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A performer seated on a trapeze is swinging back and forth with a period of 8.85 s. If she stands up, raising the center of mass of the trapeze + performer system by 35.0 cm, what will be the new period of the system?

Answer :

Final answer:

When the performer stands up on the trapeze, the center of mass is raised, resulting in a change in potential and kinetic energy. The new period of the system can be determined using the principle of conservation of energy.

Explanation:

To find the new period of the system, we need to consider the principle of conservation of energy. When the performer stands up, the center of mass of the trapeze+performer system is raised by 35.0 cm. This increase in potential energy results in a decrease in kinetic energy, which affects the period. The period of a pendulum is given by the equation T = 2π√(L/g), where T is the period, L is the length, and g is the acceleration due to gravity. Since the length of the system remains the same, the only factor that changes is the acceleration due to gravity. In this case, the gravitational acceleration becomes g' = g - (2h/3), where h is the change in height. Plugging in the values, we can calculate the new period of the system.

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