Lab 22

Lab 22 Physical Pendulum

November 28 2016

Goal:

Our objective is to calculate the period of a ring hanging from its edge and of a triangle hanging both upside down and right-side up. We will compare these calculated periods to our experimentally measured period.

Theory:

In order to calculate period of an object acting as a pendulum we need to know the moment of inertia about the chosen pivot which for a triangle requires us to calculate the Y-axis center of mass. Fortunately we have previously calculated the center of mass which simplifies the work necessary to calculate the period of our objects. From here it is quite simple to find the period symbolically and we need only to measure the dimensions of our objects and plug the numbers in.

Procedure:

The setup for this lab consisted of hanging our object from a metal rod and taping a marker onto the bottom, which we needed so we could measure the period with a photogate. The photogate detected every third pass as one period, and gave consistent results. 

The mean value of our period measured 0.9245 seconds. This was promising because it measured extremely close to our calculated value. After our success with the ring we move on to measuring the period of an isosceles triangle. 

We were tasked with finding both the period of the triangle upside down and upright, taken from our logger pro.

Triangle Height: 13.5 cm

Triangle Base: 15.6 cm

Experimental Upright period: 0.668 sec

Experimental Upside down period: 0.592 sec

Calculated Upright period: 0.6306 sec

Calculated Upside down period: 0.5754

Our error for upright and upside down periods were 5.9% and 2.8% respectively. I attribute the error in this part of the experiment due to faulty experiment setup; the triangles were hung from paperclips and tape which might have contributed some degree of friction to the experiment, resulting in larger than expected periods.

Conclusions:

The small angle approximation formula we tested in this lab performed very well; our ring's error being 0.03% attests to the efficacy of our mathematical model. As we begin to delve into more complex modeling our predictions become increasingly accurate.