In the leisenberg group generated by the vector fields (as in class) yo) and x2--+ x1 20 show that the gauge g(z, y, z) = ( (2,2 + y2)2 + 16? satisfies the following: voger, y, 2 o hi (0,0, ag(x, y,2)o h (0,0,0)

answer: the potential energy decreases from 379 j to 243 j

explanation:

for the law of conservation of energy, the total energy in a system must be conserved. the total energy of the system is given by the sum of kinetic (k) and potential (u) energy:

e = k + u

the total energy is e=675 j, and this does not change.

initially, the kinetic energy is k=296 j, so the potential energy is

at the end, the kinetic energy is k=432 j, so the potential energy is

so, we see that the potential energy has decreased from 379 j to 243 j.