Question

A rod with the density sigma(x) = 3 + sin(x) lies on the x-axis between x=0 and x = 3pi/4 find the center of mass of the rod

Answer 1

10.7 grams

Explanation:

hey there, again!

this is a similar process the mass is denisty*area HOWEVER keep in mind it's flat so the area is just x deltax while denisity is 3 + sin(x)

mass of rod = integral 0 to 3pi/4 of (3 + sin(x))*x deltax

= integral 0 to 3pi/4 of 3x + xsin(x) deltax

= 0 to 3pi/4 [3/2*x^2 + x(-cos(x)) + sin(x)]

= 10.7 grams