A 2kg Block slides on a horizontal floor with speed of 4 m/s.   It strikes a uncompressed spring and compresses it till the block is motionless.  The kinetic friction force is 15N and spring constant is 10,000 N/m.   The spring compressed by

Let the spring compresses by x  Initial K.E. of the mass  =   P.E. of the spring + work done                               due to friction   KE of the mass=   12mv2;  PE of spring=   12kx2;work done by friction=friction force . displacement substitute  12mv2=   12kx2+f.x substitute the given values ∴    12 ×2 ×42  =   12×10000× x2+15x solve the quadratic equation x=0.055 m spring is compressed by 5.5 cm