An orthogonal cutting operation is performed using a rake angle of 15°, to=0.012 in and w=0.100 in. the chip thickness ratio is measured after the cut to be 0.55, material shear strength is 40,000 lb/in^2, compute: (a) the shear force, (b) the cutting force, (c) the thrust force, and (d) the friction force.

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)?