A non-uniform beam extends from x = 0 m to x = 5.4 m.  The linear mass density of the beam, as a function of x, is given by  λ(x) = 415 x4  (kg/m). Calculate the x coordinate of the center of mass of the beam, in m. (Please answer to the fourth decimal place - i.e 14.3225)

12.3

Problem 5: A painter (of mass 71 kg) needs to reach out from a scaffolding to paint the side of a building, so he lays a plank across two bars of the scaffolding, and puts a heavy bucket of mass 27 kg directly over one of the bars (see figure). You can assume the plank is massless, and is long enough to reach to the other building. L d If the bars are separated by a distance 1.5 m, how far, d, from the bar on the the right can the painter walk before the plank starts to fall? d= m 9 HOME sin() cos( cotan() asin() tan() П ( ) 7 8 acos() E ↑AAL 4 5 7* 1 2 3 6 atan() acotan() sinh()

Gold, which has a density of 19.32 g/cm3, is the most ductile metal and can be pressed into a thin leaf or drawn out into a long fiber. (b) If, instead, the gold is drawn out into a cylindrical fiber of radius 2.100 μm, what is the length of the fiber?