Estimating Bullet Terminal Velocity from Fracture Energy of Tempered Glass

[Air]

1. The question
This question is about the design of a car seat belt. The seat belt restraints a passenger when the car is involved in an accident.

Use definitions of stress and strain to show that stress x strain has the same units as energy stored per unit volume of seat belt.

Homework Equations

Deriving question hence no specific equation required.

The Attempt at a Solution

stress x strain = force/area x extension\length = Nm/m^3 = N/m^2 = Nm^(-2)
energy stored per unit volume of seat belt = J/m^34. The problem occurring
I am not getting the same unit so it's contradicting the question. Can I have help as to where I have gone wrong. Thanks in advance.

 

[Hootenanny]

HINT: What is the definition of the Joule? (In terms of Newtons)

 

[Air]

Joules = Newton Meter

energy stored per unit volume of seat belt = J/m^3 = Nm/m^3 = N/m^2 = Nm^(-2).

Thanks.

 

[Hootenanny]

Joules = Newton Meter

energy stored per unit volume of seat belt = J/m^3 = Nm/m^3 = N/m^2 = Nm^(-2).

Thanks.

A pleasure

 

[wooz]

hi, I have a question about this relation btw Stress/Energy.
if I know the failure stress/fracture of tempered glass, (~17000 psi = 117 MPa),
how do I relate that to fracture energy of that glass? or are they completely different things?

Energy = J = Nm
Stress = N/m^2
need a volume multiplyer to get J ?

basically, I need fracture energy of tempered glass, and so far, I was only able to find
failure stress of glass.

thank you.

 

[Mapes]

Hi wooz, welcome to PF. Can you define what you mean by fracture energy here? There are several different energies associated with brittle fracture. The one often described as "fracture energy" has units J m^-2 and incorporates crack length. On the other hand, the fracture toughness of tempered glass is a material constant that doesn't depend on crack length, but does depend on loading geometry. It would help if you told us a little more about what kind of information you need.

 

[wooz]

thanks Mapes. sorry about the poor wording.
basically, I need to estimate the bullet terminal velocity from the fracture energy of tempered glass when it breaks. E = 0.5mv^2, I know the mass of bullet. I can estimate the velocity when I know the energy right?

for example, to penetrate human skin, it requires 20 J/cm^2.
I know the mass, area of bullet, then I can estimate the terminal velocity.

I guess I should say energy require to fracture/penetrate tempered glass.
not sure if failure stress of tempered glass is actually related to the fracture energy.

thanks.