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= 3.0m. The curved portions of the track 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= 1.5m 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= 3.0m. The curved portions of the track 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= 1.5m 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 loss in ME= mgh. This ME is lost its doing work against frictionn in the flat part so loss im 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` BE = 1.5 So the particle COMES to rest at the CENTRE of the flat part.