Question

Pendulum clocks are typically made so the period of the pendulum is exactly 1 second or 2 seconds, but they don't have to be. Suppose a grandfather clock uses a pendulum that is 115.00 centimeters long. The pendulum is accidentally broken, and when repaired, the length is shorter by 0.37 centimeters. How many swings will the "repaired" pendulum make in one day? Answer must be in 3 significant digits.

Answer 1

The period of a pendulum is given by:

`T=2\pi\sqrt[]{(L)/(g)}`

where L is the lenght of the pendulum and g is the acceleration of gravity.

We know that the repaired pendulum has a length of 114.63 cm, then its period is given by:

`\begin{gathered} T=2\pi\sqrt[]{(1.1463)/(9.8)} \\ T=2.149 \end{gathered}`

Therefore the repaired pendulum has a period of 2.149 seconds.

We know that a day has 86400 seconds, to determine how many swings the pendulum make in a day we divide the total amount of seconds in a day by the period of the clock, then we have:

`(86400)/(2.149)=40204.75`

Therefore the clocks swings 40200 times a day (rounded to three significant figrues)