Question

A block of mass m is moving on smooth horizontal surface. A spring of spring constant K is arranged as shown. Then maximum force applied by spring is proportional to

Answer 1

Solution

Max spring force will be at

max compression and that will

be at the instant when kinetic

energy is zero.

As spring force is conservative,

$U_i+K{E}_i=U_f+K{E}_f$ [conservation of Mechanical (Energy)]

So,

$U_i=\frac{K(0{)}^2}{2}=0,U_f=\frac{K{X}^2}{2}$

$K{E}_i=\frac{M{U}^2}{2}$, $K{E}_f=\frac{M(0{)}^2}{2}=0$

So, $\Rightarrow \frac{K{X}^2}{2}=\frac{M{V}^2}{2}$

$\Rightarrow X=\sqrt{\frac{MV}{K}}$ [max compression]

So max spring force = $KX=\left(\sqrt{KM}\right)V$