Conservation of energy

Introduction

The purpose of this lab is to test the conservation of energy in a simple oscillator. A pendulum is a great example of such an oscillator.

In one of the labs before, you examined the period of the pendulum as a function of the pendulum length, mass, and angle of oscillation. Today, we will use the pendulum to investigate the flow of energy when the pendulum swings.

There are two key positions of the swinging pendulum; one is when the bob reaches the highest point (also recognized as a starting point) and when it passes the position of equilibrium (or, the lowest point). Both are shown in Figure 1.

According to the conservation of energy, if the system does not lose its energy, the potential energy measured at the highest point shows as the kinetic energy at the lowest point. Thus,

Experimental Procedure

To test the equation above, we need to calculate the potential and kinetic energy and compare them.

Potential Energy

To know the potential energy, you need to measure h (refer to Figure 1). Figure out how to precisely measure h. Write down the method of measuring h in your lab worksheet.

Kinetic Energy

To know the kinetic energy, you need to measure the speed of the bob at its lowest position. Use a photogate to measure the time the bob blocks the photogate.

1. Place the photogate under the pendulum in such a way that the beam hits the bob centrally when it passes through the photogate (Figure 2).

2. The photogate should be in "Time Based" mode (Figure 3). Call the instructor to set it.

3. Let the pendulum swing several times through the photogate. Hit the green arrow to start collecting data (Figure 4).

4. Use "Statistics" to find the speed of the bob passing through the equilibrium (Figure 5a, b, c)

• Analyze

• Statistics

• Gate Time

Comparing the Results

The final step is to compare the results. If the percent difference is <5%, you are good to go. If not, try to identify sources of errors, eliminate them, and redo the measurements.