Question

A solid of mass 2 kg moving with velocity 10 m/s strikes an ideal weightless spring and produces a compression of 25 cm in it. Calculate the force-constant of the spring.

Answer 1

Given:

• Mass = m= 2kg
• Velocity = v = 10m/s
• Compression = x = 25cm = 0.25m

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Need to find:

• The spring constant = k =?

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Solution:

The Compression in spring = Change in its KE

Initial velocity = 0m/s,

$\dfrac{1}{2} \: k {x}^{2} = \dfrac{1}{2} m \: ( {v}^{2} - {u}^{2} )$

Substitute the given values,

$\implies \: \dfrac{1}{2} k \times .25 \times .25 = \dfrac{1}{2} \times 2 ( {10}^{2} - {0}^{2} )$

$\implies \: k \times 0.0625 = 2 \times 100$

$\implies \: k = \dfrac{2 \times 100}{0.0625}$

$\implies \: k = \dfrac{2 \times 1000000}{625}$

$\red{\boxed{\boxed{\bold {\implies \: k = 3200 N/m}}}}$

∴ The spring constant or the force constant of the spring is 3200 N/m