1.Does the bending moment at the right hand side end of a beam always have to be zero (on a bending moment diagram)? Even when there is an external couple moment applied at that point?

2.air having a pressure of 40 psig and a volumen of 8 cuft expand isothermally to a pressure of 10 psig find theexternal work performed during the expantion.

3.This is a dynamics problem I could not sove it all. Thisproblem is on pg 57 of the dynamics section.

A package is dropped from the plane which is flying with aconstant horizontal velocity of va=150ft/s. Determine thenormal and tangential comonents of acceleration and the radius ofcurvature of the path of motion (a) at the moment the package isreleased at A, where it has a horizontal velocity of va=150ft/s,and (b) just before it strikes the ground at.

The problem has a graph showing a plane at 1500ft highwhich is point A and Va=50ft/s is moving horizontaly(forward). Point B is at the ground further from theplane, obviously at an angle and the package is falling on thisdirection.

4.a volumen of 20 cu ft  of air at pressure of 50 psig is heated and expanded and to 30  cu ft  and 40psig  find the changes in the energy of air in jouls.