question p 7-9 P7-9 A 100 lb weight is suspended by two cables as shown in Fig.
ID: 1826699 • Letter: Q
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question p 7-9
P7-9 A 100 lb weight is suspended by two cables as shown in Fig. P7.9. The tensions T1 and T2 satisfy the following system of equations: 0.6T1 + 0.8T2 = 100 0.8T1 - 0.6 T2 = 0. Write the system of equations in the matrix form Ax = b, where in other words, find matrices A and b. Find T1 and T2 using the matrix the algebra method. perform all matrix computation by hand and show all steps. Find T1 and T2 using Cramer's rule. Figure P7.9: A 100lb weight suspended by two cables for problem P7-9,Explanation / Answer
a) A=
0.6 0.8
0.8 -0.6
b=
100
0
b) Write the matrix as
0.6 0.8 | 100
0.8 -0.6 | 0
0.6*6+0.8*8 0.8*6+(-0.6)*8 | 100*6+0*8
0.8*6-0.6*8 (-0.6)*6-0.8*8 | 0*6-100*8
10 0 | 600
0 -10 | -800
1 0 | 60
0 1 | 80
==> T1=60, T2=80.
c)For the coefficient matrix A, we have detA=0.6*(-0.6)-0.8*0.8=-1
We have D1
100 0.8
0 -0.6
==> det D1=-60 ==> T1=detD1/detA=60.
We ahve D2
0.6 100
0.8 0
===> det D2 = -80 ==> T2=detD2/detA=80.
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