Question

You have a heavy piece of equipment hanging from a 1.0mm diameter wire. Your supervisor asks that the length of the wire be doubles without changing how far the wire stretches. What diameter must the new wire have?

a. 1.0 mm
b. 1.4 mm
c. 2.0 mm
d. 4.0 mm

Answer 1

In physics, to maintain the same amount of stretch while doubling the length of a hanging wire, the wire's diameter must be increased by a factor of √2, making the correct answer 1.4 mm.

Step-by-step explanation:

The subject of the question is physics, specifically the concept of stress and strain related to Young's modulus for materials. When the length of a wire suspending a heavy piece of equipment is doubled, in order to keep the stretch the same, the cross-sectional area, and therefore the diameter of the wire, must increase if the material of the wire remains constant.

To maintain the same stretch, the stress (force per unit area) must remain constant. As the length of the wire doubles, the volume and mass of the wire double, which means the weight it must hold also doubles, effectively doubling the force applied. To keep the stress constant with double the force, the cross-sectional area of the wire must also double, which would require a diameter increase by a factor of √2.

For a wire of original diameter 1.0 mm, the new diameter required would be 1.0 mm × √2, which equals approximately 1.4 mm. Therefore, the correct answer is b. 1.4 mm.