Time and Displacement Mechanics is

Time and Displacement
Mechanics is an important topic concerned with motion, force and energy. Motion involves change in position in a certain time, therefore distance, time and their measurement must be considered.
Unit of time
Time has been divided into regularly occurring units: the year, the month and the day. The day can further be broken down into hours, minutes and seconds. The SI unit of time is the second, abbreviated to‘s’. It was formerly defined as a fraction of an ‘average’ year, but as the duration of a year changes slightly, a more precise definition is now in use. This new definition is based on the natural frequency of the cesium atom.
Timing devices
The sundial, the sand-glass and the water-clock (Figure 7.1) are some of the first devices that were used to measure time. Their accuracy very poor and therefore they are now only of historical interest.
The pendulum was the next development in the measurement of time. In the sixteenth century, while in a church, Galileo noted that a lamp, suspended by long cords, appeared to swing with a constant period which was not dependent on the amplitude of the swing. Galileo used his own pulse rate to time the period of the swinging object.
Together with the pendulum came the development of the mechanical clock which was controlled by the to-and-fro oscillation of a balance-wheel. This was followed by the electric clock which uses the stable 50 Hz frequency of mains electricity to operate a vibrating tuning fork. It measures time intervals accurately to 0.01 s.
The latest development is the quartz crystal watch (Figure 7.2) which usually displays the time in digits using either light emitting diodes (LED) or liquid crystal displays (LCD). The watch mechanism is regulated by a rapidly vibrating quartz crystal which is accurate to one second in three year!
The most accurate timing device is the cesium atomic clock which is based on the natural frequency of vibration of the cesium atom. It has an unmatched accuracy of one second in 3000 years and is used to check the SI unit of time the second. The Mass Transit Railway (MTR) in Hong Kong has installed an atomic cesium clock (Figure 7.3).The master clock at the MTRC headquarters controls about 1100 slave clocks which are positioned in all the underground stations in the entire MTR system.
The simple pendulum
A simple pendulum consists of a mass, the bob, attached to one end of a long, light thread. The other end of the thread is suspended from a fixed support. The pendulum length is measured from the suspension point to the Centre of mass of the bob which, for a spherical bob, is at the center. The period of oscillation T is the time taken for one complete swing of the pendulum. This depends only on the pendulum length I, and not on the mass of the bob or the amplitude of the oscillation, provided that the latter is small. Experiments show that T ∝ √I. This means that T is doubled when I is increased 4 times. One complete swing of the pendulum is one complete to-and-fro motion of the bob. This can be timed from any starting point. Two examples are given in Figure 7.4.

Stop-watch
The most common type of timing device in the science laboratory is the stop-watch or stop-clock (Figure 7.5). A typical stop-watch is accurate to the nearest 0.2 s. To measure a time interval the watch has to be started or stopped by pressing a knob. An error is therefore introduced due to the time lapse between seeing the event and starting (or stopping) the watch. This error is called the reaction time. Reaction time varies from person to person but is, on average; about 0.2 s. this type of watch is not suitable for measuring time intervals of about one second as the reaction time introduces too great an error
Example 1
In an Experiment to determine the period of simple pendulum, the time for one complete swing, measured with a stop-watch, was 1.2 s.
(a) Assuming that the reaction time was 0.2 s, what is the possible percentage error in the measurement?
(b) The time for 20 complete swings was then measured and was found to be 16.0 s. What is the period of the simple pendulum and what is the percentage error in this result?
(a) Error in starting the stop-watch = 0.2 s
Error in stopping the stop-watch = 0.2 s
Total possible error = 0.4 s
Percentage error = 0.4 s = (0.4 s)/1.2s ×100% ≈ 33 %
(b)The period of the simple pendulum = (16.0 s)/20 = 0.8 s
Total possible error in timing 20 complete swings is the same as
Before, that is, 0.4 s.
Percentage error = (0.4 s)/(16.0 s)×100%=2.5 %
Therefore, in order to obtain a more accurate result, a large number of
Complete swings of the pendulum must be timed
The mechanical type stop-watch is now gradually being replaced by the quartz crystal controlled digital stop-watch (Figure 7.6). This is much more accurate and can measure time intervals to the nearest 0.01s.However, there is no point in measuring to this accuracy when the stop-watch is switched on and off by hand which gives rise to reaction time error of about 0.4s.