A roof is supported by two cables as shown below. For each cable, determine the

Question

A roof is supported by two cables as shown below. For each cable, determine the force vector in x,y,z components.

Next, find resultant force vector as well as the magnitude of that vector. Utilize the dot product when calculating the force magnitude.

A roof is supported by two cables as shown below. For each cable, determine the force vector in x,y,z components. Next, find resultant force vector as well as the magnitude of that vector. Utilize the dot product when calculating the force magnitude.

Explanation / Answer

A(0,0,4) B(4,0,0) C(4,2,0)

Fab=Fab*Uab=100*[(4i-4k)/sqrt((4^2)+(-4^2))]=70.7i-70.7k

Fac=Fac*Uac=120*[(4i+2j-4k)/sqrt((4^2)+(2^2)+(-4^2))]=80i+40j-80k

FR=Fab+Fac=150.7i+40j-150.7k

FR magnitude= sqrt((150.7)^2+(40)^2+(-150.7)^2)=216.8 N

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