11/28/16 - Physical Pendulum Lab (Lab 22)

PURPOSE:
Derive expressions for the period of various physical pendulums. Verify your predicted periods by experiment.

THEORY:
In this lab, we created three physical pendulums using a thin metal ring and a thin isosceles triangle. The period of each pendulum is given by the equation: T = 2π/ω. Using Newton's second law, we created an equation for the sum of torques of each pendulum, This allowed us to find the angular speed of the system at the bottom of the swing, which we plugged into the original equation to find the period.

APPARATUS:
The apparatus we used consists of a ring stand, C-clamps, a metal rod, and a photogate connected to a computer with a Logger/Lab Pro set-up. The photogate is  positioned such that it can track the movement of the small piece of tape attached to the bottom of our swinging objects.

Physical Pendulum - fully assembled

EXPERIMENTAL PROCEDURE:
We used a photogate to measure the period of three physical pendulums: a thin metal ring, a thin isosceles triangle hung by its apex, and a thin isosceles triangle hung by the midpoint of the base.

Trial 1: Thin Metal Ring

Trial 2: Isosceles Triangle - Pivot at Apex

Trial 3: Isosceles Triangle - Pivot at Midpoint of Base

Notice how we attached the triangle

DATA/GRAPHS:
Trial 1:
Diameter of inside ring: 27.3 +/- 0.1 cm
Diameter of outside ring: 29.2 +/- 0.1 cm
Average diameter of ring: 28.25 cm

Trial 2 & 3:
Base of triangle: 14.4 +/- 0.1 cm
Height of triangle: 16.1 +/- 0.1 cm

Period prediction calculation for metal ring

Period prediction calculation for Isosceles Triangles 

Trial 1: Period Data

Trial 2: Period Data

Trial 3: Period Data

Period Data Results (Final)

ANALYSIS:

In order to verify that our theoretical calculations for the period of each pendulum were consistent with reality, our group had to use Logger Pro to collect experimental values for the period. Our group used a photogate to measure the  period of each pendulum, and we also used Logger Pro to calculate the mean value for each data set. We used the mean values of the period for the experimental values because we thought that it would be a more accurate representation of what the period would be. Each period data graph showcases individual data points for a given trial as well as the mean value of those data points.
CONCLUSION:
Our lab results turned out to be much better than expected. We successfully verified that our theoretical values for the period of each physical pendulum matched very closely to their real-life counterparts. In fact, our period data illustrates that our theoretical values and experimental values never exceeded a margin of error above 1%. For example, in Trial 1, our values for the period were about 0.37% different for one another. While this margin of error is clearly more than satisfactory for our circumstances, it is nevertheless a prudent endeavor to evaluate possible margins of error. One possible source or uncertainty in our calculations could have come from the tape we attached at the end of the object. As we realized in practice trials of this experiment, any added weight a distance away from the pivot can alter the angular speed of our system, thereby affecting the accuracy of our period. Another source of error in our methodology was the wobbliness of the moving object. This wobbliness indicates that some of the energy in the system is being lost due to friction at the pivot.