Question

3. The potential energy of an object is given by P=m.g.h, where m is the mass, g is the gravitational constant (9.81m/s), and h is the height of that object above some reference point. If we measure m and h, as well as their uncertainties om and Oh, and we know the value of g, which is a constant, we want an algebraic expression for the uncertainty on the potential energy, op. (a) First, lets break this up into P = (mg) ·h. What is the uncertainty of P in terms of P, (mg), h, 0(mg), and on? (Note that 0(mg) is the uncertainty on the product of m times g). (b) Now we don't have a number for 0(mg), but we can figure it out using error propagation rules and remembering that g is just a constant. Write what (mg) is equal to in terms of Om and g. (c) Now put together the results of the previous two parts and write a formula for op in terms of just P, m, h, 9, Om, and on.

Answer 1

(1) + (-а) га го 10 . ( 3 отды), ) Yи bu - (m) 4 а)

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