Chapter 6.1, Problem 15CFU

To determine

To find: the distance or length covered by the end of the bob at the end of pendulum as it travels from left to right.

Answer to Problem 15CFU

  $0.733m$

Explanation of Solution

Given information:

  $\begin{array}{c}\text{Angle swiped by pendulum}\left(\theta \right)=30°\\ \text{Length of pendulum}\left(r\right)=1.4m\end{array}$

Calculation:

The distance covered by the bob at the end of pendulum as it travels from left to right will make an arc.

Convert degree into radian by multiplying the degree by $\frac{\pi }{180°}$ as shown below.

  $\begin{array}{c}\theta =30°\left(\frac{\pi }{180°}\right)\\ =\frac{\pi }{6}\end{array}$

Now evaluate the length of arc $\left(s\right)$ as follows:

  $\begin{array}{c}s=r\theta \\ =1.4m\left(\frac{\pi }{6}\right)\left[\text{Put the value of }r\text{ and }\theta \right]\\ =0.733m\end{array}$

Thus the length of arc or distance travelled by bob is $0.733m$ .