Stopping of Two Blocks due to Friction

Stopping of Two Blocks due to Friction

Friction is an opposing force that opposes the motion of one body over the surface of another body. Like in case of a ball freely rolling on the ground, the ball eventually comes to stop, because of the force of friction that acts between ball and the ground. Friction is a force that is around us all the time that opposes relative motion between systems in contact but also allows us to move. The force of friction is parallel to the surface and opposite to the direction of intended motion.

When two masses compressed towards each other and suddenly released then energy acquired by each block will be dissipated against friction and finally block comes to rest.

i.e. F x S = E; Where, F = Friction,

S = Distance covered by block,

E = Initial Kinetic Energy of the block.

\(F\times S=\frac{{{p}^{2}}}{2m}\).

Where, p = Momentum of block.

\(\mu mg\times S=\frac{{{p}^{2}}}{2m}\) (as F = μmg)

\(S=\frac{{{p}^{2}}}{2\mu {{m}^{2}}g}\).

In the given condition p and μ are same for both the blocks.

So, \(S\propto \frac{1}{{{m}^{2}}}\Rightarrow \,\frac{{{S}_{1}}}{{{S}_{2}}}={{\left[ \frac{{{m}_{2}}}{{{m}_{1}}} \right]}^{2}}\).