Question

In Fig. 15-64, ademolition ball swings from the end of a crane. The length of the swinging segment of cable is 17. (a) Find the period of the swinging, assuming that the system can be treated as a simple pendulum. (b) Does the period depend on the ball’s mass?

Short answer

1. Period of swinging by assuming the system as a simple pendulum is 8.3 S.
2. The period of a simple pendulum does not depend on the ball’s mass.

Step-by-step solution

The given data

• Mass of the ball,$\left(m\right)=2500kg$.
• Length of a cable,$\left(L\right)=17m.$.

Understanding the concept of SHM

Using the formula of the period of the simple pendulum we can find the period of swinging, and hence, we can determine whether the period of the simple pendulum depends on the ball’s mass or not.

Formula:

The period of oscillation,$T=2\pi \sqrt{\frac{L}{g}}$

(a) Calculation of period

From equation (i), we can find the period of oscillations of the ball as:

$$\begin{gathered} T=2\pi \sqrt{\frac{17}{9.8m/s^2}} \\ =8.3s \end{gathered}$$

Therefore, the period of swinging by assuming the system as a simple pendulum is

(b) Checking whether the period of the ball depends on the ball’s mass or not

From equation (i) of the period of a body’s oscillation, it can be clearly seen that the term “period” only depends on the body’s length and acceleration.

From this relation, we can say that period is independent of the mass because this equation does not contain term .