Question

A small particle slides along a track with elevated ends and a flat central part, as shown in figure. The flat part has a length $3m$, the curved portions of the track are frictionless, but for the flat part, the coefficient of kinetic friction is $\mu =0.2$. The particle is released at a point $A$, which is at a height $h=1.5m$ above the flat part of the track. The position where the particle finally come to rest is:

• A. left to mid-point of the flat part
• B. right to the mid point of the flat part
• C. mid point of the flat part
• D. none of these

Answer 1

The correct option is C mid point of the flat part

Initial mechanical energy

$E_{mech}=U_{grav}=mgh=\frac{1}{2}ngL$

Energy loss due to friction in every time going through the flat part

$W_{fric}=-{\mu }_{x}mgL$

Consider that the particle moves $n$ tyrips

$\Delta E=W=n.W_{fric}$

$-\frac{1}{2}mgL=m_x.{\mu }_{x}mgL$

$n=\frac{1}{2\mu k}=2.5$

So the particle will stop at the middle part of the flat surface.