Question

A 5 kg block is sliding on rough horizontal surface with speed 10 m/s at the moment when it just starts compressing a uncompressed spring of spring constant 400 N/m. If kinetic friction force between the block and surface is 10N , then the spring is compressed by nearly

Answer 1

Dear student,

Change in Kinetic energy = Work done by all forces.

W_f = Work done by spring

W_f = Work done by friction

Let the spring be compressed by x m
$$\begin{gathered} \frac{1}{2}m{v}^2=\frac{1}{2}k{x}^2+fx \\ \frac{{\displaystyle 1}}{{\displaystyle 2}}\times 5\times {10}^3\times {10}^2=\frac{{\displaystyle 1}}{{\displaystyle 2}}\times 400\times x^2+10\times x \\ or20000x^2+x-25=0 \\ onsolvingx=3.5cm \end{gathered}$$

Regards