Center of Gravity of a Carpenter's Square

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Homework Help Overview

The problem involves determining the center of gravity of a carpenter's square shaped like an L, with specified dimensions. The coordinates for the center of gravity are to be calculated based on the areas and positions of the rectangles formed by the L-shape.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the division of the L-shape into two rectangles and the calculation of their respective areas. Questions arise regarding the accuracy of the area calculations and the positioning of the rectangles' centers relative to the origin.

Discussion Status

Some participants have provided guidance on recalculating areas and adjusting the coordinates for the center of the second rectangle. There is acknowledgment of confusion regarding the correct x-coordinate for the center of the second rectangle, indicating an ongoing exploration of the problem.

Contextual Notes

Participants are working under the constraints of homework rules, which may limit the information they can share or the methods they can use. There is an emphasis on verifying calculations and understanding the geometric setup of the problem.

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Homework Statement



A carpenter's square has the shape of an L, where d1 = 19.0 cm, d2 = 2.00 cm, d3 = 2.00 cm, d4 = 9.0 cm. Locate its center of gravity. (Take (x, y) = (0, 0) at the intersection of d1 and d4.)

Picture ---> http://www.webassign.net/pse/p12-07alt.gif

Answer = (____ , ____) cm


Homework Equations


Xcg=(A1X1+A2X2)/(A1+A2)
Ycg=(A1Y1+A2Y2)/(A1+A2)


The Attempt at a Solution



x1=1cm
x2=3.50cm
y1=9.5cm
y2=1cm

Xcg=(38.8*1+14*3.5)/(38.8+14)=1.66cm
Ycg=(38.8*9.5+14*1)/(38.8+14)=7.47cm

This seems to be the incorrect answer, and I am not sure why...Can anyone help? Thanks.
 
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It seems you have correctly divided the L-shape into two rectangles, one covering d1 and d2 and one covering d4 - d2 and d3. If that is so, then your numbers 38.8 and x2 = 3.5 are wrong.

When you get stuck like this it is often a good idea to track backwards through your work and check all results once more. :-p
 
I recalculated the area to get 38 cm^2 instead of 38.8cm^2, but I am still confused on what the x value should be...why is it not 3.5, which is half of 7, be the correct value. 7 is the length of the second rectangle for (d4-d2) and d3? What should the value of X be then?
 
The x and y coordinates should represent the center of each rectangle as measured from the origin. Since the first rectangle have the origin (0,0) on its lower left corner the center its center is easily found (your x1 and y1). The other rectangle however is offset a bit away from the origin such that the coordinates of its lower left corner is (d2, 0). The number you found (3.5 cm, 1 cm) is "only" the distance from the lower left of this rectangle to its center, so you are missing to include the offset in the coordinates.
 
thank you! I got the right answer now. :)
 

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