Question

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.

Answer 1

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

$$0.02\ s$$

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:

$$\frac{25}{50}=0.5\ s$$

The maximum precision error in the time for 10 oscillations:

$$\frac{0.5}{10}=0.05\ s$$

c) For 1 oscillation:

$$E_1=\sqrt{0.5^2+0.2^2}=0.54\ s$$

$$E_{10}=\sqrt{0.05^2+0.02^2}=0.054\ s$$

d)

$$t_1=1.4\ s$$