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# &quot;Oh My Elbow - Investigation Into Force Applied To Elbow Joint&quot;.

Extracts from this document...

Introduction

“OH MY ELBOW – INVESTIGATION INTO FORCE APPLIED TO ELBOW JOINT”

Aim

Diagram

Preliminary Work

Variables

Fair Test

Range of Observations

Safe Working

Sources of Error

Method One

Method Two

Chosen Method

Equipment

Prediction

Hypothesis

Simplistic View

More Complex View

Even More Complex View

Most Complex View

Results

Actual Method Used

Analysis of Results

Evaluation + Conclusions

Suitability of Procedures Used

Anomalous Results

Why My Results Were Slightly Different From My Calculated Results

Sources of Error

Accuracy

Limitations + Improvements

Reliability

Final Thoughts

Data Sources and References

## “Oh My Elbow – Investigation into Force Applied To Elbow Joint”

### Aim

The intention of this investigation is to investigate the force needed by the biceps in the arm as the forearm is held at different positions, and more precisely to test the variation of force with the angle of the forearm to the vertical.

### Preliminary Work

Before going into any theoretical observations or calculations, I conducted some preliminary work, so I could roughly identify what was going to happen in the investigation. To do this I held a dumbbell in my hand, and then changed to angle to the vertical so I could get a grasp of what I was measuring. I found there to be little change with respect to the angle, except for when the angle was zero and then this was quite obviously the easiest position to hold the dumbbell. Then I began to think about what the muscles are doing when my arm is at the different positions decided by the angle to the vertical. The muscle that is doing the “work” (experiencing the force we are trying to measure) is the biceps. Muscles can only contract (i.e. become shorter and thicker), and in doing so the muscle pulls on the bone to which it is attached (see above diagram). When the biceps relax (i.e. the arm is straight)

Middle

12.587

1.057

5.962

6.4415

20.000

154.289

24.601

20.652

2.081

11.743

7.8396

30.000

144.289

24.236

28.794

3.043

17.168

8.3918

40.000

134.289

23.763

37.048

3.912

22.070

8.6250

50.000

124.289

23.188

45.448

4.662

26.302

8.6903

60.000

114.289

22.523

54.036

5.271

29.735

8.6499

70.000

104.289

21.780

62.857

5.719

32.264

8.5368

80.000

94.289

20.975

71.959

5.993

33.813

8.3730

90.000

84.289

20.127

81.399

6.086

34.335

8.1761

100.000

74.289

19.257

88.763

5.993

33.813

7.9632

110.000

64.289

18.391

78.469

5.719

32.264

7.7531

120.000

54.289

17.557

67.659

5.271

29.735

7.5693

130.000

44.289

16.788

56.293

4.662

26.302

7.4443

140.000

34.289

16.117

44.355

3.912

22.070

7.4330

150.000

24.289

15.579

31.876

3.043

17.168

7.6543

160.000

14.289

15.205

18.945

2.081

11.743

8.5165

170.000

4.289

15.019

5.716

1.057

5.962

14.0941

180.000

-5.711

15.033

-7.607

7.46E-16

4.21E-15

-7.48E-15

NB: In Reality the arm would never get to 180° and so the force would be zero (and it almost is 10-15 is extremely small, and so this tells me that the graph will have an asymptote at ψ = 180°) In this example though, as explained before because the string is off centre of the ruler and the 5.7° has to be taken off then the lowest angle Ψ that will be possible to calculate will be (180 – 5.7) which is 174.289°,and this will result in the force no being able to measure as we will be diving by zero and so the asymptote will be at Ψ = 174.289°.

Looking at the calculated value for 174° shows me that my assumption was correct because 170° gives a value for the force as 14N, but 174 gives a value of 125N, which is increasing very rapidly to infinity:

 Angle Ψ (°) Angle θ (°) Length c (cm) Angle Σ (°) Moment of Ruler (Nm) Moment of Masses (Nm) Force (N) 174.000 0.289 15.000 0.386 0.636 3.589 125.47 174.289 0.000 15.000 0.000 0.606 3.416 ∞

As can be seen from the above graph, the relationship between the force and the angle is not linear, and it is always changing for each different angle.

So far all I have looked at is changing the angle. The other thing to change is the weight of the fixed masses, or the weight of the ruler, because from theprinciple of momentsthese two factors affect the force on the string. As I already have a basic outline of what the patter of the graph is for a ruler of mass 35.345g and fixed masses of mass 100g, I could conclude that change the mass of either of these grater than the above values would translate the graph upwards (i.e. in the positive y direction), and as a result the force on the string would be greater, whereas is the mass of the fixed masses were lowered the graph would be translated downwards (i.e. in the negative y direction) and as a result the fore4c on the string would be lowered. The below graph shows the same experiment as before but this time for 3 different masses:

Please note that only the weight of the masses have been changed and not the weight of the ruler, but if the mass of the ruler were changed the graph would look the same as above except that the proportions would be different (i.e. the lines would be closer together because the weight of the ruler is less than the weight of the masses). If time constraints permit, I will perform an experiment to prove that the above data is correct.

### Results

 EXPR One Angle to Vertical (°) Force on Spring Balance (N) 0 0 7 ± 7.1 % 7.1 ± 0.7 % 12 ± 4.2 % 8.1 ± 0.6 % 14 ± 3.6 % 8.8 ± 0.6% 16 ± 3.1 % 9.1 ± 0.6 % 25 ± 2.0 % 9.8 ± 0.5% 28.5 ± 1.8 % 9.6 ± 0.5 % 55.75 ± 0.9 % 9.2 ± 0.5 % 64 ± 0.8 % 9.7 ± 0.5 % 67.5 ± 0.7 % 8.95 ± 0.6 % 90 ± 0.6 % 8.4 ± 0.6 % 105 ± 0.5 % 7.9 ± 0.6 % 110 ± 0.5 % 7.65 ± 0.7 % 121.5 ± 0.4 % 7.5 ± 0.7 % 126 ± 0.4 % 7.2 ± 0.7 % 142 ± 0.4 % 7.5 ± 0.7 % 167 ± 0.3 % 7.2 ± 0.7 % 171 ± 0.3 % 9.2 ± 0.5 % 173.5 ± 0.3 % 10 ± 0.5 %

Conclusion

Reliability

Overall I think my results were quite reliable, and they linked back well to my initial calculations. I think there is room for improvement as there is in any case but overall I think that my investigation was conducted reliably and to as high a degree of accuracy as the involved apparatus permitted. The comparison between the actual results and calculated results was quite good, and when I take into account the thing that I missed out in my prediction – friction, I’d say that the results are very reliable, even taking into account the sources of error and other factors. I would say that with the equipment that was available the measurements taken as accurately as possible and this produced reliable results.

Final Thoughts

The uncertainty of my results due to friction, and other sources of error made my investigation less reliable and this uncertainty of the readings leaks through to my graph which is what I draw my overall conclusions from. Even taking this into account I consider my results to be reliable and accurate and I can say that my results agreed with my predictions to a certain extent and the evidence is there to back up my theory.

The relationship between the force and the angle is not linear, and is hard to explain without the use of a graph. This is because of the arm and the way it is set up and how the muscles in the arm function.

To conclude I think that given the situation and the equipment provided, I made the best use of it and even through there was room for improvement, my collected results were of a high standard and fit almost the same standard as shown when comparing to my calculated values.

### Data Sources and References

The books that I used while researching my investigation where:

• Physics 1 (Cambridge University Press: Advanced Sciences)
• Health Physics (Cambridge University Press: Advanced Sciences)

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