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

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    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

    © BrainMass Inc. brainmass.com December 24, 2021, 9:12 pm ad1c9bdddf
    https://brainmass.com/physics/gravity/youngs-modulus-slope-graph-error-354458

    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*〖10〗^(-4) )*0.877/(9.07*〖10〗^(-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.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 9:12 pm ad1c9bdddf>
    https://brainmass.com/physics/gravity/youngs-modulus-slope-graph-error-354458

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