The aim of this experiment is to test whether or not a Crunchie bar could be used as a bone replacement. If this were possible the crunchie would have to be strong enough to support the patients life style. The Crunchie bar will be used to replace a leg bone. After the experiment I will calculate the ultimate breaking stress of the Crunchie and then compare this to the ultimate breaking stress of a leg bone. I will calculate the stress by using the formula:

The apparatus is going to be set up as follows:

I will tighten both of the G-clamps by 90 at the same time, then I will read off the force on the dial of the scales.

I will read the dial from directly above otherwise parallax may occur. I am using three crunchies at the same time, as this will be more reliable. To make the measurements accurate I will calibrate the scales after the crunchies and wooden boards have been put on to it.

I will ensure that the G-clamps are placed in the middle of the blocks so that the pressure off these blocks is spread over all of the bars, and not just on one side. The safety aspect of this experiment is that the G-clamps may fall off and cause an accident.

Results

Degree turns ( )

Force in Newton’s (N)

90

58.8

180

147.0

270

264.6

360

431.2

450

617.4

540

833.0

630

1038.8

720

1185.8

810

1176.0

900

1127.0

990

1097.6

1080

1097.6

1170

1097.6

1260

1097.6

1350

1097.6

1440

1097.6

I have, as accurately as possible, measured the surface area of one crunchie, the measurements were: 140mm x 25mm

= 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.