A block of weight W is pulled up a plane forming an angle with the horizontal by a force P directed along the plane. If is the coefficient of friction between the block and the plane, derive an expression for the mechanical efficiency of the system. Show that the mechanical efficiency cannot exceed 1 2 if the block is to remain in place when the force P is removed.

4) We saw in class that an electron wavefunction can actually extend through a classically forbidden region of space (potential barrier) where the potential energy is higher than the electronâ€™s kinetic energy. This process is called quantum mechanical tunneling. In the lecture notes, we plotted th e tunneling probability for an electron as a function of barrier height and width. Using this plot, (a.) what will the probability be of finding an electron on the other side of a potential barrier 1 nm wide if its potential height is 0.5 eV higher than the kinetic energy of the electron (b.) What is the probability if the barrier is the same height as before but 5 nm wide (c.) What is the tunneling probability for a 2 nm wide barrier if the difference between electron