Question

You are operating a lathe with an 200 mm diameter manual chuck and it is started with a programmed spindle speed of 3000 RPM and a chuck key with a mass of .75 lbs. If you start the lathe with the key still inserted in the chuck how much kinetic energy will the key have when it strikes you in the head? Assume: • The spindle has reached it's programmed speed before the key comes free, • air resistance is negligible, • the center of gravity of the key is 50 mm from the outside diameter of the chuck when it is inserted fully in the chuck, Give your answer in Joules

Answer 1

Solution : Given: Diameter af manual cheick - 200mm Hg = spindle speed = 3 rooRpm mass = 0.75 lbs and : If you start the latho with the key still inseated in the check how much kinetic energy will the key have been when it strikes you in head ? Assumption : is spindle has reached it's programmed speed before the key comes free. (ii) Air Resistance is negligible (i) The centre of gravity of the key is 50mm from the outside diameter of the cut check when it is inserted fully in the buck. Statal = check t x centre = 200+ 50 = 250 mon 125m w = 2003 - 2x nx 3000 = 1oon = 314.159 hade i direction of the velocety would be perpendicular to the chick, so only tangential component take into consideration, v=rW, = 0.25 x 314.159 = 78.5398 m. Kinetic energy = 1 m u 2 m = 0.75lbs = 75 X. 4535kg, (lbs) .) = 154 kg kit. = I x 34 x (+8.5398) = 1049.03 Joule