Calculating wall's behavior at object impact

In summary, the question is asking for the effect of an impact on a wall, specifically related to its strength and ability to remain undamaged. The known data includes the mass, velocity, energy, impact area, and wall thickness. The equations used are F=ma, Ek=1/2mv^2, P=F/A, and a=1/2S/t^2. The attempt at a solution involves gathering data on different materials and calculating the kinetic energy and force of the impact. The poster also asks for help in calculating internal stress and clarifies the concept of duration of impact.
  • #1
Aragorn49
11
0

Homework Statement



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
Ek = 98 J
S (impact area) = 60 cm2
Wall thickness = 10 cm

Homework Equations



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

The Attempt at a Solution



I have gathered a large amount 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 Fx/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?
 
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  • #2
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
 
  • #3
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?
 

1. What factors affect the behavior of a wall when it is impacted by an object?

The behavior of a wall when impacted by an object is affected by several factors, including the material and thickness of the wall, the speed and weight of the object, the angle of impact, and the shape of the object. These factors all contribute to the amount of force and energy exerted on the wall, which ultimately determines its behavior.

2. How is the force of impact calculated in relation to a wall?

The force of impact on a wall is calculated using the formula F = m x a, where F is the force, m is the mass of the object, and a is the acceleration of the object at impact. This means that the force of impact increases with the mass and speed of the object, and decreases with the wall's ability to absorb the energy of impact.

3. What is the difference between elastic and plastic deformation in a wall's behavior at impact?

Elastic deformation refers to the temporary distortion of a wall when impacted by an object, which returns to its original form once the force is removed. Plastic deformation, on the other hand, occurs when the force of impact exceeds the wall's ability to bounce back, resulting in permanent damage or deformation of the wall.

4. How is the energy of impact calculated in relation to a wall?

The energy of impact on a wall is calculated using the formula E = 1/2 x m x v^2, where E is the energy, m is the mass of the object, and v is the velocity or speed of the object at impact. This means that the energy of impact increases with the mass and speed of the object, and is directly proportional to the force exerted on the wall.

5. What are some methods used to test and analyze the behavior of a wall at impact?

There are several methods used to test and analyze the behavior of a wall at impact, including computer simulations, physical experiments using specialized equipment such as impact hammers and drop towers, and mathematical models and calculations. These methods can help determine the strength and durability of different types of walls and inform the design of structures for impact resistance.

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