Investigation in to the Variables, Length and Mass, to the Sag in a Bridge

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The formula above explains why i think that in the length experiment the curve will not be directly proportional. This is because of the same amount of force is being added to each bond so as the length increase so dose the amount of bonds being stretched. This will result in a curved graph when the sag is plotted against length.

Prediction: Mass: Following the information researched in the introduction I have made the prediction that in the first experiment, were the mass added to the bridge was the only variable, the graph of mass against sag will be a straight line through the origin. The mass will increase in direct proportion to sag.

        

Length: For the experiment was length was the only variable I have predicted that the graph of length against sag will be a parabolic curve.

Method: For the first experiment… 

The method that I will use is as follows…

• Set-up two clamp stands 00cm apart.
• Onto the centre of the bridge attach a pin as a reader.
• Use another clamp to stand a ruler vertically, to measure the sag.
• Rest the bridge on the arms of the to clamps (make sure that both ends of the bridge stick out the same amount).
• Put a rubber band on the centre point and hang the weight from it.
• Take the reading of the original height add the weight then take the reading with the weight still on.
• Minus these two to get the sag.

Repeat the experiment using weights going up in 50s (do not go above 400g because the bridge might break).        

For the second experiment…

• Set up the apparatus in the same way.
• Keep the weight the same but change the length.
• Again make sure that both ends of the bridge stick out the same amount.
• Keep the reading pin central to the vertical ruler.
• Repeat the experiment remembering to increase the length by 10cm each time    (do not go above 85cm any higher than this and the arms may slip of the clamp arm)

The variables that must be kept the same are…

• The material of the bridge.
• The height of the ruler off the desk.
• The point at which the weights are hung.
• The over lap at each end of the bridge.
• Heat must be kept constant.
• Size of the bridge.
• In the first experiment: Mass
• In the second experiment: length    

Results: Length

Analysis: Length: For the length experiment I predicted that the curve would be parabolic my prediction was right but some of the points are not were I would have expected them to be the final points. The points are where the length is 95, 85, 75 the gaps between these points is far greater than I predicted. At the beginning the gradient is approximately. On further investigation I found that this was due to the bonds in the bridge reaching their elastic limit. As the weight increased the bond’s expand when the length gets to 75cm some of the bonds have started to reach there elastic limit. When bonds reach their elastic limit and the weight is taken of they do not return to their original size. Making the weight being added have more effect on the structure.  Also the beams are supporting fewer bonds as the length increases. Otherwise my results stuck well to the line of best fit. To get a straight line through the origin it is possible to cube the length this makes it easier to work out the error this means sag α length³. See sag α length³ graph. This shows up many more imperfections in my results. Such as at the point were sag is 2.10 there is a deviation from result line. This could have been an error in my reading or it could have been the point were gravity went from having more effect on the over lapping wood to the point were gravity had more effect on the centre. In this experiment the results were less accurate they had, on average approximately 0.21cm error. The last plotted point is far above the line i think this could have been caused by the bridge slipping on the supports therefore increasing the length therefore increasing the sag    

Results: Mass

Analysis: Mass

My results in this experiment are much nearer to my predicted line. There is only one point were they go completely of the line and this is the last result were the plotted point comes a lot lower then the predicted line. This is because of the bonds reaching their elastic limit when bonds reach their elastic limit the curve becomes less steep and rounds into a new trajectory. This is because when the bonds reach their elastic limit they do not return to their original shape this makes the whole structure less elastic. The line i predicted was directly proportional and it came through the origin. My graph was accurate the average error was approximately 0.15cm. I am very happy with these results          

Results: Length³

Evaluation

On the whole both my experiments went well.  The results in the first experiment were mainly good and they followed the Hookes law, which is what i predicted would happen. In the second one the results were worse than in the first but still fairly accurate under the circumstances. I think the main error came from the bridge slipping on the supports. This would have made the length larger and therefore changed the reading to a higher reading another error could have been me. My reading may not have been totally correct. To improve this experiment i would try different variables such as different materials or a different cross sectional area. It would be stupid to take this section of Hooke’s law in bridges any further because on the whole my results are accurate.