Question 4 The period of a clock pendulum T is given by the equation T = 2ñ1 L where the constant L is the length of the pendulum and g is the acceleration due to gravity. The period of the clock pendulum varies slightly depending on where it is located on earth's surface, due to small changes in g. (a) If g increases, will T increase or decrease? Does this correspond to the clock pendulum speeding up or slowing down? Explain your reasoning. (b) Find the linear approximation for T(g) centered at g = 980 cm/sec², if the length of the pendulum is 400 cm. (c) When a clock with a 400 cm pendulum is moved from a location where g = 980 cm/sec? to a new location, its period increases by .001sec. Estimate the amount by which g increases and approximate the value of g at the new location.
Question 4 The period of a clock pendulum T is given by the equation T = 2ñ1 L where the constant L is the length of the pendulum and g is the acceleration due to gravity. The period of the clock pendulum varies slightly depending on where it is located on earth's surface, due to small changes in g. (a) If g increases, will T increase or decrease? Does this correspond to the clock pendulum speeding up or slowing down? Explain your reasoning. (b) Find the linear approximation for T(g) centered at g = 980 cm/sec², if the length of the pendulum is 400 cm. (c) When a clock with a 400 cm pendulum is moved from a location where g = 980 cm/sec? to a new location, its period increases by .001sec. Estimate the amount by which g increases and approximate the value of g at the new location.
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.2: Graphs
Problem 19E
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Transcribed Image Text:Question 4 The period of a clock pendulum T is given by the equation T = 27
L
where the constant L is the
length of the pendulum and g is the acceleration due to gravity. The period of the clock pendulum
varies slightly depending on where it is located on earth's surface, due to small changes in g.
(a) If g increases, will T increase or decrease? Does this correspond to the clock pendulum speeding
up or slowing down? Explain your reasoning.
980 cm/sec2, if the length of the pendulum
(b) Find the linear approximation for T(g) centered at g
is 400 cm.
980 cm/sec to a
(c) When a clock with a 400 cm pendulum is moved from a location where g
new location, its period increases by .001sec. Estimate the amount by which g increases and
approximate the value of g at the new location.
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