bob, and the gravitational field strength g (in m/s2). Assume that the amplitude of the swing (the maximum angle that the string makes with the vertical) has no effect on the period.
We might assume that the period of a simple pendulum depends on the mass M, the length l of the string and g the acceleration due to gravity, i.e T is directly proportional to m l g. Consider the dimensions of the quantities involved to deduce the values of alpha, beta, gamma hence show that T is directly proportional to √l/g
Harvard Bridge, which connects MIT with its fraternities across the Charles River, has a length of 364.4 Smoots plus one ear. The units of one Smoot is based on the length of Oliver Reed Smoot, Jr., class of 1962, who was carried or dragged length by length across the bridge so that other pledge members of the Lambda Chi Alpha fraternity could mark off (with paint) 1-Smoot lengths along the bridge. The marks have been repainted biannually by fraternity pledges since the initial measurement, usually during times of traffic congestion so that the police could not easily interfere. (Presumably, the police were originally upset because a Smoot is not an SI base units, but these days they seem to have accepted the units.) The figure shows three parallel paths, measured in Smoots (S), Willies (W), and Zeldas (Z). What is the length of 33.0 Smoots in (a) Willies and (b) Zeldas? 32 212 258 60 216 (a) Number: i Unit: (b) Number: i Unit:
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