Three cables are connected at *A*, where the forces **P** and **Q** are applied as shown. Knowing that P=900 NP=900 N , determine the value of *Q* for which cable *AD* is just taut.




To determine the value of force \( Q \) for which cable \( AD \) is just taut, we need to break down the forces acting at point \( A \), where the cables meet. We'll work under the assumption that the system is in equilibrium.

### Step 1: Identify the forces involved
The forces acting at point \( A \) are:

1. Force \( P \) = 900 N acting along a specific direction.
2. Force \( Q \) (unknown) applied along a different direction.
3. The tension in cable \( AD \) is zero when it is "just taut."
4. Tension forces in the other cables (such as \( AB \) and \( AC \)).

### Step 2: Resolve forces into components
To find the value of \( Q \), we will resolve the forces acting on point \( A \) into their horizontal and vertical components. Assuming a 2D plane (for simplicity), the equilibrium condition requires that the sum of the forces in both the horizontal and vertical directions is zero.

We can represent the forces as vectors and set up the following system of equations:

- The sum of the forces in the \( x \)-direction must be zero.
- The sum of the forces in the \( y \)-direction must be zero.

### Step 3: Set up equilibrium equations
Let \( \theta_P \) and \( \theta_Q \) be the angles at which forces \( P \) and \( Q \) act, relative to the horizontal axis. The horizontal and vertical equilibrium equations are:

\[
\sum F_x = 0 \quad \Rightarrow \quad P \cos(\theta_P) + Q \cos(\theta_Q) = 0
\]
\[
\sum F_y = 0 \quad \Rightarrow \quad P \sin(\theta_P) + Q \sin(\theta_Q) = 0
\]

### Step 4: Solve for \( Q \)
To solve for \( Q \), we need the specific geometry or angles \( \theta_P \) and \( \theta_Q \). Could you provide more details about the directions or angles at which \( P \) and \( Q \) are applied, as well as the configuration of the cables?

Once we have this information, we can solve for \( Q \) by using trigonometric relationships and the conditions of equilibrium.

---

Would you like to provide more details on the geometry or angles? If not, I can guide you through common assumptions based on typical configurations.

Here are 5 related questions to deepen understanding:
1. How do we resolve forces in 3D if the problem extends beyond 2D?
2. What happens if the system is not in equilibrium? How would we handle acceleration?
3. How do angles of force application influence the tautness of cables?
4. How does friction or material stiffness in cables affect the solution?
5. How can we apply vector cross products to force problems?

**Tip:** Always start by resolving forces into components along the axes for clear equilibrium equations.

Three cables are connected at A, where the forces P and Q are applied as shown. Knowing that P = 900 N, determine the value of Q for which cable AD is just taut.

Solve a statics problem where cables are connected at point A, and forces P = 900 N and Q are applied. Learn how to determine the value of force Q when cable AD is just taut, using force equilibrium equations and vector resolution techniques. Suitable for Grades 10-12 physics students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation