Calculating wall's behavior at object impact

Aragorn49

1. The problem statement, all variables and given/known data

Hello and thank you for reading my question. I am attempting to calculate what effect on a wall has an impact (a car impact or as in my theoretical calculations a punch) of an object into it. With effect I mean how strong impacts can a wall a, survive and b, stay undamaged. Since car crashes deal with too great numbers I have chosen as an example for calculations a punch Known data:

a = 9 m/s²
v = 7 m/s
m = 4 kg
E_k = 98 J
S (impact area) = 60 cm²
Wall thickness = 10 cm

2. Relevant equations

F = ma
E_k = 1/2 mv²
P = F/A
a = 1/2 S/t²

3. The attempt at a solution

I have gathered a large ammount of data on concrete, brick, steel and mortar strength and fatigue limit. From what I know F = ma is only valid for stationary objects (like the force of me standing on a floor) but not for impacts. I calculated the kinetic energy of the punch but I don't know how to calculate the Force of the impact from it. Also, are the Force and the following pressure and stress from the force the only factors relevant in such an impact into a wall?

Another problem is that while I know how to calculate surface pressure of the impact, I don't know how to calculate internal stress. The equations are F_x/S, but I don't know how to acquire either of these variables. I also don't know what kind of stress a punch (or car crash) is, is it shear stress or flexural stress?

technician

To calculate Force in an impact you need to use:
Force = rate of change in MOMENTUM
You need to have some idea of the time duration of the impact and also whether the impact is elastic or ineleastic.
As an example, your 4kg moving at 7m/s has momentum of 28Ns.
If the collision lasts for 0.1 secs and the collision is inelastic then the rate of change in momentum is 28/0.1 = 280N.... this is the force due to the collision.
Hope this helps

Aragorn49

Thank you very much. It helped me a lot. Now that I know the force I only need to learn how to calculate internal stress in the wall.

Btw, one small question, by duration of the impact you mean how long the hand or the car stays touching the wall, right?