A speed reducer has 20 deg full depth teeth and consisct of a 20 tooth steel spur pinion driving a 50 tooth cast iron gear. the horse power transmitted is 12 at a pinion speed of 1200 rev/min. for a dimateral pitch of 8 teeth/ in and a face width of 1.5 in find the contact stress. the yuong's modulus of the steel is 30E6 and young's modulus of cast iron is 15E6. use a poisson's ratio of 0.3 for both materials. use equation 14-14 to calc the contact stress in the gear only.

An external consultant recommends that a plant installs a bank of capacitors for power factor correction. this will reduce the peak electrical demand charges by an average of 93 kw every month. the plant current pays $13 per kw in peak demand charges. the capacitor bank will include 223 kw of fixed capacitors, and 183 of variable capacitors. the fixed capacitors cost $59 per kw, and the variable capacitors will cost $65 per kw. the consultant charges 21% of the equipment costs to install the capacitors. because this project will reduce the demand for the electric utility, they are prepared to provide a one-time rebate of $42 per kw of reduced demand. what is the simple payback period for this project (in years)?