Chapter 4, Problem 1EP

Scientists use models and theories to describe physical phenomena. When a new model is developed, it must be tested to find out if it is an accurate representation. No theory or model of nature is valid unless its predictions are in agreement with experimental results. The laboratory provides an environment where extraneous factors can be minimized and specific predictions can be tested. The process of making, testing, and refining models is usually called the scientific method (see Experiment 1).

An example of this method will be demonstrated in this experiment for a simple pendulum. A “simple” pendulum is one in which a small but substantial mass is suspended on a relatively light string, like the one pictured in Fig. 4.1. If one were to observe the motion of the mass swinging back and forth, which of the following statements do you think would be the most accurate? (It is understood that the motion takes place in a single plane.)

The time for the mass to swing back and forth (from point A to B, and back to A in Fig. 4.1.)

1. (a) changes randomly from one swing to the next.
2. (b) gets consistently bigger from one swing to the next.
3. (c) gets consistently smaller from one swing to the next.
4. (d) stays about the same from one swing to the next.

(Circle your choice)

To determine

The most accurate statement regarding the motion of a simple pendulum.

Answer to Problem 1EP

Option (d) The time for the mass to swing back and forth stays about the same from one swing to the next.

Explanation of Solution

The time for the mass of the simple pendulum to swing back and forth is termed as the period of oscillation. The period of oscillation of the pendulum depends only on the length of the pendulum and it can be obtained from the relation,

  $T=2\pi \sqrt{\frac{L}{g}}$

Here, $T$ is the period, $L$ is the length of the pendulum, and $g$ is the acceleration due to gravity.

For a pendulum of fixed length, the period of oscillation remains the same for all oscillations, unless the pendulum is subjected to considerable friction or air resistance.

Conclusion:

Since the time for the mass of the pendulum to swing back and forth stays about the same from one swing to the next, option (d) is correct.

The period of the simple pendulum does not change randomly from one swing to the next. Thus, option (a) is incorrect.

The period of the simple pendulum does not get consistently bigger from one swing to the next. Thus, option (b) is incorrect.

The period of the simple pendulum does not get consistently smaller from one swing to the next. Thus, option (c) is incorrect.