Answer :
In order to calculate the new period of the trapeze performer system, we can use the formula for the period of a simple pendulum: T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity (approximately 9.81 m/s²).
Initially, the period is 8.60 s. After the performer stands up, the center of mass of the system is raised by 35.0 cm (0.35 m). To find the new length (L2) of the pendulum, we can use the formula L1/L2 = (T1/T2)². We have L1, T1 (8.60 s), and T2 is the new period we need to find.
First, calculate L1 using the initial period: L1 = (T1² * g) / (4π²) = (8.60² * 9.81) / (4π²) ≈ 5.98 m. Then, calculate L2 = L1 - 0.35 = 5.98 - 0.35 = 5.63 m.
Now, use the formula to find the new period (T2): T2 = 2π√(L2/g) = 2π√(5.63/9.81) ≈ 8.42 s.
So, the new period of the system when the performer stands up is approximately 8.42 seconds.
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