You pull on a string with a horizontal force F = 45 N that is attached to a block of mass mb = 7.5 kg, then to the axle of a solid cylinder of mass mc = 5.4 kg and radius r = 0.4 m, then to a spring of spring constant k = 50 N/m. This is all done on an inclined plane where there is friction ( char16.pngs = 0.60 and char16.pngk = 0.40 ), and the incline angle is char12.png = 25 degrees. Everything starts at rest, and the spring is unstretched. The block slides down the plane, the cylinder rolls down the plane (without slipping), and the spring stretches.
1. First, what is the speed of the block and cylinder after you have pulled the block and cylinder 48 cm down the plane?
2. How far have you pulled the block and cylinder when everything stops?