A particle slides along a track with elevated ends and a flat central part as shown in Fig. The flat part has a length l = 3.0 m. The curved portions of the track are frictionless. For the flat part the coefficient of kinetic friction is mu_(k)=0.20, the particle is released at point A which is at height h = 1.5 m above the flat part of the track. Where does the particle finally come to rest ?

A particle slides along a track with elevated ends and a flat central

1.	A particle slides along a track with elevated ends and a flat central part as shown in Fig. The flat part has a length l = 3.0 m. The curved portions of the track are frictionless. For the flat part the coefficient of kinetic friction is mu_(k)=0.20, the particle is released at point A which is at height h = 1.5 m above the flat part of the track. Where does the particle finally come to rest ?
Answer» Solution :As initial Mechanical Energy (ME) of the particle is mgh and FINAL is zero, so loss in ME = mgh. This ME is LOST in doing work against FRICTION in the flat part, so loss in ME = WD against friction `mgh = mu mgs` i.e., `s=(h)/(mu)=(1.5)/(0.2)=7.5m` After starting from B the particle will reach C and then will rise up till the remaining KE at C is converted into potential energy. It will then again DESCEND and at C will have the same value as it had when ascending, but now it will move from C to B , the same will be repeated and finally the particle will come to rest at E such that `BC+CB+BE=7.5=3+3+BE=7.5` B = 1.5 So the particle comes to rest at the centre of the flat part.