How Do You Find the Center of Gravity of a Non-Uniform Plank?

AI Thread Summary
To find the center of gravity of a non-uniform plank supported by three trestles, one must consider the vertical reaction forces at each support. The reactions are 100N at each end and 300N in the middle, totaling 400N. Instead of using the mass-based equation, a moment of forces equation should be applied, ensuring the sum of the moments equals zero. This approach accurately accounts for the varying density of the plank. Understanding these principles is crucial for calculating the center of gravity effectively.
recoil33
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Solved, thank you.
 
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Hi recoil33! :smile:
recoil33 said:
Three trestles support a 4.00m long plank, of non-uniform density, one at each end and one at the middle. These exert vertical reactions of 1.00 x 10^2N and 3.00 x 10^2N at the ends, and 4.00 x 10^2N at the middle. Calculate

A) The position of the centre of gravity.
…
Could i use this equation to calculate the centre of gravity?

R = (m1r1 + m2r2 + m3r3) / (m1 + m2 + m3)

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but you're not actually using masses, are you?

Technically, you should be using a moment of forces equation: the sum of the moments of the four forces on the beam (three reaction forces and the weight) has to be zero. :wink:
 

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