- #1

Satvik Pandey

- 591

- 12

## Homework Statement

A ball of mass 1kg is dropped from a height 1m . Estimate how long the ball is in contact with the ground in seconds ?

Details and assumption

Simplify the question by modeling the ball as an ideal spring of spring constant 100Nm .

Take gravitational acceleration if necessary as 9.8m/s

^{2}

## Homework Equations

Work done by spring = 1/2kx^2.

Change in kinetic energy = Work done.

## The Attempt at a Solution

Let the spring stops(ball) after it is bring displaced from

*X*m from its mean position.

Using the work energy theorem-

mgX-[itex]\frac{kx^{2}}{2}[/itex]=0-m/2*2gh

where m is the mass of spring.I got square of velocity before impact as 2gh(h is the height mentioned above).

So I got the displacement of spring from its mean position to stop.

I tried to use equations of motion but acceleration is not constant.So I tried to use calculus.

I got Acceleration as a function of x =g-kx/m .Could you please help me in solving this question further.