Comparing force of mass at rest vs falling mass

[BTT]

What equations can be used to compare the force of a resting X mass to the force of a smaller Y mass falling Z distance.

Specifically, how much resting mass would equal the force of 300 pounds being dropped from 10 feet up?

 

[mfb]

A force from what, where?
The gravitational force between Earth and some other mass depends on the distance between the objects, but on the scale of a building you can neglect this effect.

 

[BTT]

yes, Earth's gravitational force applied to a resting mass and a falling mass. I am quite sure that a falling mass produces considerably more force than a mass at rest.

 

[mfb]

The gravitational force is the same.

The force applied on a surface can be larger at the time the falling mass hits it, as it gets decelerated rapidly. The force depends on details of the collision process.

 

[BTT]

I think backing up and restating this might help.

Let us say we are comparing the force of a 2000 kg inelastic sphere at rest on an inelastic floor vs a 200kg but same size inelastic sphere dropped 10 ft at sea level on earth.

 

[mfb]

Initially the second sphere will have a force of zero because it does not touch the floor, then it will have a large force for a very short time (where "large" and "short" depend on details of the collision process), then (resting on the floor) it will have 1/10 of the force.

 

[BTT]

That much I understand just fine. I want to know what number "large" is. The collision process is something I have simplified as much as possible. It is a point impact between two solid inelastic bodies. Can I get some actual math in here?

 

[haruspex]

That much I understand just fine. I want to know what number "large" is. The collision process is something I have simplified as much as possible. It is a point impact between two solid inelastic bodies. Can I get some actual math in here?

As mfb wrote, it's indeterminate in general. It depends on the details of the impact.
In reality, all impacts involve deformations. The deformation takes some short time, and the force varies over that time. Typically, the force will increase from zero, at first more or less uniformly with the degree of deformation. Some peak may then be reached and the force stay fairly constant for a while.
What you can say is that the integral of the force over time will equal in magnitude the momentum of the incoming object. If you try to claim the impact takes zero time then you will get the crazy result that the force is infinite.