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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.

Question-Answer › Category: Engineering Mechanics › 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.
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Beer Johnston asked 1 year ago

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.

5.60 m B D 4.20 m 3.30 m 4.20 m 2.40 m

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1 Answers
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Sazid Ahmad answered 1 year ago

Step 1

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:
Mechanical Engineering homework question answer, step 1, image 1
Determine the torque vectors for the following:
Mechanical Engineering homework question answer, step 1, image 2

Step 2

Apply equilibrium conditions:
Mechanical Engineering homework question answer, step 2, image 1
TAB+ TAC+ TAD+Pj=0
TAB is the torque along AB.
TAC is the torque along AC.
TAD is the torque along AD.
Mechanical Engineering homework question answer, step 2, image 2
Compare the coefficients with the zero vector:
Mechanical Engineering homework question answer, step 2, image 3
Given that TAD=481 N
Substitute TAD in equation 3.
Mechanical Engineering homework question answer, step 2, image 4
Substitute TAC in equation 1.
Mechanical Engineering homework question answer, step 2, image 5
Substitute all known values in equation 2.
Mechanical Engineering homework question answer, step 2, image 6
Thus, the vertical force exerted by the balloon is 913.9 N.

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