Answer :
Final answer:
The period of an acrobat swinging on a trapeze can be calculated using the simple pendulum formula T = 2π√(L/g). For a trapeze with cables approximately 3.5 m long, the period is roughly 3.76 seconds. This formula accounts for the length of the cables and the acceleration due to gravity.
Explanation:
Calculating the Period of a Trapeze Swing
The period of an acrobat swinging on a trapeze can be modeled as a simple pendulum. The formula to find the period (T) of a simple pendulum is given by:
T = 2π√(L/g)
Where:
- T = Period of the pendulum
- L = Length of the pendulum (in this case, the length of the cables, approximately 3.5 m)
- g = Acceleration due to gravity (approximately 9.81 m/s²)
We can now substitute the values into the formula:
- Substituting for L = 3.5 m and g = 9.81 m/s²:
T = 2π√(3.5/9.81)
Calculating the value:
- First, calculate 3.5 / 9.81 = 0.3567.
- Now take the square root: √0.3567 = 0.5972.
- Finally, multiply by 2π: T = 2 3.1416 0.5972 ≈ 3.76 seconds.
Thus, the period of an acrobat swinging on this trapeze is approximately 3.76 seconds.
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