Question

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

(a) 8.5cm 

(b) 5.5cm

(c) 2.5cm 

(d) 11.0cm

Answer 1

b) : Let the spring be compressed by x
Initial kinetic energy of the mass = potential energy of the spring + work done due to friction

1/2 x 2 x 4² = 1/2 x 10000 x x² + 15x

or 5000x² + 15x – 16 = 0
or x = 0.055m = 5.5cm.