Assuming the vectors in Fig. 9.49 are in equilibrium, find T₁ and T₂. See Example 6.

Data from Example 6

An 865-lb crate of building supplies is hanging from two cables as shown in Fig. 9.38. Find the tensions T₁ and T₂ assuming that the forces are in equilibrium.

The table below shows the x- and y-components of the three vectors:

Setting the sums of the x- and y-components equal to zero gives us the following system of equations:

This system can be solved by the substitution method as described in Section 5.3. We solve the first equation for T₁ and then substitute the result into the second equation to solve for T₂.

Lastly, the solution for T₂ can be used to find T₁:

T₁ = 0.7555(617.4) = 466 lb

Therefore, the tensions in the two cables are T₁ = 466Ib and T₂ = 617 lb.

Fig. 9.49 T T 60.4 51.0 975 lb