There are a number of different labs you can do to show conservation of energy but I decided to keep it simple and just use a pendulum. Before we started the lab, I lectured a bit about energy, explaining the difference between kinetic energy (energy of motion) and potential energy. We talked about roller coasters and how the cart’s energy is all potential energy at the top of the first hill before it starts accelerating down the slope and at the lowest point all that energy (ignoring frictional losses) has been transferred to kinetic energy. The Physics Classroom has some nice examples and explanations for conservation of energy, including an interactive roller coaster where you can design the hills and ramps and then let the cart go, while it shows you the kinetic energy, KE and potential energy, PE.

For the lab, the students used the Video Physics app to take a movie of the pendulum swinging through at least one full oscillation. The movie below shows the red marks the student put on the ball in each frame of the movie. The meter stick in the background is used to give the app scale and the origin is set by the students so that the lowest point of the pendulum is (x=0,y=0). You can see the pendulum starts with zero velocity and at its highest point, so all its energy is potential energy but as it swings through the lowest point, its potential energy goes to zero as its kinetic energy reaches its maximum.

The Video Physics app doesn’t let you do much with the data so the students open their data in the Graphical Analysis app also by Vernier, which is what produced the graph below – this is data from a different group than the movie above.

In the data above, the red data points are the x-position of the pendulum, and the blue data points represent the velocity of the pendulum in the x-direction (along the horizontal). You can see that when the pendulum went through the origin (x=0) at t=1s, the velocity was negative and at its maximum, therefore KE was also at its maximum. When the pendulum reaches the turning point at t=1.4s, the velocity goes to zero and then becomes positive as it reverses direction. Students made graphs for motion in the y-direction as well and were able to read off maximum height (y) and maximum velocity (in the x-direction) for the pendulum from the data tables. They then used those numbers to calculate the maximum KE = 1/2 m v^{2} and maximum PE = mgy. The students found that their values for the maximum kinetic energy were very close, if not the same as their maximum potential energy, demonstrating the conservation of energy.

The Physics Class room has a nice animation for pendulums and conservation of energy.

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