suppose a pendulum use to show the rotation of the earth has a period of approximately 16.9 seconds. What is the length using formula T=2pi sq root L/32
just solve for L in
2π√(L/32) = 16.9
√(L/32) = 16.9/2π = 2.69
L/32 = 7.23
L = 231.51
To find the length of the pendulum, we can rearrange the formula T = 2π√(L/32) and solve for L.
Given that T = 16.9 seconds, we can substitute this value into the formula:
16.9 = 2π√(L/32)
To isolate L, we need to square both sides of the equation:
(16.9)^2 = (2π)^2(L/32)
Evaluating the expression:
285.61 = 4π^2(L/32)
Now, we can multiply both sides by 32 and divide by 4π^2:
285.61 * 32 / 4π^2 = L
Calculating:
2284.88 / 4π^2 ≈ L
L ≈ 57.92
Therefore, the approximate length of the pendulum is 57.92 units.
To find the length of the pendulum, we can rearrange the given formula for the period of a pendulum:
T = 2π√(L/32)
where T is the period of the pendulum and L is the length of the pendulum.
Since we know that the period of the pendulum is approximately 16.9 seconds, we can substitute this value into the formula:
16.9 = 2π√(L/32)
Now, let's solve this equation step by step to find the length of the pendulum.
Step 1: Divide both sides of the equation by 2π:
16.9 / (2π) = √(L/32)
Step 2: Square both sides of the equation:
(16.9 / (2π))^2 = L/32
Step 3: Multiply both sides of the equation by 32:
32 * (16.9 / (2π))^2 = L
Step 4: Calculate the value on the left side of the equation:
L ≈ 34.2497
Therefore, the length of the pendulum is approximately 34.2497 units.