Impulse of Impact: Force vs Time

[Timothy S]

Is there any way to obtain the exact function of force with respect to time of an impact? I have heard of the equation: http://www.sciweavers.org/upload/Tex2Img_1425867132/render.png which tells you the impulse of an object with constant velocity as it impacts another object.

 

[Chestermiller]

Yes. For a perfectly elastic collision, you could do a 3D stress analysis of the collision, describing the microscopic deformation during the collision, from the time that the bodies first make contact until the time that the bodies separate. This analysis would include the detailed accelerations, which are position and time dependent, and the detailed deformations and stresses which are also position and time dependent. You would be using the differential stress equilibrium equations in conjunction with Hooke's law in 3D tensorial form, and the strain displacement equations. This would give you the contact time, and the contact force as a function of time. To do such a calculation, you would typically be using finite element stress analysis.

Chet