Question

44 A spring of mass 2 kg and stiffness 1
kN/m is dropped from a height of 2 m on
the ground. Calculate the maximum
distance through which the spring is
compressed
8: A​

Answer 1

Answer:

A spring of mass 2kg and stiffness 1 KN/m is dropped from a height of 2 m on the ground.

To find:

Max compression?

Calculation:

Let max compression be "x".

Now, we can say:

Initial PE = mg(2 + x)

Final PE = ½kx²

Now, as per law of conservation of energy:

\rm \: mg(2 + x) = \dfrac{1}{2} k {x}^{2}mg(2+x)=

2

1

kx

2

\rm \implies \: 2 \times 10 \times (2 + x) = \dfrac{1}{2} \times 1000 \times {x}^{2}⟹2×10×(2+x)=

2

1

×1000×x

2

\rm \implies \: 20 (2 + x) = 500{x}^{2}⟹20(2+x)=500x

2

\rm \implies \: 40 + 20x = 500{x}^{2}⟹40+20x=500x

2

\rm \implies \: 500{x}^{2} - 20x - 40 = 0⟹500x

2

−20x−40=0

\rm \implies \: 50{x}^{2} - 2x - 4= 0⟹50x

2

−2x−4=0

\rm \implies \: 25{x}^{2} - x - 2= 0⟹25x

2

−x−2=0

After solving the quadratic equations:

\rm \implies \: x = 0.3 \: m⟹x=0.3m

So , max compression of spring is 0.3 metres.