In an experiment, different masses are hung from the end of a steel beam that is

Question

In an experiment, different masses are hung from the end of a steel beam that is fixed at the other end. The relationship between the force, F, also called the load on the end of the beam and the amount the beam bends (deflects), d, is given by the following relationship:

Where Y is Young’s Modulus, w is the width of the beam, t is the thickness of the beam and L is the length of the beam. In this particular experiment, w=3±1 cm, t=1.04±0.02 cm and L=55.3±0.5 cm. A plot of the deflection as a function of load is shown.

a) Using the data given determine the Young’s Modulus for this beam.

b)Using the data given determine the uncertainty in Young’s Modulus by combining the uncertainties in all the measure quantities, including the slope of the best fit line.

Explanation / Answer

From graph, equation becomes, d = 0.0001722*F+ 1.44*10-5

At d=0.0002 m, F = 1.0778 Newton

Using the given equation

We get youngs modulus, Y = 1.0802*1011 pascal

(b) to find error we first find error in force

Err F= F*((err m/m)+(err b/b))

And then differentiating and adding all the errors we get final error.

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