A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes an uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10000 N/m. The spring is compressed by (in cm):

Options

A. 8.5 cm
B. 5.5 cm
C. 2.5 cm
D. 11.0 cm

Answer

B

Explanation

Let the block compress the spring by x before stopping.
kinetic energy of the block =(P.E of compressed spring).
+ work done against friction
`(1)/(2)xx2xx(4)^(2)=(1)/(2)xx10,000x^(2)+15xxx`
`10,000x^(2)|30x-32-0`
`implies5000x^(2)+15x-16=0`
`thereforex=(-15pmsqrt((15)^(2)-4xx(5000)(-16)))/(2xx5000)=5.5cm.`