High School

A performer, seated on a trapeze, is swinging back and forth with a period of 8.90 s. If she stands up, thus raising the center of mass of the trapeze and performer system by 44.0 cm, what will be the new period of the system?

Treat the trapeze and performer as a simple pendulum.

Answer :

Final answer:

To find the new period of the trapeze + performer system, we need to calculate the change in length caused by the performer standing up and use the equation for the period of a simple pendulum.

Explanation:

To solve this problem, we need to recognize that the swinging of the performer on the trapeze can be modeled as a simple pendulum. The period of a simple pendulum can be calculated using 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.

In this case, when the performer stands up, the center of mass of the trapeze + performer system is raised by 44.0 cm. This change in the length of the pendulum will affect its period.

We can calculate the new period using the equation T' = 2π√((L+d)/g), where T' is the new period, L is the original length of the pendulum, d is the change in length, and g is the acceleration due to gravity.

Plugging in the values, we get T' = 2π√((L+0.44)/g). This equation gives us the new period of the system.

Answer:

8.800s

Explanation:

When the performer swings, she oscillates in SHM about Lo of the string with time period To = 8.90s.

First, determine the original length Lo, where for a SHM the time period is related to length and the gravitational acceleration by the equation

T = 2π×√(Lo/g)..... (1)

Let's make Lo the subject of the formulae

Lo = gTo^2/4π^2 ..... (2)

Let's put our values into equation (2) to get Lo

Lo = gTo^2/4π^2

= (9.8m/s^2)(8.90s)^2

------------------------------

4π^2

= 19.663m

Second instant, when she rise by 44.0cm, so the length Lo will be reduced by 44.0cm and the final length will be

L = Lo - (0.44m)

= 19.663m - 0.44m

= 19.223m

Now let use the value of L into equation (1) to get the period T after raising

T = 2π×√(L/g)

= 2π×√(19.223m/9.8m/s^2)

= 8.800s