Question

Two tugboats are towing a loaded barge and the magnitude of the resultant is 8000 pounds directed along the axis of the barge (see figure). Find the tension (in pounds) in the tow lines when they each make an 18° angle with the axis of the barge. (Round your answers to one decimal place.)tension in tow line from tugboat A lbtension in tow line from tugboat B lb

Answer 1

we have that

Let

A -----> total tension in tugboat A

B -----> total tension in tugboat B

we have

Ax+Bx=8,000 ------> equation 1

Ax=Acos(18)

Bx=Bcos(18)

substitute

Acos(18)+Bcos(18)=8,000 -----> equation 2

and

Ay=By

Asin(18)=Bsin(18)

A=B

therefore

Acos(18)+Bcos(18)=8,000 ------> Acos(18)+Acos(18)=8,000

2Acos(18)=8,000

A=8,000/(2cos(18))

A=4,205.8 pounds

answer is

total tension in tugboat A is 4,205.8 pounds

total tension in tugboat B is 4,205.8 pounds