Question

Two parallel wires A and B of same meterial are fixed to rigid support at the upper ends and subjected to same load at the lower ends. The subjeted to same load at the lower ends. The lengths of the wire are in the ration 4 : 5 and their radii are in the ratio 4 : 3 the increase in the length of wire A is 1 mm.

a. Calculate the increase in the length of wire A is 1mm.

Answer 1

The increase in the length of wire A can be calculated using the formula: ΔL = (F * L) / (A * Y). By setting up an equation using the given ratios, we can solve for the force applied.

Step-by-step explanation:

The increase in the length of wire A can be calculated using the formula:

ΔL = (F * L) / (A * Y)

Where ΔL is the increase in length, F is the force applied, L is the original length of the wire, A is the cross-sectional area of the wire, and Y is the Young's modulus of the material.

In this case, the lengths of wire A and wire B are in the ratio 4:5, and the radii are in the ratio 4:3. Let's assume the original lengths of wire A and wire B are 4x and 5x units, respectively.

Since the increase in the length of wire A is given as 1 mm, we can set up the following equation:

1 mm = (F * 4x) / (A * Y)

From the given ratios, we can substitute the values of the lengths and radii:

1 mm = (F * 4x) / (16 * A * Y)

By solving this equation, we can determine the value of the force applied.