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A trapeze artist swings in simple harmonic motion with a period of 4.9 seconds. The acceleration due to gravity is 9.81 m/s². Calculate the length of the cables supporting the trapeze. (Answer in units of meters)

Answer :

To calculate the length of the cables supporting a trapeze artist in simple harmonic motion, the formula for the period of a simple pendulum is used: T = 2π√(L/g). With a given period of 4.9 s and using the value for gravity 9.81 m/s², the length is found to be approximately 5.962 meters.

The question is asking to calculate the length of the cables supporting a trapeze artist, which is effectively a pendulum problem in physics. The period of the pendulum, which is 4.9 seconds in this case, is given. The formula for the period of a simple pendulum is T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity. Solving for L, we get L = (T/(2π))²*g. Plugging in the numbers (T = 4.9 s and g = 9.81 m/s²), we calculate the length of the supporting cables.

First, calculate the square of the period over 4π²:

(4.9 s / (2π))² = (4.9 / 6.28318530718)² = (0.779422863405)^2 = 0.60746332373

Now multiply by g:

0.60746332373 * 9.81 m/s² = 5.962 m

Hence, the length of the cables supporting the trapeze is approximately 5.962 meters.

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