Question #95071
A student measured the time for 10 oscillations of a simple pendulum as 14.0 s , using a stop clock that gives 50 ticks in 25 seconds. The student has a reaction time of 0.2 s and she is known to have started and stopped the watch too late.
(a) what is her maximum reaction error in taking the measurement for 10 oscillations and for 1 oscillation?
(b) what is the maximum precision error in the time for 10 oscillations and for 1 oscillation?
(c) Calculate the total error in the time for 10 oscillations and for 1 oscillation.
(d) hence write down the time for 1 oscillation, to an appropriate number of significant figures.
1
Expert's answer
2019-09-24T09:08:24-0400

a) The  maximum reaction error in taking the measurement for 10 oscillations is


0.02 s0.02\ s

The  maximum reaction error in taking the measurement for 1 oscillation is 0.2 s.

b) The maximum precision error in the time for 1 oscillation:


2550=0.5 s\frac{25}{50}=0.5\ s

The maximum precision error in the time for 10 oscillations:


0.510=0.05 s\frac{0.5}{10}=0.05\ s

c) For 1 oscillation:


E1=0.52+0.22=0.54 sE_1=\sqrt{0.5^2+0.2^2}=0.54\ s


E10=0.052+0.022=0.054 sE_{10}=\sqrt{0.05^2+0.02^2}=0.054\ s

d)

t1=1.4 st_1=1.4\ s


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