Eric Murray, Spring 2006
If a system is isolated and non-dissipative, the mechanical energy
Emech = K + U
is conserved, where K is the kinetic energy of the system and U is the potential energy. Your system will be the Earth-cart system, where the potential energy will be local gravitational potential energy,
U = mgh
where m is the mass of the cart, g is the acceleration of gravity, and h is the height of the cart above some arbitrary zero point. You will push your cart so it coasts up an inclined track, and will use the point at which the cart stops before it rolls back down as the zero point of gravitational potential energy. Since the kinetic energy of the cart is zero at that point, this choice of the zero point of gravitational potential energy results in the mechanical energy of the system being zero at that point. If mechanical energy is conserved, it will be zero at all other points, as well.
Note that h will be negative, and will depend on the position of the cart and the incline angle of the track.
By making measurements of the position and velocity of the cart at various times in its motion, you will be able to find the average mechanical energy, along with its experimental uncertainty. If you find that it is not zero, within your measure of experimental error, then you will have to consider systematic errors. You should also consider whether your measure of experimental uncertainty, the standard error, truly reflects random error in this experiment.
Analysis Note: Although collection of the substantial amount of data in these experiments is not difficult, the amount of data collected may make its analysis rather time-consuming. Sample data and calculated results for one trial are tabulated below. Make sure you know how the analysis is performed, and can get these same results, before coming to lab. An Excel spreadsheet may be helpful in the lab, and you may want to plan it beforehand.
Lab 13, Experiment 1. Cart, Low Riser.
Cart Mass = 484 g
Riser Height = 2.4 cm
Support Separation = 100 cm
Minimum Position = 0.277 m
| Time measured |
Position measured |
Velocity measured |
Kinetic Energy calculated |
Potential Energy calculated |
Mechanical Energy calculated |
| 3.23 s | 0.311 m | -0.144 m/s | 5.0 mJ | -3.9 mJ | 1.1 mJ |