Question

please help with number 8

7. Two cords each at an angle of 32 with the horizontal are suspending a 140 N sign that reads, “I am Ironman” above the ground. If the system is in equilibrium, what is the tension in the two cords? (Construct a diagram and label all forces with your solution.)

8. From problem #7 above, if one of the cords were at an angle of 62 instead of 32, what will the tension in the two cords be?

Answer 1

7.

Diagram :

Solution :

Let the tensions in two cords are T₁ and T₂

Equilibrium of forces in vertical direction :

T₁sin(32°) + T₂sin(32°) = 140 N

(T₁+T₂)sin(32°) = 140

T₁ + T₂ = 140/sin(32°) = 264.19

T₁ + T₂ = 264.19 N ............(1)

Equilibrium of forces in horizontal direction :

T₁cos(32°) = T₂cos(32°)

T₁ = T₂ = T

From equation (1) , we have :

2T = 264.19 N

T = 264.19/2 = 132.095 N

(8.)

Equilibrium of forces in vertical direction :

T₁sin(32°) +T₂sin(64°) = 140

(0.5299)T₁ + (0.8988)T₂ = 140 ......(1)

Equilibrium of forces in horizontal direction :

T₁cos(32) = T₂ cos(64)

T₁ = (0.5169)T₂ ..............(2)

From equation (1)and (2) , we get :

(0.274)T₂ + (0.8988)T₂ = 140 N

T₂ = 140/1.173 = 119.35 N

And T₁ = (0.5169)(119.35) = 61.69 N