Hands-On
Homework 6
Presented By:
Evan Reilly
EGN 3310
MWF 7:30 – 8:20
ev481324
Problem:
We are required to calculate the centroid and calculate the moment of inertia of that centroid.
We are then to compare and discuss the results.
Method one: Analytically
Method two: Physically
Objective:
The objective of this assignment is to solve the centroid by hand using centroid of areas as well as
solving for the moment of inertia and then physically by creating a physical model of the centroid
assigned. We are then to compare both answers.
Solving Analytically:
Solved by using Centroid of Areas:
Description for Centroid of Areas:
Solving the problem analytically we can start by deciding how we will cut up the composite figure
assigned to us. We will then create a graph listing the necessary things needing to be solved to get our
final answer. After the graph has been drawn out, we then will solve for the area, the x and y, and the
AiXi and AiYi of each shape. Once we have solved and completed this we will find the sum of area and
AiXi and AiYi which will then lead us to solving for the x̄ and ȳ. The x̄ is equal to 90.33 mm while the ȳ is
equal to 59.424 mm.
Solved using Moment of Inertia:
Description for Moment of Inertia:
Using the information solved previously we can use the equations given to us to solve for the moment of
inertia of each shape. Solving for the larger rectangle we get Ix and Iy being 88,746,666.67 and
20,650,666.67. For the smaller rectangle we will get Ix and Iy being 46,506,666.67 and 33,706,666.67.
Solving semi-circle 3 we will get Ix and Iy being 1,005,309.649. Solving for the circle we will get Ix and Iy
being -125,663.706. The summation of both Ix and Iy is 136,132,979.3 mm^4 and 55,236,979.28 mm^4.
Solving Graphically:
Description:
Solving the problem physically we had to start off by accurately measuring and cutting out the composite
figure assigned. After the figure has been cut out, we will then hang up the figure to find its center of
gravity. After that, we will draw both lines until they meet up at an exact point. From there you will
measure the x and y which are equal to the x being 94 mm and the y being 59 mm.
Percent Error:
X
Y
Analytically
90.33 mm
59.424 mm
Physically
94 mm
59 mm
%Error
4.06 %
.7 %
Looking at the percentage error we can evaluate that solving analytically and graphically were both a
success. The cause of both percent errors can be summed up to possible human error while measuring
the physical model.
Conclusion:
Comparing the answers of both the analytical and physical parts of the hands-on homework we can see
that both X’s and Y’s were very similar to each other. For X we have a 4.06% error and for Y we have a
meager .7% error. The X’s percent error is less than 5% which can most likely be summed up to a
measurement error during the physical portion of the assignment. However, it seems that both answers
are correct and both parts of the assignment were successful.