Impact force

[ahmedelshfie]

This following applet is Impact force
Created by prof Hwang Modified by Ahmed
Original project Impact force

Two objects with m1 and m2 respectively, released from the same height h to the ground.
Under the condition: mass m2=2*m1

The time for object to reach the ground are T1 and T2 respectively,
Normally, the air reststance can be ignored for heavy objects, and we know that
T2=T1=, where g is the gravity.

If the impact forces are F1 and F2 respectively.
 What is the relation between F1 and F2?
A. F2>2*F1
B. F2=2*F1
C. F2<2*F1

The impact force F=△P/△T, where △P is the momentum change during the impact and △T is the impact time.
Both object drop from the same height, so the velocity when impact start is ,
So △P2=2*△P1.
We need to know the relation between △T2, △T1 in order to compare F2/F1.
If △T2= △T1, then F2=2*F1.
However, is it true that △T2= △T1 
If △T2> △T1 , how to find out relation between F1 and F2?
You can check out the answer with the following simulation:

The impact time △T and Faverege will be shown. F(t) is available, too!

The impact force is modeled with.

Embed a running copy of this simulation
<applet code='users.br.ahmed.fallingobjectforce_pkg.fallingobjectforceApplet.class' archive='http://www.phy.ntnu.edu.tw/ntnujava/ejsuser/37048/ejs_fallingobjectforce.jar' name='fallingobjectforce6387' id='fallingobjectforce6387' width='672' height='449' mayscript=true><param name='draggable' value='true'></applet>
Embed a running copy link(show simulation in a popuped window)
<a href='http://www.phy.ntnu.edu.tw/ntnujava/msg.php?smfejs=6387' target='smfejs'>Run simulation</a>

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Press the Alt key and the left mouse button to drag the applet off the browser and onto the desktop. This work is licensed under a Creative Commons Attribution 2.5 Taiwan License

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[ahmedelshfie]

In mechanics, an impact is a high force or shock applied over a short time period when two or more bodies collide. Such a force or acceleration usually has a greater effect than a lower force applied over a proportionally longer time period of time. The effect depends critically on the relative velocity of the bodies to one another.

At normal speeds, during a perfectly inelastic collision, an object struck by a projectile will deform, and this deformation will absorb most, or even all, of the force of the collision. Viewed from the conservation of energy perspective, the kinetic energy of the projectile is changed into heat and sound energy, as a result of the deformations and vibrations induced in the struck object. However, these deformations and vibrations can not occur instantaneously. A high-velocity collision (an impact) does not provide sufficient time for these deformations and vibrations to occur. Thus, the struck material behaves as if it were more brittle than it is, and the majority of the applied force goes into fracturing the material. Or, another way to look at it is that materials actually are more brittle on short time scales than on long time scales: this is related to time-temperature superposition.

Different materials can behave in quite different ways in impact when compared with static loading conditions. Ductile materials like steel tend to become more brittle at high loading rates, and spalling may occur on the reverse side to the impact if penetration doesn't occur. The way in which the kinetic energy is distributed through the section is also important in determining its response. Projectiles apply a Hertzian contact stress at the point of impact to a solid body, with compression stresses under the point, but with bending loads a short distance away. Since most materials are weaker in tension than compression, this is the zone where cracks tend to form and grow.

Data and images from http://en.wikipedia.org/wiki/Impact_(mechanics)