HELP Simple center of Gravity problem

AI Thread Summary
To solve the center of gravity problem involving a uniform board with a mass of 1.5 kg and various weights at its ends, the calculations require converting all weights to kilograms and distances to meters. The user calculated the center of mass using the formula but arrived at 0.645 m instead of the expected 0.511 m. Clarifications were requested regarding the units used in the calculations, as there appeared to be inconsistencies between grams and kilograms. Additionally, the significance of the board's mass was questioned, suggesting it should not be considered negligible. The discussion emphasizes the importance of accurate unit conversion and considering all masses in the calculations.
Rha1828
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2) A Uniform Boars has a mass of 1.5kg and length of 100cm, Note the Weight is negligible.

A) Where should it be supported so that it will balance a 10g mass places at an end, a 60kg mass on the other end, and a 40kg mass placed 30 cm to the 10g mass?

The answer should be 0.511m


a. First you need to convert all g to kg and cm to m

Therefore,

(10g)(1X10-3kg1g) = 0,010kg

(40g)(1X10-3kg/1g) = 0.040kg

(60g)(1X10-3kg/1g) = 0.060kg

(30cm)(1X10-2m/1cm) = 0.30m

(100cm)(1x10-2m/1cm) = 1.0m

(0cm)(1x10-2m/1cm)= 0 m



Using the center of mass equation you get

Xcg = W1X1 + W2X2 + W3X3 / W1 + W2 + W3
0A


Therefore,

Xcg = (0.010kg)(0m) + (0.060kg)(1.0m) + (0.040kg)(0.30) / (0.010kg) + (0.060kg) + (0.040kg)


= 0.0720kg.m / 0.110 kg

= 0.645 m


I am not sure where I went wrong and why I have a higher number then the answer. Any help would be great!

thank you!
 
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Sorry, I don't understand your units. What are they g's or kg? They looked mixed in your use of them.

Also the mass of the board is not insignificant. Is this another typo?
 
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