1. How do I show a sample calculation of finding the uncertainty in total energy
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Question
1. How do I show a sample calculation of finding the uncertainty in total energy by estimating the uncertainty of measurements of the angle of the track and the position of the cart. Perform the calculation for a data point where the kinetic energy and potential energy is approximately equal. How do I estimate the uncertainty of the angle of the track if it was 10 degrees? How do I estimate the uncertainty of the position of the cart? Please show me how to set this calculation up.
This experiment included launching a cart up an incline with a motion sensor at the end of the incline.Through this, position and time was recorded. Potential and kinetic energy were calculated to find total energy to see if it was conserved.
Explanation / Answer
In quantum mechanics, the uncertainty principle is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, such as position x and momentum p, can be known simultaneously. The more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa.[1] The original heuristic argument that such a limit should exist was given by Werner Heisenberg in 1927, after whom it is sometimes named, as the Heisenberg principle. A more formal inequality relating the standard deviation of position sx and the standard deviation of momentum sp was derived by Earle Hesse Kennard [2] later that year (and independently by Hermann Weyl [3] in 1928), where h is the reduced Planck constant.
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