A uniform crate of mass 30 kg must be moved up along the 15 incline without tipping. Knowing that the force P is horizontal, draw the free-body diagram needed to determine the largest allowable coefficient of static friction between the crate and the incline, and the corresponding force P.

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 electron’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