13.61 United Nations Pendulum A large pendulum with a 200-lb gold-plated bob 12

Question

13.61

United Nations Pendulum A large pendulum with a 200-lb gold-plated bob 12 inches in diameter is on display in the lobby of the United Nations building. The pendulum has a length of 75 ft. It is used to show the rotation of the Earth-for this reason it is referred to as a Foucault pendulum. What is the least amount of time it takes for the bob to swing from a position of maximum displacement to the equilibrium position of the pendulum? (Assume that the acceleration due to gravity is g = 9.81 m/s^2 at the UN building.)

Explanation / Answer

Let T be the period of the oscillation,then

T = 2*pi*sqrt(l/g)

l is the length of the pendulum = 75 ft = 75*0.3048 = 22.86 m

g= 9.81 m/s^2

then T = 2*3.142*sqrt(22.86/9.81) = 9.6 s

then the time taken by the bob to travel from maximum dispalcement to equlibrium position is T/4 = 9.6/4 = 2.4 S

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