The schematic view of the free-body diagram for the given image in the question is attached in the image below.
From the image;
- The tension acting on the rope by teams 1, 2, and 3 are F₁, F₂, and F₃ respectively.
Resolution of Forces:
Component of forces along the x-axis = Fcosθ
Component of forces along the y-axis = Fsinθ
Thus, the resolution of forces into x-direction and y-direction is shown in the second image below.
From the second image, the resolution of force along the horizontal direction(x-component) of the force of team A is:
Vertical direction(y-component) is:
However, T₃ (tension in force F₃) counters the x-component of T₁ and it is higher than the component of T₁.
∴
T₃ wins here.
Similarly, the T₂ force counters the y-component of T₁, and the T₂ force is greater than T₁.
∴
T₂ wins here.
This implies that in the same force case, T₁ lost.
Now, we are left with 0.5F of T₂, and 0.134 of T₃ which are perpendicularly working to each other.
Hence, in the first year, the resultant force along T₂ is the winner.
However, For T₁ to win next year provided the team doesn't change their position;
T₁ has to do the following:
- F' cos 30 ≥ F
- F' sin 30 ≥ F
Taking the minimum condition;
F'cos(30) = F
[tex]F' = \dfrac{F}{cos (30)}[/tex]
F' = 1.15 F
F'sin(30) = F
[tex]F' = \dfrac{F}{sin (30)}[/tex]
F' = 2F
Therefore, we can conclude that for team 1 to win in the next year if they did not change their position, they need to apply a force greater than or equal to 2F or twice the force of the other team.
Learn more about resultant force here:
https://brainly.com/question/17232218?referrer=searchResults
