= 3500mm
To use the stress formula the surface area needs to be in m , to get this I will:
3500 x 1000000
= 0.0035m
As I have used three crunchie bars I will need to times the above value by 3:
0.0035 x 3
= 0.0105m
Using the above results table I have constructed a graph. As it and the results table shows the crunchie bars held up against a great force, then went the force reached 1190.0N, the crunchie bars crumbled. This meant the up ward force from the crunchie bars went and the force dropped down to1097.6N this force continued when the G-clamps were continued to be turned.
Calculations
By doing the following calculations I will determine the ultimate breaking stress of the crunchie bars for one leg.
Stress ( ) = force (f)
Area (A)
Stress ( ) = 1190.0 N
0.0105 m
Stress ( ) = 113333.3 Pa
= 11 x 10 Pa
Due to inaccuracies of the scales I am going to calculate the maximum and minimum values of the force and then calculate the breaking stress due to these differences.
Maximum force = 1200 N
Minimum force = 1180 N
Maximum Stress = 1200 N
0.0105m
= 114285.7 Pa (1dp)
= 1.14 x 10 Pa
Minimum Stress = 1180 N
0.0105m
= 112380.9 Pa (1dp)
= 1.12 x 10 Pa
I have accounted for the inaccuracies of the scales and of the turning of the G-clamps by drawing error boxes on the graph. The size of the error boxes is 20N x 36 .
Further calculations will determine whether or not the crunchie bar would be a suitable replacement for a leg bone.
Average mass of human = 60kg
Weight = mass x gravity
= 60 x 9.8
= 588 N
Area of crunchie bar = 0.0105m Area for two legs: 0.0105 x 2
= 0.021m
Stress = F
A = 600N
= 600N 0.021m
0.0105m = 28571.4 (1dp)
= 2.8 x 10 Pa
Stress = 57142.9 Pa (1dp) (1 leg)
= 5.7 x 10 Pa
By using question eight from the section Spare Part Surgery in the Salters Horners Advanced Physics book I can see that the crunchie bar would not be able to be used as a bone replacement. This is because the value given in the book for stress on the leg bone when someone standing still is 10 Pa and so is bigger than the 2.8 x 10 Pa, therefore the crunchie would shatter when under this stress.
When investigating further and by using question nine from the section Spare Part Surgery in the Salters Horners Advanced Physics book I found that there is a bigger value for stress when the person moves or in the case of question nine, jumps off a wall. The below calculations show that the crunchie bar would be unable to with stand the stress of the patient moving:
Height of wall = 1.5m
Time taken = 0.1s
Gravity = 9.8ms = 9.8Nkg
Mass = 70kg
a = v
t
= 5.42
0.1
= 54.2 ms
F= ma
= 70kg x 54.2ms
= 3.80 x 10 N
Calculations for crunchie bars:
Area of both legs = 60 x 10 m Area of crunchies = 0.0105m
Calculations for bone: Man lands on two legs = 0.0105 x 2
Stress = F = 0.021m
A
Stress = F
= 3.80 x 10 N A
60 x 10 m = 3.80 x 10 N
= 6.3 x 10 Pa 0.021m
= 18095238.1 Pa
= 1.8 x 10 Pa
These calculations show that the crunchie bar could not with stand the stress when the patient moved. This is shown in the calculations because the value of stress on the crunchie bars when put in this situation is greater than that of the leg bones. Therefore the crunchie bars would break.
Overall this experiment has shown that a crunchie bar could not be used as a suitable bone replacement as it would not be able to with stand the ultimate breaking stress of a person if they were standing still or if the person was moving.
If I had more time to continue this experiment I would make a piece of apparatus, like a protractor, that enabled me to measure the degree turns that I made when turning the G-clamps making my measurements more accurate. Using the apparatus I could also make more turns such as 45 turns as well as 90 turns.
