A child sits on a swing supported by ropes of length 3.0 m. With what frequency will she need to apply the driving force to maintain swinging?
To find the frequency at which the child needs to apply the driving force to maintain swinging, we can use the formula for the period of a pendulum-like motion:
T = 2π√(L/g)
Where:
T is the period of the swing,
L is the length of the swing ropes, and
g is the acceleration due to gravity.
First, let's convert the length of the ropes to meters:
L = 3.0 m
Second, we need to determine the value of g. The standard value of acceleration due to gravity is approximately 9.8 m/s².
Now, we can substitute these values into the formula:
T = 2π√(L/g)
T = 2π√(3.0/9.8)
Simplifying the equation:
T = 2π√(0.3061)
T = 2π * 0.553
T ≈ 3.48 seconds
The period of the swing is approximately 3.48 seconds. Since frequency is the inverse of the period, we can find the frequency using the formula:
f = 1/T = 1/3.48
f ≈ 0.29 Hz
Therefore, the child needs to apply the driving force with a frequency of approximately 0.29 Hz to maintain swinging.