Center of Mass. Confused on part b.

AI Thread Summary
To find the center of mass of the inverted U-shaped system, the x-coordinate was calculated as 24.5 cm, but the y-coordinate calculation was causing confusion. The vertical rods' centers of mass should be considered at 24.5 cm (49/2 cm) above the ground, rather than at 0 cm. Adjusting the calculation to account for the correct vertical positions of the rods led to a new y-coordinate of 37.7541 cm, which was still deemed incorrect. Further clarification on the correct method and final answer for the y-coordinate is sought.
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In Fig. 9-39, three uniform thin rods, each of length L = 49 cm, form an inverted U. The vertical rods each have a mass of 14 g; the horizontal rod has a mass of 33 g. What are (a) the x coordinate and (b) the y coordinate of the system's center of mass? (Give your answer in cm)

http://edugen.wiley.com/edugen/courses/crs1650/art/qb/qu/c09/fig09_37.gif
Fig. 9-39
Problem 4.

a) 24.5cm

b) ? cm

(m1*x1+m2*x2+m3*x3)/(m1+m2+m3)

(33g*49cm+14g*0cm+14g*0cm)/(33g+14g+14g)

(33*49)/(33+14+14)=1617gcm/61g=26.5082cm <--incorrect

any help towards the correct answer will be extremely appreciated. thanks!
 
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Why are you considering all of the mass of the vertical rods to be concentrated on the ground (0 cm) when, in fact, their individual centres of mass are actually located in their centres (i.e. 49/2 cm above the ground)?
 
because i never considered that when i should've, but i just did the adjustment for (24.5*14*2+33*49)/61 and got 37.7541 and it is still wrong unfortunately.
 
What is the correct answer, and how do you know that it is correct?
 

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