Statics & dynamics

Please see attached question and answer, i have gone wrong somewhere, can you please correct me with a worked solution. My feedback comments are wrote on this, as you can see they are not too helpfull. (See attached file for full problem description)

Shear stress problem

My shear force diagram is wrong for the attached answer. Can you correct me please? (See attached file for full problem description)

Vector integral - stokes therom

This is question #10, section 9.9 in kreyszig's book advanced engineering mathmatics 8th ed. Evaluate the line integral by stokes theorem (clock wise as seen by a person standing at the origin). Calculate this integral by stoke's theorem for the following C adn F (referred to right-handed cartesian coordinates). F=[y, 1/2 z, 3/2 y] C the circle x^2 + y^2 +z^2 = 6z, z=x+3

Statics & dynamics

Statics & dynamics --- (See attached file for full problem description)

Statics Problem Concerning Centroids & direct integration.

PLEASE LOOK AT THE ATTACHED PDF - Specifically where the Ybar sub el is calculated - this is the only part of the problem I need an explanation on. My problem is this: When finding the centroid between two curves, we have the equations for the xbar and ybar: xbar=1/Area integral of an element of x, dA ybar=1/Area integral of an element of y, dA where dA is y * dx an element of y - denoted in my book by Ybar(sub)el=1/2 (Y) with these equations, I am trying to solve the following problem: We have two curves plotted in cartisian co-ordinates: it doesn't really matter what they are - but I do have an exact example. if we find the area, or mathmatically Area=integral dA - then we... click for more