### Three cables are used to tether a balloon as shown. Determine the vertical force P exerted by the balloon at A knowing that the tension in cable AD is 481 N.

1 Answers

Step 1

Let us consider that

The tension along AB is *T*AB.

The tension along AC is *T*AC.

The tension along AD is *T*AD.

Express the forces in unit vectors:

Determine the torque vectors for the following:

Step 2

Apply equilibrium conditions:

*T*AB+ *T*AC+ *T*AD+*P*j=0

*T*AB is the torque along AB.

*T*AC is the torque along AC.

*T*AD is the torque along AD.

Compare the coefficients with the zero vector:

Given that *T*AD=481 N

Substitute TAD in equation 3.

Substitute TAC in equation 1.

Substitute all known values in equation 2.

Thus, the vertical force exerted by the balloon is 913.9 N.

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