Question

A 2kg block slides on a horizontal floor with a speed of 4 m/s it strikes a and compressor is 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 compresses by

Answer 1

$\underline{ \underline{ \sf{ \maltese \:Question }}} :$

A 2kg block slides on a horizontal floor with a speed of 4 m/s it strikes a and compressor is 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 compresses by

$\underline{ \underline{ \sf{ \maltese \: Answer}}} :$

$\rm \red{Given }$

$\sf{k = 10000 \: N/m}$

$\sf{force \: of \: friction \: (f_k) \: = \: 15 \: N}$

$\sf{mass \: of \: block \: = \: 2 \:Kg }$

$\sf{initial \: velocity \: of \: the \: block \: = 4 \: m/s}$

$\sf \pink{Suppose \: block \: gets \: the \: state \: of \: rest \: after \: compressing \: the \: spring}$

$\sf \pink{Applying \: \: work - energy \: theorem}$

$\sf{i.e., \: work \: done \: by \: all \: the \: forces \: = \: change \: in \: kineic \: energy}$

$\sf{f_k(x) + \frac{1}{2}k {x}^{2} = \frac{1}{2} m {v}^{2} - 0 }$

$\implies \sf{15x + \frac{1}{2} k {x}^{2} = \frac{1}{2} m {v}^{2} - 0 }$

$\implies \sf{15x + 5000 {x}^{2} = 16 }$

$\implies \sf{5000 {x}^{2} + 15x - 16 = 0 }$

$\sf \pink{By \: solving ; \: }$

$\sf{x = \frac{- 15 \: \pm \: \sqrt{225 - 4 \times 5000x - 16} }{2 \times 5000} }$

$\sf{x = \frac{- 15 \: \pm \: \sqrt{225 + 320000}}{10000} }$

$\sf{x = \frac{- 15 \: \pm \: \sqrt{ 320225}}{10000}}$

$\sf{x = -0.00 15 \: \pm \: \sqrt{32.0225} }$

$\sf{x = - 0.0015 \: \pm \: 5.5}$

$\sf{x = 5.5}$

$\sf{x= 5.5 \: cm}$

Answer 2

A 2kg block slides on a horizontal floor with a speed of 4 m/s it strikes a and compressor is 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 compresses by