Question

A 169.8-N bird feeder is supported by three cables as shown in the figure below. Find the tension in each cable.left cable 158.5 Incorrect: Your answer is incorrect.Your response differs from the correct answer by more than 10%. Double check your calculations. Nright cable 258.5 Incorrect: Your answer is incorrect.Your response differs from the correct answer by more than 10%. Double check your calculations. Nbottom cable 3101.3279 Incorrect: Your answer is incorrect.Your response differs from the correct answer by more than 10%. Double check your calculations. NA bird feeder is suspended from a vertical cable. The top of the cable is tied to two other cables. The left and right cables go up and to the left and up and to the right, respectively, from the connection point to a horizontal bar. The left cable makes an angle of 60° with the bar. The right cable makes an angle of 30° with the bar.

Answer 1

Given:

Weight = 169.8 N

Angles: 60°,30°

x-coordinate:

TACx = TBCx

TAC cos 60 = TBC cos 30

TAC 1/2 = TBC √3/2

TAC = TBC √3 (1)

y-coordinates

TCD = 169.8 N

TACy + TBCy = TCD

TAC sin 60 + TBC sin 30 = 169.8

TAC (√3/2) + TBC (1/2) = 169.8

TAC √3 + TBC = 339.6 (2)

Substitute Equation (1) in equation (2)

(TBC √3) √3 + TBC = 339.6

3TBC + TBC= 339.6

4 TBC = 339.6

TBC= 339.6/4

TBC= 84.9N

TAC =TBC √3

TAC = 84.9 √3 N

Answers:

TAC (left cable) = 84.9 √3 N

TBC (right cable) = 84.9 N

TCD (bottom cable) = 169.8 N