Learning the Resistance Coefficients of Pendulum Motion Using Balls of Various Sizes

Abstract

In order to obtain the damping and resistance coefficients of a pendulum, we constructed an optical system containing a photogate for measuring the speed of the pendulum at the lowest point of motion. The photogate consisted of a photoresistor, a laser, a mechanical body, and a pendulum ball. A 3D printer was used to produce the mechanical body and pendulum balls of various sizes. Furthermore, we used Arduino to automate measurement of the speed at the lowest point of motion and increase the precision. We found that the resistance coefficient was proportional to the size of the balls, regardless of the ball mass, in agreement with the drag equation for a small Reynolds number.

Investigating damped oscillations in simple pendulum

“…Our study has re-investigated the effects of cross-section of the string on pendulum bobs of different mass, size and material. The values of the air resistance coefficients are found to be of the same order of magnitude as reported by others [5].…”

“…In [5] it has been reported that damping, contrary to expectations, is significantly more with pendulum bob of lighter mass. Our findings reveal that factors like mass, shape, size and thickness are all important but effects of size/shape and thickness are more significant than mass of the pendulum in affecting the coefficients of damping.…”

“…To obviate these deficiencies, educators have tried to automate the process of time measurements with the help of sensors like light dependent resistor (LDR), infrared (IR) based photogates and mobile-phone [1][2][3]. Recently [4,5], damped harmonic motion has been studied to determine the effect of size of the pendulum bob and thickness of the string on the motion of the pendulum. Study of damped motion using the simple pendulum is useful because it can help us to determine air-resistance which students find very less convincingly covered in their curricula.…”

“…In [4] the role of string width on the damping coefficient has been studied by using a very heavy pendulum bob (485 g) suspended to a long string (length 200 cm). In [5], the values of damping coefficient have been determined by taking different masses of the pendulum bob ranging between 6 g and 24 g. A different approach [6] uses a physical pendulum consisting of a mirror attached to a ruler fixed at one of its ends to study damped oscillations with the Arduino board connected to an LDR sensor.…”