A wedge Y with mass of 10 kg and all frictionless surfaces and the inclined surface making 37° with horizontal. A block X with mass 2 kg is placed at the highest point of the wedge as shown in figure is at rest. At t = 0 wedge (Y) is pulled toward right with constant force (f) of 24 N. Taking the block X at rest at t = 0 , the time taken by it to slide down 8.8 m on the slope, while Y is on the move, is _____ s. (tak

Step-by-step solution

Horizontal acceleration of the wedge (assuming the block and wedge move together horizontally): A = f M + m = 24 10 + 2 = 2 m/s ^2 Working in the non-inertial frame of the wedge, the block experiences a pseudo force mA directed opposite to the wedge's acceleration. The components along the incline are: Component of gravity down the incline: g 37^ Component of pseudo force up the incline: A 37^ Net relative acceleration of the block down the incline: a_ rel = g 37^ - A 37^ Using 37^ = 0.6 and 37^ = 0.8 : a_ rel = 10