(Solved): Problem #1: ( 40 points) A rectangular slab of mass m=2500kg is supported by cables DA,DB, and DC, w ...
Problem #1: ( 40 points) A rectangular slab of mass
m=2500kgis supported by cables
DA,DB, and
DC, which are connected to a shorter cable at point
Dattached to a crane hook as shown in Figure 1. The center of mass at point
Gof the slab is located directly below point
Dat the center of the rectangle. Use a right-handed
x-y-zcoordinate system (not drawn on the figure) that has its origin at point
G, the positive
z-axis directed from point
Gto
D, and the positive
y-axis directed from point
Gto
C. a) Find the unit vector
u_(as)(directed from point
Dto point
A), the unit vector
u_(cs)(directed from point
Dto point
B), and the unit vector
u_(\infty c)(directed from point
Dto point
C). Express the results in terms of the unit vectors
i,j, and
k. b) Express the force
T_(as)in cable
DA, the force
T_(se)in cable
DB, and the force
T_(ax)in cable
DCin terms of the tensions
T_(in),T_(in), and
T_(in)and the unit vectors
i,j, and
k. c) Draw a free body diagram of point
D, and without solving them, find the three scalar equations of equilibrium that determine the tensions
T_(at),T_(ce), and
T_(cc).
