Answer :
The performer stands up on the trapeze, the center of mass of the system shifts upwards, causing a change in the moment of inertia of the system. As a result, the new period of the system will be different from the initial period. To calculate the new period, we can use the conservation of mechanical energy principle, which states that the total mechanical energy of the system remains constant.
The highest point of the swing, all of the potential energy of the system is converted into kinetic energy, and at the lowest point, all of the kinetic energy is converted back into potential energy. Using this principle, we can equate the initial and final mechanical energies of the system initial mechanical energy = final mechanical energy (1/2) mv^2 + mgs = (1/2) mv'^2 + mg (h + Δh) where m is the mass of the performer and trapeze, v is the initial velocity of the system, h is the initial height of the center of mass, v' is the final velocity of the system, h + Δh is the final height of the center of mass (36.6 cm higher than the initial height), and g is the acceleration due to gravity. We can rearrange this equation to solve for the final velocity of the system v' = sqrt [(2gh + 2gΔh) / m] Substituting the values given in the problem, we get v' = sqrt [(2(9.8 m/s^2) (0.5 m) + 2(9.8 m/s^2) (0.366 m)) / m] = 4.26 m/s The new period of the system can then be calculated using the forms T = 2πL / v' where L is the length of the pendulum Assuming that the length of the pendulum remains constant, we can calculate the new period T = 2π(0.5 m) / 4.26 m/s = 2.93 s Therefore, the new period of the system is approximately 2.93 seconds.
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