Lab Concept
In Lab 8 your lab group will use three mathematical models of a physical pendulum in order to determine the acceleration due gravity in the lab room. You will use models of increasing complexity to reduce the number of required assumptions and compare the results of the three models using a number-line analysis. In this experiment you are provided with a pendulum consisting of a thin aluminum rod and a flat acrylic plate attached to a PASCO rotational motion sensor. The rotational sensor can read the angular position of the pendulum as it swings. From a DataStudio graph of angular position versus time you can determine the period of the oscillation. Using this period and other measurements you can solve for the acceleration due to gravity using the three model equations. Additional measurement devices consist of a meter stick and a triple-beam balance.
2. Theory Tutorial
The least complex model of a pendulum is the “simple pendulum.” The simple pendulum equation of motion is very similar to the equation of motion for a spring-mass system that you worked with in lesson 31. Starting with the equation for the period of a simple pendulum (Section 15-6 of HRW), solve for the acceleration due to gravity. This equation is your first model equation.
Figure 1. Diagram of a simple pendulum
(Halliday et al., Fundamentals of Physics, 9ed.)
What assumptions about your physical pendulum system are necessary to apply the equation you used in your answer to part a. ?
To improve the model equation from part a. you can model the system as a physical pendulum. In this model you account for the distribution of mass about the axis of rotation. Using the equation for the period of a physical pendulum (Section 15-6 of HRW) solve for the acceleration due to gravity. This is your second model equation.
Figure 2. Diagram of a physical pendulum
(Halliday et al., Fundamentals of Physics, 9ed.)
What assumptions must you...