Question

A massless spring of length l and spring constant k is placed vertically on a

table. A ball of mass m is just kept on top of the spring. The maximum velocity

ofthe ball is​

Answer 1

Given:

A massless spring of length l and spring constant k is placed vertically on a table. A ball of mass m is just kept on top of the spring.

To find:

Maximum velocity of the ball upon release of the spring.

Calculation:

Let's assume that the spring was compressed downwards by a displacement of x.

Now , the maximum velocity of the ball will be achieved only when all the potential energy stored within the spring is converted into the kinetic energy of the ball.

$\therefore \: (KE)_{ball} = (PE)_{spring}$

$= > \: \dfrac{1}{2} m {v}^{2} = \dfrac{1}{2} k {x}^{2}$

$= > \: m {v}^{2} = k {x}^{2}$

$= > \: {v}^{2} = \dfrac{ k {x}^{2} }{m}$

$= > \: v = \sqrt{ \dfrac{ k {x}^{2} }{m}}$

So , maximum velocity of the ball will be :

$\boxed{ \sf{ \: v = \sqrt{ \dfrac{ k {x}^{2} }{m}}}}$