Elwin, the bungee clown, swings back and forth like a simple pendulum at the end of a bungee cord. If a student determines the time of one complete swing is 6.9s, how long is the bungee cord when Elwin is swinging from it?
T^2 = 2πL/g
so plug in your numbers to find L
oops
T = 2π√(L/g)
so
(T/2π)^2 = L/g
To find the length of the bungee cord, we can use the formula for the period of a simple pendulum:
T = 2π√(L / g)
Where:
T = period of the pendulum (in seconds)
L = length of the pendulum (in meters)
g = acceleration due to gravity (approximately 9.8 m/s^2)
Given that the period T is 6.9 seconds, we can rearrange the formula to solve for L:
L = (T / (2π))^2 * g
Now, let's substitute the given values:
L = (6.9 / (2π))^2 * 9.8
Calculating this expression, we get:
L ≈ 6.9^2 * 9.8 / (2π)^2
L ≈ 47.79 m
Therefore, the length of the bungee cord when Elwin is swinging from it is approximately 47.79 meters.
To find the length of the bungee cord when Elwin is swinging from it, we can use the formula for the period of a simple pendulum, which is the time taken for one complete swing. The formula is:
T = 2π√(L/g)
Where:
T is the period (in seconds)
π is a mathematical constant (approximately 3.14159)
L is the length of the pendulum (in meters)
g is the acceleration due to gravity (approximately 9.8 m/s²)
In this case, we are given the period T as 6.9 seconds. Let's substitute this value into the formula and solve for L:
6.9 = 2π√(L/9.8)
First, let's simplify the equation by dividing both sides by 2π:
6.9 / (2π) = √(L/9.8)
Now, we can square both sides of the equation to isolate L:
(6.9 / (2π))^2 = L/9.8
Simplifying further:
(6.9 / (2π))^2 * 9.8 = L
Using a calculator, we can evaluate the left-hand side of the equation:
(6.9 / (2π))^2 * 9.8 ≈ 42.205
Therefore, the length of the bungee cord when Elwin is swinging from it is approximately 42.205 meters.