A trapeze artist swings in simple harmonic motion with a period of 3.2 s. The acceleration of gravity is 9.81 m/s2 . Calculate the length of the cables supporting the trapeze. Answer in units of m.
The formula for the period P of a pendulum is
P = 2 pi sqrt(L/g)
Use it to calculate L.
247.608
To calculate the length of the cables supporting the trapeze, we can use the formula for the period of a simple harmonic motion:
T = 2π * √(L / g)
where T is the period, L is the length of the cables, and g is the acceleration due to gravity.
Given:
T = 3.2 s
g = 9.81 m/s^2
Rearranging the formula, we get:
L = (T^2 * g) / (4π^2)
Substituting the given values:
L = (3.2^2 * 9.81) / (4π^2)
L = 31.9392 / (4π^2)
L ≈ 0.81 m
Therefore, the length of the cables supporting the trapeze is approximately 0.81 meters.
To calculate the length of the cables supporting the trapeze, we need to use the formula for the period of a simple harmonic motion system:
T = 2π√(L / g)
Where:
T is the period of motion,
L is the length of the cable,
and g is the acceleration due to gravity.
We are given that the period of motion is 3.2 s and the acceleration due to gravity is 9.81 m/s^2.
Substituting these known values into the formula, we can rearrange to solve for L:
3.2 s = 2π√(L / 9.81 m/s^2)
First, let's cancel out the 2π by dividing both sides of the equation by 2π:
3.2 s / 2π = √(L / 9.81 m/s^2)
Next, let's square both sides of the equation to isolate L:
(3.2 s / 2π)^2 = (L / 9.81 m/s^2)
Simplifying the equation:
(3.2^2 s^2 / (2π)^2) = (L / 9.81 m/s^2)
Using a calculator to evaluate the left side of the equation:
L = (9.81 m/s^2) * (3.2^2 s^2 / (2π)^2)
L ≈ 16.32 m
Therefore, the length of the cables supporting the trapeze is approximately 16.32 meters.