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.
Let us consider that
The tension along AB is TAB.
The tension along AC is TAC.
The tension along AD is TAD.
Express the forces in unit vectors:
Determine the torque vectors for the following:
Apply equilibrium conditions:
TAB+ TAC+ TAD+Pj=0
TAB is the torque along AB.
TAC is the torque along AC.
TAD is the torque along AD.
Compare the coefficients with the zero vector:
Given that TAD=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.