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

a) first we need the length of the pendulum

T=2 (L/g)

1=2 (L/9.8)

L=.248 m

b)now we can find the change in height of the bob

h=L(1-cos)

h=L(1-.05/L)

h=.248(1-.05/.248)

h=.19823269

now we can use PE at this max height to find the total energy

E=mgh

E=.5(9.8)(.19823269)

E=.9714 joules

c) the total energy stored in the large mass is

E=mgh

E=5(9.8)1.1

E=53.9 joules

the pendulum loses .9714(.02) every second

t=53.9/(.9714*.02)

t=2774.45 seconds=.032 days

hope that helps

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