# Dependence of deceleration of a moving body with the medium's density

by s0ft
Tags: body, deceleration, density, dependence, moving
 P: 69 Is there a relation between the deceleration experienced by a body in motion to the density of the medium? Stokes' law of viscosity is there for fluids. But how would one calculate the drag on a moving body in solids?
 P: 3,172 For low speeds density is not enough information, because the material's structure plays a role. At high speeds, inertia of the material in your way becomes the main factor, so there might be something like a velocity squared law.
 P: 69 So is there no theoretical model for it? I'm sure there is something regarding this.
P: 69

## Dependence of deceleration of a moving body with the medium's density

I don't know but would an equation like this be feasible? Just a direct manipulation of the definition of bulk modulus of a material. It doesn't include the density of the medium. nevertheless it's given below:
a = AB/dV;
where,
A = Total Surface Area of the projectile
B = Bulk Modulus of the medium
d = Density of the projectile's matter
V = Volume of the medium
and
a = Deceleration experienced by the body
 Mentor P: 11,904 There are two main effects contributing to the drag force in a fluid. One is proportional to velocity v, the other is proportional to v2. Linear drag depends on the viscosity of the fluid, and dominates at lower speeds. Quadratic drag depends on the density of the fluid and dominates at higher speeds. The speed range at which the two become comparable depends on the size and shape of the object, and the viscosity and density of the fluid. Details can be found at the wiki page: Linear drag link Quadratic drag link
 P: 69 Does that what you said also hold for rigid, solid bodies? And is the equation I posted earlier true?
 P: 69 No more response?
Mentor
P: 11,904
 Quote by s0ft Does that what you said also hold for rigid, solid bodies?
No, what I said holds for objects moving through gases and liquids.

Moving through solids? I have no idea. Are you thinking in terms of the solid medium being ripped apart as the object moves through it?

 And is the equation I posted earlier true?
Not that I know the correct answer, but I don't see how the volume of the medium could possibly come into play. But perhaps you haven't really described the situation you are thinking of accurately.
P: 69
 ...but I don't see how the volume of the medium could possibly come into play
As a result, yes that seems funny.

 Are you thinking in terms of the solid medium being ripped apart as the object moves through it?
Yes, exactly, like a bullet being shot into a block of wood.

 But perhaps you haven't really described the situation you are thinking of accurately.
I fear the same.
Could you help me find out what is wrong here and how I could better describe the situation mathematically?

If you're willing to check this, I am sure you would get the same result by simple manipulation of the definition of the bulk modulus of a substance taking into account the deformities caused by a penetrating projectile.
 PF Patron Thanks P: 2,944 For a solid, you need to use the tensorial Hooke's law relationship between the stress tensor in the solid and the strain tensor. You also need to include the kinematic relationships between displacements and strains. What you solve for is the displacements as a function of position at time. Included in the differential force balance are the forces resulting from the stresses and the dynamics associated with accelerations of infinitesimal masses (density times differential volume). Mechanical engineers solve problems like this all the time, and, if you want to know more about it, get a book on solid mechanics. Chet
 P: 69 Thank you. I'll try to get some info on solid mechanics though I know nothing about tensors.

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