Force required to break tempered glass with apple?

[sheaehs]

Hello! I'm new to the forums, have SOME physics under my belt as a civil engineering major. I have a hypothetical question to solve that has been driving me bonkers. At first, it sounded simple enough. Now, I must assume MANY things and don't know which set of equations to use to solve my problem!

SO, an apple (of unknown hardness) of assumed mass=0.125 kg is thrown by a child at a window at a speed of approx.= 15 m/s from a distance of approx: 20 meters at a height of approx. = 1.5 m. The apple strikes the residential window (assume: tempered, not fully, glass) and embeds itself (i.e.: breaks the glass). What force was required to break this window? Or, in other words I guess, what is the maximum force the window can exert on the apple before it critically deforms?

At first, I thought: PROJECTILE MOTION! But, that really just deals with pathways, not forces, rights? So, what about Newtonian balance of forces, F=MA? Or, should I skip all of this and use KE=1/2mv^2, PE=mgh and W=FD? But, how?? ARGH! Help a gal out, would ya? THANKS!

 

[Simon Bridge]

Welcome to PF;

What you want to know is the change in momentum of the apple ... in your example, the apple is embedded in the window so all the KE of the apple gets to the glass.

So think: conservation of energy and momentum.
You also need material properties of window glass - the glass will be able to flex somewhat in it's frame.
Think - youngs modulus, and tensile strength ... breaking strain, that sort of thing.

The type and thickness of the glass will count, as will the distance from the frame and how much give is in the frame.

That help?

 

[sheaehs]

Thank you Simon! I was going through my old Halliday and Resnik text and came across the chapter on Impulse and thought this may have been a good start! I guess the concept of momentum has always been difficult for me to wrap my mind around. I get that force is mass times acceleration, and the second law is expressed in terms of momentum, but what is P? i.e. momentum? is it just a vector quantity?

I figured I'd have to dig into some materials concepts. I have been wading through charts and data and am not sure which variables to pay attention too. There is modulus of elasticity, tensile strength, etc...I imagine it all comes into play. I'll put together some equations later today and see what I can come up with. Ok if I post what I do for feedback?

FYI: this is not a homework problem, I'm trying to help out a friend! But its driving me nuts now. Plus, GREAT concept review!

 

[Simon Bridge]

Yep - impulse and change in momentum.
H&R will fill you in on the concepts for momentum, yep: it's a vector ... in a collision where the objects bounce off, the force vs time graph will look like an inverted quadratic with the time between the roots being the period of contact. The area under this graph is the change in momentum or "impulse".

To guide you in what you need to pay attention to, you need to think about what you want to use the results for.
Real life collisions can get very complicated, which is why we usually just do a bunch of experiments and report the findings.

It's OK to post what you do for feedback - the feedback is why people like me do this stuff ;)

 

[amazingawesome]

May I introduce a new question re Tempered glass breaking ...?
I recently cracked (5 cms) a tempered glassbench top about which is 8mm thick , and 1 metre width
I placed a very hot pan on the glasstop and then didn't realize until I heard a strange sound !

What I am curious about is if the crack continued ,would it follow in the same pattern/direction ?

Could the crack continue because the glass is weakened of it's own accord

To me this defies all logic !

 

[Simon Bridge]

Welcome to PF;
thermal cracking is actually a different subject to the kinetic impact discussed in this thread.
the material expands when it is heated - expanding the most at the hottest places. This stresses the material - so too big-a thermal gradient will make it crack or even shatter.

You are more likely to get such strong gradients in rapid cooling though.

The first crack would be more likely to appear along lines of imperfection in the glass - once there, yes, further stresses can be expected to extend the existing crack rather than make a new crack. The crack would extend in the same sort of way i.e. if it kinda curves off to the left it will probably keep doing that. Only "probably" - these things are very sensitive to small changes in the situation. I wouldn't expect the crack to continue of its own accord unless there is some overall stress on the material.

 

[amazingawesome]

Thank you for your response to my question . logical in relation to glass cracking .It would follow it's original pathway if the crack were to continue ... unless forced by stress to take another direction,,with small implosions at the pressure points/ variations in the angle of the depth of the crack .
Thank you ...I find this fascinating

 

[Simon Bridge]

A random additional stress would tend to continue the crack. Once a crack has formed in one way it gets harder to make it go another way. You can try it out - pit a small rip in a bit of card or paper - however you further stress the paper will tend to continue the tear that is already there. To get a new one, or continue the old one in a different way, you have to pinch and rip again. Still, you do get more complicated cracks in glass as there are multiple weak-lines.