Question

Two 40-ft long wires made of different materials are supported from the ceiling of a testing laboratory. Wire 1 is made of material H and has a diameter of 3/8 in. Wire 2 is made of material K and has a diameter of 3/16 in. When a load of 225 lb is applied to its lower end, wire 1 stretches 0.10 in. When the same 225 lb load is applied to the lower end of wire 2, wire 2 stretches 0.25 in. Compare materials H and K. Which material has the greater modulus of elasticity? Which is the stiffer material?

Answer 1

Yes! I can help with.

Step-by-step explanation:

To compare materials H and K, we need to determine the modulus of elasticity for each material. The modulus of elasticity is a measure of a material's stiffness, specifically the amount of stress required to produce a given amount of strain.

We can use the formula:

stress = force / area

strain = change in length / original length

modulus of elasticity = stress / strain

Let's start by calculating the stress on each wire:

For wire 1:

stress = force / area = (225 lb) / ((pi/4) * (3/8 in)^2) = 7,655 psi

For wire 2:

stress = force / area = (225 lb) / ((pi/4) * (3/16 in)^2) = 30,620 psi

Next, we can calculate the strain on each wire:

For wire 1:

strain = change in length / original length = 0.10 in / 480 in = 0.000208

For wire 2:

strain = change in length / original length = 0.25 in / 480 in = 0.000521

Finally, we can use the formula to calculate the modulus of elasticity for each material:

For material H:

modulus of elasticity = stress / strain = 7,655 psi / 0.000208 = 36,824,038 psi

For material K:

modulus of elasticity = stress / strain = 30,620 psi / 0.000521 = 58,745,334 psi

Therefore, material K has the greater modulus of elasticity and is the stiffer material.