When measuring the diameter of a cylinder the following measurements are obtained. 16.4 millimeters 16.8 millimeters 16

Question

When measuring the diameter of a cylinder the following measurements are obtained.
16.4 millimeters
16.8 millimeters
16.9 millimeters
16.6 millimeters
16.8 millimeters
Find the percent uncertainty in the measurements.
(Keep 2 decimal places in the percentage.)

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Thanh Hà 2 months 2021-07-21T12:31:04+00:00 1 Answers 2 views 0

Answers ( )

    0
    2021-07-21T12:32:41+00:00

    Answer:

    a. 1.80 %

    b. 0.60 %

    c. 1.20 %

    d. 0.60 %

    e. 0.60 %

    Explanation:

    In order to calculate percent uncertainties in each case, we forst need to calculate the average value:

    Average Diameter = (16.4 mm + 16.8 mm + 16.9 mm + 16.6 mm +16.8 mm)/5

    Average Diameter = 16.7 mm

    Now, the formula for percent uncertainty is:

    % Uncertainty = (Uncertainty/Average) * 100 %

    where,

    Uncertainty = |Value – Average|

    For Each Case:

    a. 16.4 mm:

    Uncertainty = |16.4 mm – 16.7 mm| = 0.3 mm

    Therefore,

    % Uncertainty = (0.3 mm/16.7 mm) * 100%

    % Uncertainty = 1.80 %

    b. 16.8 mm:

    Uncertainty = |16.8 mm – 16.7 mm| = 0.1 mm

    Therefore,

    % Uncertainty = (0.1 mm/16.7 mm) * 100%

    % Uncertainty = 0.60 %

    c. 16.4 mm:

    Uncertainty = |16.9 mm – 16.7 mm| = 0.2 mm

    Therefore,

    % Uncertainty = (0.2 mm/16.7 mm) * 100%

    % Uncertainty = 1.20 %

    d. 16.6 mm:

    Uncertainty = |16.6 mm – 16.7 mm| = 0.1 mm

    Therefore,

    % Uncertainty = (0.1 mm/16.7 mm) * 100%

    % Uncertainty = 0.60 %

    e. 16.8 mm:

    Uncertainty = |16.8 mm – 16.7 mm| = 0.3 mm

    Therefore,

    % Uncertainty = (0.1 mm/16.7 mm) * 100%

    % Uncertainty = 0.60 %

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