A Foucault pendulum is designed to demonstrate the effect of the Earth's rotation. A Foucault pendulum displayed in a museum is typically quite long, making the effect easier to see. Consider a Foucault pendulum of length 16 m with a 109-kg brass bob. It is set to swing with an amplitude of 3.1°.

(a) What is the period of the pendulum?


(b) What is the maximum kinetic energy of the pendulum?


(c) What is the maximum speed of the pendulum?

To find the period of the pendulum, we can use the formula:

T = 2π√(L/g)

Where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.

(a) To find the period:
Given:
Length of the pendulum, L = 16 m
Acceleration due to gravity, g = 9.8 m/s²

Using the formula:
T = 2π√(16/9.8)

Calculating it:
T ≈ 6.31 seconds

So, the period of the pendulum is approximately 6.31 seconds.

To find the maximum kinetic energy of the pendulum, we can use the formula:

KE = (1/2)mv²

Where KE is the kinetic energy, m is the mass of the bob, and v is the velocity of the bob.

(b) To find the maximum kinetic energy:
Given:
Mass of the bob, m = 109 kg
Amplitude, θ = 3.1°

Using the formula:
v = 2π(L) / (T(180/θ))

Substituting the given values:
v = 2π(16) / (6.31(180/3.1))

Calculating it:
v ≈ 1.87 m/s

Now, using the formula for kinetic energy:
KE = (1/2)(109)(1.87)²

Calculating it:
KE ≈ 193.79 Joules

So, the maximum kinetic energy of the pendulum is approximately 193.79 Joules.

To find the maximum speed of the pendulum, we can use the formula:

v = 2π(L) / (T(180/θ))

Where v is the velocity of the bob, L is the length of the pendulum, T is the period, and θ is the amplitude.

(c) To find the maximum speed:
Given:
Length of the pendulum, L = 16 m
Period, T = 6.31 seconds
Amplitude, θ = 3.1°

Using the formula:
v = 2π(16) / (6.31(180/3.1))

Calculating it:
v ≈ 1.87 m/s

So, the maximum speed of the pendulum is approximately 1.87 m/s.