The diameter of a cooler is 0.3 m and it is filled with a blue liquid to a height of 0.55 m. Then, a can of soda is placed into the cooler that is half filled with water (density of water, p = 1000 kg/m3 ) such that it floats upright in the unknown pink liquid. The can of soda has a mass of 0.020 kg when empty, a diameter of 0.062 m, and its volume is 332 cm^3.Given that the length of the can above the blue liquid is 0.032 m, what is the density of this blue liquid?

Consider the particle-in-a-box problem in 1d. a particle with mass m is confined to move freely between two hard walls situated at x = 0 and x = l. the potential energy function is given as (a) describe the boundary conditions that must be satisfied by the wavefunctions ψ(x) (such as energy eigenfunctions). (b) solve the schr¨odinger’s equation and by using the boundary conditions of part (a) find all energy eigenfunctions, ψn(x), and the corresponding energies, en. (c) what are the allowed values of the quantum number n above? how did you decide on that? (d) what is the de broglie wavelength for the ground state? (e) sketch a plot of the lowest 3 levels’ wavefunctions (ψn(x) vs x). don’t forget to mark the positions of the walls on the graphs. (f) in a transition between the energy levels above, which transition produces the longest wavelength λ for the emitted photon? what is the corresponding wavele

Find v(t), given acceleration a(t)=7j and initial velocity v(0)=k

Aspring has a natural length of 8 m. if a 12-n force is required to keep it stretched to a length of 10 m, how much work w is required to stretch it from 8 m to 16 m? (round your answer to two decimal places.)