Experiences

Inclined plane. Testing the principle of the conservation of me-chanic energy.

Gomboli Sandro

Italy

Vocational School

Physics

Laboratory

Direct

A cart is left freely slide with zero initial speed on an inclined plane realized with a rail air cushion with negligible friction.
Noting, for various inclinations, travel times for a distance of 2 m with a stopwatch, occurs roughly the consistency of mechanical energy during the experience is transformed from potential energy into kinetic energy.
This experience shows how the principle of conservation of mechanical energy, in particular conditions, simplifies the study of dynamics.
An inclined plane is made of an air cushion trackway, to make friction negligible, and a few rectified metal shims to set its heights and hence the proportionate inclinations.
A moving truck with a negligible friction activates a couple of photoelectric sensors connected to a digital chronometer which detects with a fair approximation the travelling times on a 2m long predetermined section of the trackway measured with an absolute error of 4mm.
The error in the distance between the two optical lines depends on the instrumental error of a scale integral with the trackway itself and on random errors due to the positioning of photocells and the dimensions of their laser beam. Different inclinations of the trackway are set; for each of them the measurements of the times are repeated at least three times for a statistical evaluation of random errors.
Given the zero value of the heights, to calculate potential energy, coinciding with the finishing line, and given that the starting speed is null, coinciding with the starting of the chronometer ,it will be proved that the potential energy of the truck on the starting line (first post) is equal to the kinetic energy on the finishing line (second post).
What we are basically testing is the principle of the conservation of mechanic energy for isolated physical systems with ideal constraints as approximately our inclined plane is.
If the test is carried out properly, we will be able to get satisfying results in most cases.
The errors in the results (mechanic energy and kinetic energy) are due to instrumental errors in the measuring of times and distances and their propagation in calculations. Random errors are in most cases unimportant and negligible.
The discrepancy between the two values is contained within the limits of their errors and allows us to perfectly test the validity of the principle on examination.
This test shows the simplification introduced by the principle of conservation of mechanic energy in the calculations relating to the study of the mechanics of isolated systems with ideal constraints.
The measurements of the times and heights detected in the test can also be used to calculate indirectly with a fair approximation the acceleration of gravity by drawing on geometrical considerations and applying the second law of dynamics.