Falling

[KingNothing]

If an object of mass m is falling, and hits the ground at velocity v, and makes an indent in the ground of length d, what is the force F that he hits with?

I'm jsut asking what equations you would use.

[Adrian Baker]

Sounds like a momentum question....

Ft=change in mv.
You have mv change, and are asked for F, so you need t. Calculate this from s=d/t


... and post questions like this in the HWK section!

[Chen]

How do you know how long the interaction with the ground was (dt)?

[ZapperZ]

Originally posted by Adrian Baker
Sounds like a momentum question....

Ft=change in mv.
You have mv change, and are asked for F, so you need t. Calculate this from s=d/t


... and post questions like this in the HWK section!

This is not quite right. s=d/t is only valid for constant velocity motion. You certainly do not have that here.

There are typically three simple kinematics equations that I tell most students to remember, or be able to derive. Most intro physics courses use these, and they are (under the assumption of constant acceleration a):

s=s_{0} + ut+ 1/2 at^{2}

v=u + at

v^{2} = u^{2} + 2as

where s=displacement at time t, u is the initial velocity, and v is the velocity at time t. Note that these are NOT three separate equations. They are the same thing, only expressed in different "forms", which means that they are derivable from each other.

Now there are several ways to do this problem. Since F=ma is obvious, if we can find "a" during the relevant part of this problem, we are done. The 3rd equation I listed above has all the necessary ingredients necessary to find the acceleration if you assume that the deceleration is a constant, since you know the distance travelled, s (=d), you know v (i.e. zero), you know u (equivalent to the "v" in the problem -- I know, this can be confusing).

Zz.

[Integral]

I do not see how you can get any meaningful answer without some knowledge of the "ground". The same ball falling at the same speed will make a way different dent in sand then granite. The concept of the dent implies that the material did some work stopping the falling body, this work is the force times the distance in this case the distance will be the depth of the dent, the force will be either the change in momentum or mass times acceleration, for either of those we need to know the time required to stop the falling body, this would come from knowing the properties of the material.

[ShawnD]

Originally posted by Decker
If an object of mass m is falling, and hits the ground at velocity v, and makes an indent in the ground of length d, what is the force F that he hits with?

I'm jsut asking what equations you would use.

I would use the same equation I posted for your other question.

F_{ground} = \frac{\frac{1}{2}mv^2 + mgd}{d}


g is gravity.

[Dr.Brain]

apply v(square) - u(square)=2as

u=v is the initial as it stops after penetrating ...v=0


u can calculate "a" from here

then F=ma is the resistance provided by the ground when it is penetrating in the ground...

And the force with which it hits the ground = ma

find the "a" from kinematics equations