Question

a ball of mass m is dropped from a height h on a pan fixed on a spring. the pan is compressed by distance x. caliculate the spring constant​

Answer 1

When, the ball is dropped from a height h,

Change in kinetic energy = Work done by gravity on the ball

Change in the kinetic energy = mgh

Now, as the Ball comes in constant with the spring pan, it will compress the spring until it stops that is again the change in kinetic energy = mgh

Now, we know that Work done by spring = Change in kinetic energy

So,

1/2kx^2 = mgh

or

k = 2mgh/x^2

This will be the spring constant of that spring.

Answer 2

Answer:

ball mass= m is dropped from height h

change in potential energy = mgh

Energy stored in spring =

$\frac{1}{2} k {x}^{2}$

Change in potential energy= energy stored in spring

$mgh = \frac{1}{2} k {x}^{2}$

$k = \frac{2mgh}{ {x}^{2} }$

$\fcolorbox{black}{red}{spring \: constant} = \frac{2mgh}{ {x}^{2} }$