Question

A 3m beam has two ends A and B. Its linear density varies. At a point...

A 3m beam has two ends A and B. Its linear density varies. At a point x meters away from end A, its linear density is given by the expression x^3 kg/m.

a. What is the total weight of this beam?

b. What is its average density?

c. Where is the center of mass relative to the ends A and B?

Math   Calculus   
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Answer #1

Integration of kx^n is kx^(n+1)/(n+1)

a> weight is integration of differential mass that is density * length , total wieight = 20.25 kg

b> average density is 6.75kg/m

c> center of mass is 2.4 m from A.

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