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/s2
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 Xm from its mean position.
Using the work energy theorem-
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.