PLEASE ANSWER AT LEAST PART (B) (I will post other parts separately) A ‘grand-fa

Question

PLEASE ANSWER AT LEAST PART (B) (I will post other parts separately)

A ‘grand-father clock’ is to be built from a large pendulum
so that it will take 1 s for the pendulum to go from right to left and 1 more s to go from left to right.

(A) If the pendulum were to be made of a single point mass, how long would it have to be to have the
desired period of oscillation?

!!!!!(B) If the bob of the pendulum has a 500 g mass and it is to oscillate with a 5 cm amplitude (10 cm from left to right), what will the energy be? (Hint: at maximum amplitude there is no kinetic energy, so all the
energy is potential).

(C) Because of air friction and friction on the bearings, the pendulum is found to lose 2% of its energy for every oscillation cycle. A 5 kg mass is attached to a string wound around a pulley of negligible mass, itself attached to the top pivot of the pendulum, so that the falling mass can provide the energy lost to friction through its steady descent (a special “escapement gear” stops the motion of the falling mass at small regular intervals so that there is no net acceleration of the falling mass). If the total length of the string is 1.1 m, how many days will it take before the pendulum stops oscillating?

Explanation / Answer

C ) The lost energy will be made up by the decreasing potential energy of the descending mass. I will assume you found the energy in (b). 2% of this energy is lost during every 2 s ("oscillation cycle"). Let's call this lost energy E. Over the course of 1 day, then, the total energy lost is Et = E/2s * 3600s/hr * 24hr/day will give you the daily energy loss. The descending mass initially has energy Ep = mgh = 5kg * 9.8m/s² * 1.1m = 53.9 J Divide Ep (energy in the hanging mass) by Et (energy lost by pendulum per day) and you will have the number of days the pendulum can run between windings.

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