In gear boxes of automotive vehicles, the gears are mounted on their shafts through splined connections to allow the axial motion between the gears and shafts during the gear shifting. on one of these shafts, the splined connection consists of 10 splines cut in a 60 mm shaft diameter. the height of each spline is 6 mm and the keyways in the hub are 50 mm long. determine the power that may be transmitted at 3000 rpm. use steel 60 as material of both the shaft and gear