Two cables exert forces on the pipe. Determinethe magnitude of the projected component of F1

Описание: Two cables exert forces on the pipe. Determine
the magnitude of the projected component of F1 along the
line of action of F2.
Determine the angle u between the two cables
attached to the pipe.























Answer


*Given Problem:*
Two cables exert forces on a pipe.
Need to determine:
1. *Magnitude of the projected component of F₁ along the line of action of F₂.*
2. *Angle (u) between the two cables attached to the pipe.*

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*Step 1: Find the Projection of F₁ Along the Line of Action of F₂*
The projection of *F₁* along the line of action of *F₂* is given by:
*F₁_proj = F₁ * cos(θ)*
Where:
*θ* is the angle between the two force vectors *F₁* and **F₂**.
*F₁* is the magnitude of force **F₁**.
*F₁_proj* is the component of *F₁* along the line of action of **F₂**.

To find **θ**, you can use the dot product formula:
*F₁ · F₂ = |F₁| * |F₂| * cos(θ)*
Solve for *cos(θ)* and then find **θ**.

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*Step 2: Determine the Angle (u) Between the Two Cables*
The angle between the two cables is the same as the angle between their respective force vectors, *F₁* and **F₂**.
Use the formula:
*cos(u) = (F₁ · F₂) / (|F₁| * |F₂|)*
Solve for *u* by finding the inverse cosine:
*u = cos⁻¹[(F₁ · F₂) / (|F₁| * |F₂|)]*

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*Final Answer:*
*Magnitude of the projected component of F₁ along the line of action of F₂ = ____ N.*
*Angle u between the two cables = ____°.