An investigation into the bending of a cantilever beam and an attempt to determine the mathematical concepts involved.

ln1 = lnx + lnk  

Procedure

• A depression of 20cm is required, which is why you have to find a weight which will cause this successfully. The values of l and x should be measured carefully. The beam should be reduced until a reasonable amount of reading have been achieved. The values for l and x should be recorded each time new readings are found out.

Results

This is the reading for the first beam

First beam gradient

Gradient of the best fit line         = 0.49/1.25

                                = 0.392

Error in best fit line                 = 3.69- 4.25

                                   1.39- 3.00

                                = 0.348

Total error in graph _                = 0.392- 0.348

                                = 0.04

These are the results for the second beam

Gradient of the best fit line        = 1.25/3.25

                                = 0.385

Error in the best-fit line        = 3.69- 4.03  

                                   1.61-2.67

                                = 0.377

Total error in graph                = 0.007

The average value of n                = 0.385 + 0.392

                                                  2

                                        = 0.389

The average value of k                = 3.05 + 3.10

                                                2

                                        =3.075

Conclusion

• The value that we obtained for n was ≈ 0.389 ± 0.051, and the value of k was ≈3.08 ± 0.025. These two values are directly proportional to the load increase.