# Young's Modulus from the slope of the graph and find the error

Calculations: Young's Modulus

The Cross section of the wire is 9.07 x 10 -8 m2

length = 0.877 m

Net Load (g) Elongation

100 1.11.x 10-4m

200 2.15.x 10-4m

300 3.33.x 10-4m

400 4.37.x 10-4m

500 5.34.x 10-4m

600 6.23.x 10-4m

700 7.11.x 10-4m

800 8.00.x 10-4m

900 8.89.x 10-4m

Now plot the curve with load in N on abscissa and resulting elongations in meters as ordinates.

Compute Young's modulus from the slope of the graph and find the error compared to known value of 9.2 X 10^10

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

Calculations: Young's Modulus

The Cross section of the wire is 9.07 x 10 -8 m2

length = 0.877 m

Net Load (g) Elongation

100 1.11.x 10-4m

200 2.15.x 10-4m

300 3.33.x 10-4m

400 4.37.x 10-4m

500 5.34.x 10-4m

600 6.23.x 10-4m

700 7.11.x 10-4m

800 8.00.x 10-4m

900 8.89.x 10-4m

Now Plot of curve with load in N on abscissa and resulting elongations in meters as ordinates.

Compute young's modulus from the slope of the graph

find the error compared to known value of 9.2 X 10^10

________________________________________

SOLUTION:

First we need to convert the Load units from grams (g) to Newton (N);

The formula to use is F=m*g

where F is the load in N, m is mass in kg, and g is the value of acceleration due to gravity which we may assume to be 10m/s^2.

Now, to convert our units of load from g to kg, we need to divide by 1000 (this is because 1000g = 1kg), and then multiply the result by 10m/s^2 to get the load in N. (Effectively, we need to just divide the load in g by 100 to get the load in N. see below;

Net Load (N) Elongation

1 1.11.x 10-4m

2 2.15.x 10-4m

3 3.33.x 10-4m

4 4.37.x 10-4m

5 5.34.x 10-4m

6 6.23.x 10-4m

7 7.11.x 10-4m

8 8.00.x 10-4m

9 8.89.x 10-4m

Now, to plot the curve with load in N on abscissa (abscissa means x-axis or horizontal axis) and resulting elongations in meters as ordinates (ordinates means y-axis or vertical axis), we'll get

The slope of this graph is 0.97*10-4 m/N

(Note that you should get about the same value if you plot the graph manually, not necessarily this exact value).

The Young's Modulus is defined as;

Young's Modulus = tensile stress/tensile strain

where tensile stress=F/A, and tensile strain=e/l

Therefore, Young's Modulus = F/A*l/e.

F is the load in N, A is the cross section of the wire in m^2 (that is 9.07 x 10 -8 m^2 as given), e is the elongation in m, and l is the original length of the wire in m (that is 0.877m as given).

Now, we know that the slope of the graph is e/F (this is because we plotted the elongation e on the y-axis, and the load F on the x-axis).

And we can re-write the Young's Modulus as

Young's Modulus = F/e*l/A

so that we can replace F/e with the reciprocal of slope (1/slope) to get;

Young's Modulus = 1/slope*l/A

And so our final answer is;

Young's Modulus = 1/(0.97*ã€–10ã€—^(-4) )*0.877/(9.07*ã€–10ã€—^(-8) )

=9.97*1010 Nm-2

Finally, the error compared to the value of 9.2 X 10^10 is;

9.97*1010 - 9.2*1010 Nm-2

=0.77*1010 Nm-2

hope you find this helpful, :),

danoski.

https://brainmass.com/physics/gravity/youngs-modulus-slope-graph-error-354458