Center of gravity (x and y coordinates) of mechinist's square

AI Thread Summary
The discussion focuses on calculating the center of gravity (CG) for a machinist's square, which consists of a rectangular blade and handle. The user attempted to find the x and y coordinates of the CG using specific mass and distance values but found discrepancies with the book's answers. The calculations provided were x_cg = 9.3 cm and y_cg = 5.67 cm. A key suggestion was to reconsider the placement of the dimensions and their corresponding masses before recalculating. Accurate consideration of the component positions is essential for obtaining the correct CG values.
chinnie15
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Homework Statement


The machinist's square shown in the figure consists of a thin, rectangular blade connected to a rectangular handle. Determine the x and y coordinates of the center of gravity. Let the lower corner be x=0, y=0.
problem53.png


Homework Equations


x_cg = (m_1 * x_1)+(m_2 * x_2).../(m_1+m_2+...)
y_cg = ...... (same thing, but y)

The Attempt at a Solution

p

I have gotten an answer, but it is not matching up with the back of the book. Here are the numbers I used to get my answer:

x_1 = 4cm
x_2 = 12cm
y_1 = 11cm
y_2 = 3.0cm

for x_cg I have: [(4cm*40g)+(12cm*80g)] / (40g+80g)= 9.3cm
for y_cg I have: [(11cm*40g)+(3.0cm*80g)] / (40g+80g)= 5.67cm

What did I do wrong? Thank you for any help! :smile:
 
Physics news on Phys.org
You did not think about where the cm for the components were. You simply took the given dimensions and started plugging in numbers. Go back and think about these quantities carefully before you start calculating. Then you will get the right answer.
 

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