How Can You Calculate the Impact Force of a Free-Falling Object?

[leden]

I wonder how could I calculate impact force of an object (eg. a stone) in a free fall impacting on the perfectly inelastic (perfectly hard) floor.
I know:
- m -mass of the falling object
- h -height of the fall
- v -speed at the time of impact
- t -time it takes from highest point to the lowest
- I can also calculate kinetic energy of an object at the impact point
I DO NOT know dwell time (how long the object and the floor are in contact).
So I cannot calculate the impact force with F = \delta p * \delta t.

How can I calculate the impact force?

 

[PBRMEASAP]

I DO NOT know dwell time (how long the object and the floor are in contact). So I cannot calculate the impact force with F = \delta p * \delta t.

You have answered your own question with this statement. You cannot determine the force, or even the average force, of the impact without knowing how long they are in contact. All you can figure out is the impulse delta p. In your example of a stone falling on a perfectly hard (rigid) floor, the stone isn't going to deform elastically, so it must bounce or shatter. In this case, the time spent in contact is nearly zero. Since the impulse is certainly not zero, the average force is practically infinite. So for elastic "billiard ball" type collisions, it is not meaningful to talk about force of impact--momentum/energy transfer is the best you can do.

edit: I should clear up a likely source of confusion. Even though one normally thinks of "elastic" as being stretchy or rubbery, that is not what it means in physics jargon. An elastic collision means that there as just as much kinetic energy after the collision as there was before. This can (and often does) apply to objects that are perfectly hard. An example of an inelastic collision is a lump of clay smashing into another lump of clay and sticking to it. Momentum is conserved, but kinetic energy is not. Some of it was used up in changing the shape of the lumps.

 

[charng]

To calculate the impact force of an object in free fall, you can use the equation F = ma, where F is the force, m is the mass of the object, and a is the acceleration due to gravity (9.8 m/s^2). In this case, the acceleration will be negative since the object is slowing down as it falls towards the ground.

To determine the acceleration, you can use the equation v = u + at, where v is the final velocity (which is 0 at the point of impact), u is the initial velocity (which is equivalent to the velocity at the highest point of the fall), and t is the time it takes for the object to reach the ground.

From there, you can rearrange the equation to solve for a, which will give you the acceleration due to gravity. Once you have the acceleration, you can use the F = ma equation to calculate the impact force of the object on the floor.

However, it is important to note that this calculation will only give you an estimate of the impact force, as it does not take into account the potential energy of the object at the highest point of the fall or the energy lost during impact due to factors such as deformation of the object or the floor. To get a more accurate calculation, you would need to know the dwell time (the time the object and the floor are in contact) and use the equation F = \delta p * \delta t, where \delta p is the change in momentum and \delta t is the dwell time.

In summary, to calculate the impact force of an object in free fall, you can use the equations F = ma and v = u + at, but keep in mind that these will only give you an estimate and a more accurate calculation would require knowledge of the dwell time.