6.  Use the SHELL method to find the volume of the solid obtained by rotating the region bounded by the curves y = , x = 1, x = 3 and y = 0 about the y-axis. Document your work well and clearly to increase opportunities for points.                 

4.  Find the volume of the solid obtained by rotating the region bounded by the curves               y = x4 ,x = 0, x = 2 and y = 0 about the x-axis.    

For a given area and origin, a particular set of reference points P and Q lie on Mohr’s Circle where P lies to the left of the center and Q to the right and the POI about the P-Q axes is non-zero.  The P axis on the cross-section ________.

A particular set of axes are principal for a given area.  Can these axes be non-symmetric axes for the area?

The clamping brake mechanism is composed of members ABC and BDE and they are pinned to a bike frame at B.  The applied force in the cable is known and fixed at C.  Assuming that no other unknowns have been solved for previously, from the FBD of the clamping member ABC, determine the single equation of equilibrium that will allow for the normal brake force at the rim at A to be found directly without requiring the use of any other equations of equilibrium.

The tables will not separate and they weigh 114 lb total applied at G.  μ between the ground and the table is 0.28.  Determine the smallest magnitude of P required to cause the loss of static equilibrium.

The clamping brake mechanism is composed of members ABC and BDE and they are pinned to a bike frame at B.  If the applied tensile force in the cable is 42.4 lb at C, determine the normal force at the rim at A.

Determine the magnitude of the resultant force if F = 178 lb.  

Consider the following gas phase reaction: A(g) + B(g) ⇌ 2 C(g)    Kp = 36 If initially 2.0 atm of A and 2.0 atm of B are placed in a chamber and then the reaction is allowed to proceed, calculate the equilibrium partial pressure of C.

Phosphorus trichloride reacts with chlorine gas in an equilibrium process to produce phosphorus pentachloride: PCl3(g) + Cl2(g) ⇌ PCl5(g)     ∆Hrxn = −88 kJ/molrxn The following particle-level diagram represents the contents of the vessel in an equilibrium mixture at 546 K If each particle in the diagram represents a partial pressure of 1.00 atm, what is the value of Kp for the equilibrium mixture at 546 K? Enter your numeric answer to 3 decimal places