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 truck are fricionless. 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 truck are fricionless. 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 ME of the particle is mgh and final is zero, so loos 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 each 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 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` BE = 1.5 So the particle comes to rest at the centre of the flat part.