ANNOUNCEMENTS FOR CONSERVATION OF MECHANICAL ENERGY LAB
(Updated September 23, 2008)
General Announcements : Uncertainty : Inclined Plane : Conservation of Mechanical Energy : Collisions - Conservation of Momentum : Conservation of Rotational Kinetic Energy : Simple Harmonic Motion : Velocity of Sound in Air : Standing Waves on a String
In the first lab experiment, Uncertainty, each group measured the acceleration due to gravity, g. Below is a histogram of the results from the entire course, plotted together with a Gaussian (or "normal," or "bell-curve") distribution. The best estimate for g from this combined data is g = 10.52 +/- 0.11 m/s2. The standard deviation of these results is s = 1.96 m/s2; this result says how much a given group's result typically varies from the average value (and indicates what the uncertainty is on a given group's answer). About two thirds of the students in the class should have obtained a value of g within one standard deviation of 10.52 m/s2. The standard error of our results (or "standard deviation of the mean") is only d = 0.11 m/s2. By averaging the results of 342 groups, we learn the value of g (as measured by this experiment) much better (uncertainty is only 0.11 m/s2) than if we took only one student's result (for which the uncertainty is almost 13 times larger). This averaging makes the statistical uncertainty of our result very small (d = s /sqrt(N) ).
The discrepancy between the best measured result (g = 10.52 +/- 0.11 m/s2) and the accepted value (g = 9.81 +/- 0.02 m/s2) means either gravity has strengthened on the 4th floor of Rockefeller since October 21, 2003, the accepted value is wrong, or there were systematic errors in the experiment (such as using the small angle approximation in the derivation of our theoretical relationship between the length and period of the pendulum). Minimizing and estimating the sizes of such systematic errors is a key to successful physics experiments at all levels.
Section D. Gravitational Potential Energy
The picture below shows the general setup of this experiment.
Section D.1, Paragraph 1
You may discover that it's impossible to adjust the track so that the cart moves at constant speed over the entire length of the track; at several lab stations one will observe that the cart accelerates towards the center of the track and slows at the ends. Can you think of a plausible explanation for this behavior, one that you can check with equipment you have at hand? If you are working at one of these stations, you will need to incorporate this behavior into your error estimates.
Section E. Energy Stored in a Spring
The picture below illustrates how to use a ruler and either a knot or piece of tape to help you measure the position of the spring.
General : Uncertainty : Inclined Plane : Conservation of Mechanical Energy : Collisions - Conservation of Momentum : Conservation of Rotational Kinetic Energy : Simple Harmonic Motion : Velocity of Sound in Air : Standing Waves on a String