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

Options

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

Answer

B

Explanation

(b) Let the block compess the spring by `x` before stopping kinetic energy of the block `= (P.E of compressed spring ) + work done against friction .
`(1)/(2) xx 2 xx(4)^(2) = (1)/(2) xx 10000 xx x^(2) + 15 xx x `
`10000 x^(2) + 30x - 32 = 0`
`rArr 50000 x^(2) + 15x - 16 = 0`
`x = (-15 +- sqrt((15)^(2) - 4 xx (50000)(-16)))/(2 xx 5000)`
`:. 0.055m = 5.5 cm`.