Answer :
Therefore, the new period of the system is 6.89 seconds.
A performer seated on a trapeze is swinging back and forth with a period of 9.02 seconds.
If she stands up, thus raising the center of mass of the
trapeze + performer system by 30.4 cm,
what will be the new period of the system?
Treating trapeze + performer as a simple pendulum, we need to figure out the new period of the system.
The period of a simple pendulum is given by the equation:
T = 2π√(L/g)
where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.
The period is dependent on the length of the pendulum and the acceleration due to gravity.
By raising the center of mass of the system by 30.4 cm, we are effectively increasing the length of the pendulum.
We can use the following equation to calculate the new length:
L_new = L_old + Δh
where L_new is the new length, L_old is the old length, and Δh is the change in height.
We are given that the period of the system is 9.02 seconds, so we can use this to solve for the old length:
L_old = (T/2π)² g
We can use the old length to calculate the new length:
L_new = L_old + Δh
Substituting the given values:
L_old = (9.02/2π)² (9.81) = 10.44 m
L_new = 10.44 + 0.304 = 10.74 m
We can now use the new length to calculate the new period:
T_new = 2π√(L_new/g)
T_new = 2π√(10.74/9.81)
T_new = 2π(1.098) = 6.89 seconds
to know more about mass visit:
https://brainly.com/question/26789700
#SPJ11
