The "Great Swing" at a country fair consists of a vertical central shaft with a number of horizontal arms attached at its upper end. Each arm supports a seat suspended from a 5.00m long rod, the upper end which is fastened to the arms at a point of 3.00m from the central shaft.
Find the time of one revolution of the swing if the rod supporting the seat makes an angle of 30 degrees.
To find the time of one revolution of the swing, we can use the concept of pendulum motion.
The time period of a simple pendulum is given by the formula:
T = 2π√(L/g)
Where T is the time period, L is the length of the pendulum, and g is the acceleration due to gravity.
In this case, the length of the pendulum is the distance from the central shaft to the seat, which is given as 5.00m. However, we need to find the effective length of the pendulum, which is the distance from the pivot point (where the rod is attached to the arm) to the seat.
To find the effective length of the pendulum, we can use the concept of trigonometry. The effective length (L') can be found using the formula:
L' = L × sin(θ)
Where L is the length of the pendulum rod and θ is the angle made by the pendulum rod with the vertical, which in this case is 30 degrees.
L' = 5.00m × sin(30 degrees)
L' = 5.00m × 0.5
L' = 2.50m
Now, we have the effective length of the pendulum, which is 2.50m. We can substitute this value into the formula for the time period:
T = 2π√(L/g)
T = 2π√(2.50m/9.81m/s^2)
T ≈ 2π√(0.255s^2/m)
T ≈ 2π × 0.505s
Therefore, the time of one revolution of the swing is approximately 3.18 seconds.
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it might be somethin' up there