Recall that a wave packet moves with group velocity vg = ∂ω ∂k . for the wave packet above, find vg, evaluated at the central wavenumber k0. if the momentum of a particle is mvg and the kinetic energy is 1 2mv2 g , find the momentum and kinetic energy in terms of k0 and other constants.

Africtionless piston-cylinder contains 50 l of saturated liquid r-134a. the piston has a mass and an area resulting in an applied pressure of 500 kpa on the refrigerant. the refrigerant is now heated until its temperature rises to 70∘c. calculate the work (in kj) done during this process.

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Electric field of the earth. the earth has a net electric charge that causes a field at points near its surface equal to 150 n> c and directed in toward the center of the earth. (a) what magnitude and sign of charge would a 60-kg human have to acquire to overcome his or her weight by the force exerted by the earth’s electric field? (b) what would be the force of repulsion between two people each with the charge calculated in part (a) and separated by a distance of 100 m? is use of the earth’s electric field a feasible means of flight? why or why not?