Chapter 4, (GL) Simple Pendulum Parameters (Angle, Mass, Length, and Damping) Video Solutions, Physics Laboratory Experiments

Problem 1

It was suggested that you measure the time for several periods and determine the average period, rather than timing only one period.
(a) What are the advantages of this method?
(b) How and why would the result be affected if a very large number of periods were timed?

Darshan Maheshwari

Numerade Educator

03:47

Problem 2

In general, the results of Procedure 2 may not have shown clear-cut evidence that the period increases as dramatically with the angle as Eq. (4.1) might suggest. To understand why, write Eq. $(4.1)$ as
$$
T=T_{1}\left(1+\frac{1}{4} \sin ^{2} \frac{\theta}{2}+\frac{9}{64} \sin ^{4} \frac{\theta}{2}\right)
$$
and compute $T$ in terms of $T_{1}\left(\right.$ where $\left.T_{1}=2 \pi \sqrt{\frac{L}{g}}\right)$ for angles of $5^{\circ}, 20^{\circ}$, and $60^{\circ}$.
Comment on the theoretical predictions and experimental accuracy in relation to your results in Data Table $1 .$

Ankit Gupta

Numerade Educator

01:28

Problem 3

Is air resistance or friction a systematic or a random source of error? (See Experiment 2 for error descriptions.) Would it cause the period to be larger or smaller than the theoretical value? (Hint: Consider what would happen if the air resistance were much greater-for example, as though the pendulum were swinging in a liquid.)

Averell Hause

Carnegie Mellon University

01:26

Problem 4

Thomas Jefferson once suggested that the period of a simple pendulum be used to define the standard unit of length. What would be the period of a pendulum with a length of $1.0 \mathrm{~m}$ ?