A cord supported at A and B carries a load of 10 kN at D and a load of W at C as shown in
figure. Find the value of W so that CD remains horizontal.

To solve the problem of determining the value of the load W so that the segment CD remains horizontal, we need to analyze the forces acting on the cord and apply some principles of static equilibrium. This involves understanding how loads affect the tension in the cord and the angles at which the cord is positioned.

Understanding the Setup

Imagine a cord supported at two points, A and B, with a load of 10 kN hanging at point D and an unknown load W at point C. For the segment CD to remain horizontal, the vertical components of the forces acting on the cord must balance out. This means that the sum of the vertical forces must equal zero.

Analyzing Forces

Let’s break down the forces acting on the cord:

• The downward force due to the load at D, which is 10 kN.
• The downward force due to the load W at C.
• The tension in the cord segments AC and BC, which will have vertical components that counteract the loads at C and D.

Setting Up the Equations

For the cord to remain in equilibrium, the sum of the vertical forces must equal zero:

Tension in AC (T1) + Tension in BC (T2) = Load at D + Load at C

In a horizontal configuration, the vertical components of the tensions must balance the loads. If we denote the angle of the cord segments with respect to the horizontal as θ, we can express the vertical components of the tensions as:

• Vertical component of T1 = T1 * sin(θ1)
• Vertical component of T2 = T2 * sin(θ2)

Applying Equilibrium Conditions

Assuming that the angles θ1 and θ2 are equal (which is often the case in symmetrical setups), we can simplify our equation:

T1 * sin(θ) + T2 * sin(θ) = 10 kN + W

Factoring out sin(θ), we get:

(T1 + T2) * sin(θ) = 10 kN + W

Finding the Value of W

To find W, we need to express T1 and T2 in terms of known quantities. If we know the tensions or can calculate them based on the geometry of the setup, we can substitute those values into the equation. For instance, if T1 and T2 are equal due to symmetry, we can denote them as T:

2T * sin(θ) = 10 kN + W

Rearranging gives us:

W = 2T * sin(θ) - 10 kN

Conclusion

To find the exact value of W, you would need to know the tension T and the angle θ. Once you have those values, you can substitute them into the equation to find W. This approach ensures that the segment CD remains horizontal under the given loads. If you have specific values for T and θ, we can calculate W together!