Question

You wish to design a pendulum which moves a mass along an arc of length 40 cm when the angle with the vertical changes by 20 degrees. What should be the length L in meters of the pendulum? Enter the numerical answer without units. Your answer must be within 5% of the exact answer to receive credit.

Answer 1

The length of the pendulum cord is approximately 114.592 centimeters.

Step-by-step explanation:

We include a representation of the motion of the pendulum in the image attached below. The trajectory described by the pendulum is represented by the following geometrical expression:

`s = \theta \cdot r` (1)

Where:

`\theta` - Angular change with the vertical, measured in radians.

`r` - Length of the pendulum cord, measured in centimeters.

`s` - Arc, measured in centimeters.

If we know that
`\theta = (\pi)/(9)` and
`s = 40\,cm`, then the length of the pendulum cord is.

`r = (s)/(\theta)`

`r = (40\,cm)/((\pi)/(9) )`

`r \approx 114.592\,cm`

The length of the pendulum cord is approximately 114.592 centimeters.