richnfg Posted December 2, 2004 Posted December 2, 2004 I am trying to calculate whether someone would break their leg when jumping off a 4m wall. Check this out and please comment on if it is correct. Thanks. Will I Break My Leg If I Jump Off This Wall? For the physics presentation I will be including a calculation to show whether someone will break their leg if they jump off a wall. I already know these certain figures: the boy weighs 65 kg and the wall is 4m high. This calculation will only be an estimate but should give a rough idea of how to go about working this out and we will have to go through a few equations to get to the tensile stress. First we should calculate the speed that the person is travelling at and we can achieve this by: v² = u²+2as v² = 0 + 2 x 10 x 4 v² = 80 v = 8.9m/s(2 s.f.) We can then take the speed to work out the acceleration from the full speed to hitting the ground (the acceleration is useful for working out force in the next equation). The change in speed is 8.9m/s because the final speed will be zero and the time it takes to change from 8.9m/s to zero when you hit the floor would be estimated at around 0.01 of a second. a = (v-u)/t a = 8.9/0.01 a = 890ms-² We can then take this acceleration and times it by the mass of the person to calculate the force at which is exerted on the person (the mass of the boy is 65kg remember): f = ma f = 65 x 890 f = 57850 N Finally, knowing the cross sectional area of the bone (roughly .28 m² as I calculated earlier) we can work out the tensile stress that is put onto the bone: s = f/a s = 57850/.28 s = 206607 Pa s = 206.607 MPa We said that the bone would require 200 MPa to break and in this case it would. THanks!"
Ophiolite Posted December 2, 2004 Posted December 2, 2004 My reservations would not be with your equations, but with your assumptions, in particular the time to deccelerate. Were you given the .01 as part of the problem when it was set? This appears to disregard the compressibility of the flesh in the heels. In that case if the decelaration takes 0.02 seconds, still a short time, the bone does not break. The difficulty is that you are arrivng at an answer that is right on the bounary between break and not break. Perhaps I am making this needlessly complicated. Hopefully this will prompt someone who actually knows what they are tallking about to throw in their views.
richnfg Posted December 2, 2004 Author Posted December 2, 2004 It was just a very rough number that my teacher told me to use (so i thought I should use that one!)...apart from that, is the way I got to an answer acceptable?
5614 Posted December 2, 2004 Posted December 2, 2004 well the maths and the equation seems fine.... but again, take into account that they're going to bend their knees when they land and flesh and all... also that the bone could bend a tiny bit before snapping and that it could just fracture a bit... and all the other tiny things like resistance and landing material (difference between spikes, concrete and a trampolene (how do you spell that word?))... but you know what i mean. im not sure, its your physics assignement... looks ok, but take into note above post (and this one too).... and possibly and more to come too!
Cap'n Refsmmat Posted December 2, 2004 Posted December 2, 2004 What do all of the variables stand for? I need to know how to do that for something that I am doing.
richnfg Posted December 2, 2004 Author Posted December 2, 2004 Phew. I'm glad all my physics was correct and such. ok, I will keep to this equation then say afterwards that other materials can actually have an effect and also the fact that if you bend your knees etc. It is really only a rough calculation to show that you can actually do these things. I got the limit 200MPa from my AS Advancing Level Physics book. Im guessing that is right! Variables: 1st equation: v = final speed and u = starting speed a = acceleration due to gravity s = distance 2nd: a = acceleration t = time 3rd: f = force m = mass 4th: s = stress a = cross-sectional area
5614 Posted December 2, 2004 Posted December 2, 2004 still i think that factors as mentioned here would bring around a strong possibility that you wouldnt break your bone. also remember footware. as has been said, its very borderline, additional factors not included in the equations (i think) will bring it just below the threshold... so i dont think you would break your leg. other factors: footware flesh bend knees landing ground the bone can bend slightly before breaking resistive forces (or wind etc) altitude????? (possibly as different altitudes, different forces of gravity, whilst almost insignificant as this is so borderline it could make a difference)
Cap'n Refsmmat Posted December 2, 2004 Posted December 2, 2004 Thanks for the variables. Now I can do what I need to do...
5614 Posted December 2, 2004 Posted December 2, 2004 also, hmmm, i hate biology, whats the fluidy stuff in the knee caps.... that'd soften the landing a bit too. also bone compression (doubt that makes a difference, but i'll say it just incase)!
Cap'n Refsmmat Posted December 2, 2004 Posted December 2, 2004 Note: When I tried the equations, I came out with a slightly higher number. Odd. edit: No, it's because my calculator includes all of the decimals and such, which changes the numbers a bit. Works out to 58,137.767 N on the calculator.
richnfg Posted December 2, 2004 Author Posted December 2, 2004 thats cool hey if you need my presentation I will be happy to send it to you it might be of some help!
Cap'n Refsmmat Posted December 2, 2004 Posted December 2, 2004 No, I'm fine. I've just been doing some math here... I'm glad I spotted your equations! However, I'd like to know: how could I fit something like spring rate (kg of force absorbed per meter, or a similar scale) in that equation?
swansont Posted December 2, 2004 Posted December 2, 2004 still i think that factors as mentioned here would bring around a strong possibility that you wouldnt break your bone. also remember footware. as has been said' date=' its very borderline, additional factors not included in the equations (i think) will bring it just below the threshold... so i dont think you would break your leg. other factors: footware flesh [b']bend knees[/b] landing ground the bone can bend slightly before breaking resistive forces (or wind etc) altitude????? (possibly as different altitudes, different forces of gravity, whilst almost insignificant as this is so borderline it could make a difference) I would estimate that bending the knees alone adds at least an order of magnitude to the impulse time. Also not landing flat-footed.
richnfg Posted December 3, 2004 Author Posted December 3, 2004 No' date=' I'm fine.I've just been doing some math here... I'm glad I spotted your equations! However, I'd like to know: how could I fit something like spring rate (kg of force absorbed per meter, or a similar scale) in that equation?[/quote'] ok, no idea
swansont Posted December 4, 2004 Posted December 4, 2004 No' date=' I'm fine.I've just been doing some math here... I'm glad I spotted your equations! However, I'd like to know: how could I fit something like spring rate (kg of force absorbed per meter, or a similar scale) in that equation?[/quote'] In which equation?
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