Question

a spring of spring constant. 10 N/m and natural length 10cm is compressed to 7 cm. a mass of 2kg is projected by it when the spring is released. find the speed of projection of the mass.​

Answer 1

$\color{red}\huge{\underline{\underline{\bf GIVEN\dag}}}$

• $\bf spring \: constant (k) = 10N/m$
• $\bf natural \: length = 10cm$
• $\bf compressed \: to = 7cm$

$\color{red}\huge{\underline{\underline{\bf SOLUTION\dag}}}$

By energy conservation,

$KE_{i}+PE_{i}=KE_{f} +PE_{f}$

Where,

• KE : Kinetic Energy.
• PE : Potential Energy

Initially It was at rest, therefore Kinetic energy initial is '0'.

And potential energy final is '0'.Because potential energy converted into kinetic energy.Therefore protecting the body.

And initially Potential energy is due to spring.

$\implies0 + \frac{1}{2} k(( {x_{i})}^{2} - ( {x_{f}})^{2} ) = \frac{1}{2} m {v}^{2} + 0$

$\implies \frac{1}{2} (10)( {(10)}^{2} - {(7)}^{2} ) = \frac{1}{2}(2) {v}^{2}$

$\implies 5(51) = {v}^{2}$

$\implies {v}^{2} = 225$

$\implies v = \sqrt{225}$

$\orange{ \boxed{ \therefore v = 15 {ms}^{ - 1} }}$

Therefore, the velocity of protection is 15m/s.

HOPE THAT HELPS!!