if the swinging pendulum (pirate ship) swings on an arc with a radius of 10 meters, how much time does it take to swing through 5 swings?
The length of the pendulum string is
L = 10 m.
T =2•π•sqrt(L/g).
t =5•T
To find the time it takes for the swinging pendulum, also known as the pirate ship, to swing through 5 complete swings, we can use the formula for the period of a pendulum.
The period (T) of a pendulum is the time it takes to complete one full swing back and forth. The formula to calculate the period of a pendulum is:
T = 2π√(L/g),
where L is the length of the pendulum's arm (in this case, the radius of the arc), and g is the acceleration due to gravity (approximately 9.8 m/s² on Earth).
In this case, the radius of the arc is 10 meters. Plugging this value into the formula, we get:
T = 2π√(10/9.8).
Now, to find the time it takes to complete 5 swings, we need to multiply the period by the number of swings. So, the total time (t) required to complete 5 swings is:
t = 5T.
Substituting the value of T into the equation, we have:
t = 5 * (2π√(10/9.8)).
Now, let's calculate this value.
t ≈ 5 * (2π * √(10/9.8))
≈ 5 * (2π * √1.02040816327)
≈ 5 * (2π * 1.01015293877)
≈ 5 * 6.36619772368
≈ 31.8309886184 seconds.
Therefore, it takes approximately 31.83 seconds for the swinging pendulum to swing through 5 complete swings.