Physics clicker question: pendulum period miscalculation

Physics 5A, Fall Semester 2007
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Problem 10.60

Students were asked the following clicker question (Classroom Performance System, einstruction.com) near the end of their learning cycle:

[0.6 participation points.] A mass of weight 10.0 N has a period of 1.0 s. The length of the pendulum string is _____ m.

Sections 0906, 0907
"0.25" : 20 students
"24" : 7 students
"10" : 3 students
"5": 2 students
(Other responses, 1 student each: "0.06," "1.02," "2," "3.2," "21.7")

Correct answer: 0.25 m

The period of a pendulum is given by:

T = 2*pi*sqrt(L/g).

Note that the weight, or mass of the pendulum bob does not matter. Solving for L:

L = g*(T/(2*pi))^2.

However, many students did not watch how the order of operations were performed on their graphing calculators. Typically they entered the following:

1/2*pi
ANS^2
ANS*9.8

Because of the factor of pi multiplying the 0.5 evaluated just before it, this results in the incorrect answer of 24 (m?!?), which dangerously resembles the correct answer, apparently only with a misplaced decimal error ("did we need to convert to centimeters?").

In order to force the pi to be evaluated in the denominator, parentheses could be used (or each step could be executed separately, step-by-step):

1/(2*pi)
ANS^2
ANS*9.8

This gives the correct answer of 0.25 m.