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. Assume that the pendulum has a length of 78.4 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 full period of a pendulum with only half the length of the pendulum described above.
(in s)
To find the period of a pendulum with half the length of the given pendulum, we can use the formula for the period of a simple pendulum:
T = 2π * √(L/g)
where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.
In this case, the given pendulum has a length of 78.4 ft. So, to find the period of the pendulum with half the length, we need to calculate the length of the new pendulum.
Half the length of the given pendulum is:
78.4 ft / 2 = 39.2 ft
Now that we have the length, we can calculate the period using the formula:
T = 2π * √(L/g)
The acceleration due to gravity, g, is approximately 32.2 ft/s².
T = 2π * √(39.2 ft / 32.2 ft/s²)
T ≈ 2π * √1.2186 s²
T ≈ 2π * 1.1049 s
T ≈ 6.94 s
Therefore, the full period of the pendulum with half the length is approximately 6.94 seconds.