How can the force of impact on a falling spring mass system be calculated?

[chandran]

i have a spring with stiffness k. The spring is resting on the ground. Now a mass is kept over the spring. Now the spring deforms by an amount x=mg/k
where g is the gravity's acceleration.The force acting on the spring is mg Newtons and the reaction force from the ground is also equal to mg Newtons
since this is a statics problem.


Now i take the same spring and the mass over it and drop it over another spring of stiffness k1 fixed to the ground. The spring mass has an initial velocity of v.Now how can i calculate the force exerted on this system by the ground due to the impact.

After calculating this suppose i find that the force of impact is equal to x times mg can is replace the mass by a mass equal to xm and do a static analysis to find deflection.

 

[QuantumKing]

are you asking a question?

 

[Astronuc]

Now i take the same spring and the mass over it and drop it over another spring of stiffness k1 fixed to the ground. The spring mass has an initial velocity of v.Now how can i calculate the force exerted on this system by the ground due to the impact.

You'll have to clarify the interaction between the springs.

When the mass m, falls with the spring, there is no 'weight' pushing down on the spring, since the mass and spring are accelerating with gravity. So while falling the spring k is not deflected, i.e. there is not stored energy.

When the mass, m, and spring of constant k, hit the spring of constant k1, the mass and spring have an initial velocity and kinetic eneryg. Assuming an elastic response, both k and k1 will deflect, each absorbing some of the kinetic energy of m and k (assuming the spring has some mass). Then its a matter conservation of energy.