Question

A spring of mass 2kg and stiffness 1KN/m is dropped from a height of 2m on the ground calculate the maximum distance through which spring is compressed​

Answer 1

Maximum compression is 0.3m

Explanation:-

Given:-

A spring of mass 2kg

stiffness 1 KN/m

height of 2 m

To find:

=Maximum compression

Calculation:

Assume maximum compression be "x".

So, we can say:

Initial PE = mg(2 + x)

Final PE = ½kx²

Now, as per law of conservation of energy:

$mg(2 + x) = \frac{1}{2} k {x}^{2}$

$2 \times 10 \times (2 + x) = \frac{1}{2} \times 1000 \times { x }^{2}$

$20(2 + x) = 500 {x}^{2}$

$40 + 20x = 500 {x}^{2}$

$500 {x}^{2} - 20x - 40 = 0$

$50 {x}^{2} - 2x - 4 = 0$

$25 {x}^{2} - x - 2 = 0$

After solving the quadratic equations:-

$x = 0.3m$

So , maximum compression of spring is upto 0.3 metres.