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An investigation into the relationship between the force applied on a cantilever and its deflection.

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Introduction

An investigation into the relationship between the force applied on a cantilever and its deflection

I aim to investigate the relationship between the force applied on a cantilever and its deflection.

Research – A cantilever is a projecting structure such as a beam, which is supported at one end and carries a load at the other end or along its length.

To measure the deflection, I will place a ruler, vertically at the end of the cantilever with the force applied. I will record the amount of deflection with no force (only gravity) and calculate the difference.

Before I did the experiment, I carried out some preliminary work so that I could find out the best length of the cantilever, material of the cantilever, and maximum and minimum force applied to the cantilever.

I learnt from my preliminary experiment what my ranges should be and how many results I would need to prove my prediction. Also I learned how to set up my apparatus and how big or small my overhang should be.

I chose to use a meter ruler for my cantilever, as it is a widely available object to use and it is already marked in measurements.

I will use a wooden meter ruler, as it can take more force that a plastic one, I know this from my preliminary work.

I will use a maximum load of 7 Newtons (700 grams)

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Middle

0.00

168

0

1.00

203

035.00

2.00

233

065.00

3.00

267

099.00

4.00

282

114.00

5.00

316

148.00

6.00

331

163.00

7.00

365

197.00

Set 2

Force applied (N)

Deflection (mm)

Difference (mm)

0.00

172

0

1.00

198

026.00

2.00

224

052.00

3.00

251

079.00

4.00

276

104.00

5.00

302

130.00

6.00

326

154.00

7.00

350

178.00

Set 3

Force applied (N)

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Conclusion

Evaluation –

My procedure was good enough to make my measurements reliable as I got another person to read them as well as me.

I can tell that my results are reliable as my line of best fit is a straight one which passes through the point 0, 0 and all of the points lie close to the line of best fit. I can tell that they are also reliable as they graph agrees with Hook’s law.

I did not have any anomalous results in my investigation as all of my results fit in with my pattern.

From the above, I believe that my results were accurate enough, although if I was to do the investigation again I would take more results at more regular intervals. E.g. Every 0.5 N so that my results were even more accurate because I would be taking more results.

My graph shows me what I needed to see, but if I had more results, I would be able to see a better line. This would allow me to get a better conclusion of my results. From my graph I can see that when the force is doubled so is the deflection.

Overall, I believe that my investigation was conclusive enough for what I wanted to know but could have been more accurate if I wanted it to be. My results show that the deflection is directly related to the Force, and that when the force is doubled the deflection is doubled this agrees with Hook’s law.

Jack Cummins 10LB

...read more.

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