Question

23
A spring of stiffness 1 kN/m is attached
to a block of mass 4 kg on a surface that
has frictional co-efficient 0.4. The spring
is compressed and released, and the
block accelerates at 2 m/s2 just as it is
released. The work done in compressing
the spring is:​

Answer 1

Given:

A spring of stiffness 1 kN/m is attached to a block of mass 4 kg on a surface that has frictional co-efficient 0.4. The spring is compressed and released, and the block accelerates at 2 m/s2 just as it is released.

To find:

Work done in compressing spring ?

Calculation:

• Let's say that spring is compressed by x distance !

According to FBD :

$\rm f_{spring} - friction = ma$

$\rm \implies \: kx - \mu(mg) = ma$

$\rm \implies \: 1000x - 0.4(40) = 4 \times 2$

$\rm \implies \: 1000x - 0.4(40) = 8$

$\rm \implies \: 1000x - 16= 8$

$\rm \implies \: 1000x = 24$

$\rm \implies \: x = 0.024 \: m$

Now, work done in compressing is :

$\rm \: W = \dfrac{1}{2} k {x}^{2}$

$\rm \implies\: W = \dfrac{1}{2} \times 1000 \times {(\dfrac{24}{1000} )}^{2}$

$\rm \implies\: W = \dfrac{576}{2000}$

$\rm \implies\: W = 0.288 \: joule$

So , work done is 0.288 J.