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How is the sag of a bridge affected by the load applied at it's mid-point?

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Introduction

Alex Jenkins

How is the sag of a bridge affected by the load applied at it’s mid-point?

Planning:

This experiment is to see how the sag of a ruler, in millimeters, is affected by the weight put on it, the method of attachment, the method of support, the length of the ruler, the width of the ruler and the thickness of the ruler.

Preliminary Work:

I will do a series of experiments using a 1kg weight to try and determine the best:

a) Length of ruler.

b) Width of ruler.

c) Thickness of ruler.

d) Method of support.

e) Method of attachment.

The best results are the ones, which give the greatest sag.

Firstly I did an experiment to check which constant length of ruler I should do:

Length (cm)

Sag (mm)

Wooden:

100

150

80

100

60

50

40

22

20

18

Plastic:

100

185

image00.png

From this graph I can now see that using a 100cm plastic ruler will give me the best results.

...read more.

Middle

        Finally, I need to find out the best method of attachment, either on top of the rulers or hanging underneath:

Method of Attachment

Sag (mm)

Hung under

150

On top

145

image03.png

This graph shows me that hanging the weight underneath will give me the best results.

Key factors to vary and keep constant:

Now that I have figured out which apparatus to use, I can now work out what key factors I need to vary and keep constant.

Things to vary:

Load (N). (+100g per reading)

Things to keep constant:

The length of the ruler, (100cm)

The width of the ruler, (1 ruler width)

The thickness of the ruler, (1 ruler thickness)

The method of support, (resting on two stools)

The method of attachment. (Hanging under the ruler)

Method and equipment:

Diagram:

image07.png

Method and Equipment:

image04.png

I set up the experiment as shown in the diagram. I will measure the initial height of the ruler and then take readings from the top of the ruler when it sags.

...read more.

Conclusion

lass="c6 c1">30

29

S

31

32

30.50

1.5

3.445

51

49

M

52

53

51.25

2

4.445

73

71

A

75

76

73.75

2.5

5.445

93

94.5

N

93

95

93.88

1

6.445

117

115

T

121

120

118.25

2.5

7.445

145

147

L

147

150

147.25

2.5

8.445

178

176

E

178

180

178.00

2

9.445

207

208

208

209

208.00

1

10.445

230

231

232

232

231.25

1

I then made a graph of the average sag against the load:

image05.png

Evaluating evidence:

        After checking through my results, I can see that the load is not directly proportional to the sag because the line of best fit is not a straight line through the origin. This may be because the accuracy of the ruler used to measure the sag was measured to 1 millimeter. This means that there will be a small margin of error for each reading. The uncertainty also shows that the readings have a small margin of error. The apparatus was set up in a way in which the sag could not be measured accurately as when the load was too great, the ends of the ruler had to be held in order to stop the ruler from slipping off the stools. This will have affected the results.

...read more.

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