Please help out with Question C Many thanks xxoo A gas turbi

Please help out with Question C. Many thanks!! xxoo

A gas turbine is rotating at a constant angular speed of 3000 r.p.m. Due to fatigue, a blade of the turbine breaks 1 ms after the blade has passed the horizontal position. The blade is very small and can be considered as a single 1.5 kg panicle, at a distance from the rotor axis of 400 mm and with a distance from the stator casing of 100 mm. Calculate the time to impact of the blade with the casing and its position in Cartesian coordinates (centered at the shaft axis). For this part A you can neglect gravity. Considering that the impact blade-stator casing is characterised by a null coefficient of restitution e = 0 and that the mass of the casing plate participating to the impact is 15 kg, calculate the remaining kinetic energy of the blade after the impact (consider the impact to be a direct central impact). Including air resistance as a force with a direction opposite to velocity and a magnitude F_aero = C_aero v^2 (with C_aero = 0.1 Ns^2/m^2), calculate the acceleration components (horizontal and vertical) at the instant just after the impact blade-casing.

Solution

(c) It is given there collision with e=0 means no relative motion of particle after collision.so plade will start rotating with shaft and velocity is tangential to the circular motion so at any point aer resistance is Faero in opposite direction to velocity.You know the impact location from part (b).Now at that location use Faero in direction opposite to velocity.F/m will give you accelration then take the components.