Two parakeets sit on a swing with their combined center of mass 15.0 cm below the pivot. At what frequency do they swing?
f=1/T =1/2πsqrt(L/g)=...
To determine the frequency at which the parakeets swing, we need to consider the physical principles involved. The frequency of a swinging object can be calculated using the formula:
f = 1 / T
Where:
f is the frequency in Hz (Hertz)
T is the period of the swing in seconds
In this case, we're given that the combined center of mass of the parakeets is located 15.0 cm below the pivot. The period of the swing is the time it takes for one complete swing.
To find the period, we need two things: the length of the swing and the acceleration due to gravity. The length of the swing is twice the distance from the pivot to the center of mass.
Here's a step-by-step breakdown on how to calculate the frequency:
1. Convert the distance from centimeters to meters. Divide the given value (15.0 cm) by 100 to get 0.15 m.
2. Calculate the length of the swing. Since the combined center of mass is below the pivot, the length is twice the distance from the pivot to the center of mass. Thus, the length is 2 * 0.15 m = 0.3 m.
3. Find the acceleration due to gravity. The standard value for gravity is approximately 9.8 m/s^2.
4. Calculate the period (T) using the formula:
T = 2π * √(L / g)
Where:
- T is the period in seconds
- L is the length of the swing in meters
- g is the acceleration due to gravity in m/s^2
Plug in the values:
T = 2π * √(0.3 / 9.8)
5. Solve for T. Using a calculator, evaluate the expression within the square root, and then multiply it by 2π. Finally, take the reciprocal of the result to obtain the period T.
T ≈ 1.071 seconds
6. Finally, calculate the frequency (f) using the formula: f = 1 / T. Divide 1 by the obtained period.
f ≈ 0.934 Hz
Therefore, the frequency at which the parakeets swing is approximately 0.934 Hz.