ht In the problems below, use g- 9.8 m/s m/s2 An small spherical bob with a mass
ID: 1776819 • Letter: H
Question
ht In the problems below, use g- 9.8 m/s m/s2 An small spherical bob with a mass of 151.5 g is attached to one end of a string of length L. The other end is attached to a support stand thus forming a pendulum as you have seen in the lab (see figure above). You now bring the bob to an init ial angle of ·15.29 with respect to the vertical, hold it still momentarily and then release it. When the bob passes the point of the lowest vertical height, the kinetic energy of the bob is found to be 0.09 (a) Defining the gravitational potential energy of the pendulum bob to be zero when the bob is at the lowest vertical height, what is the gravitational potential energy of the bob when it is at the initial release angle? 0.0925 (b) What is the speed of the bob when the bob passes the point of the lowest vertical height? 1.105m/s (c) What is the length of the pendulum L? (d) Using the small angle approximation, find the period of the pendulum motion.Explanation / Answer
initial gravitational potential energy Ui = m*g*h
from the figure
costheta = (L-h)/L
costheta = 1 - h/L
h/L = 1 - costheta
h = L*(1-costheta)
energy Ui = m*g*L*(1-costheta) = 0.0925
151.5*10^-3*9.8*L*(1-cos15.2) = 0.0925
length L = 1.78 m
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part (d)
time period T = 2*pi*sqrt(L/g)
T = 2*pi*sqrt(1.78/9.8)
T = 2.68 s
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