To solve this problem, we need to use the formula for stress and strain. Stress is the force per unit area, and strain is the change in length divided by the original length. The elastic modulus (E) is the ratio of stress to strain.

First, we need to calculate the cross-sectional area of the wire. The diameter is given as 1.50 mm, so the radius is 0.75 mm or 0.00075 m. The area (A) of a circle is given by the formula πr², so:

A = π * (0.00075 m)² = 1.77 * 10^-6 m²

Next, we calculate the stress (σ) in the wire, which is the force (F) divided by the area (A):

σ = F / A = 500 N / 1.77 * 10^-6 m² = 2.82 * 10^8 N/m²

The strain (ε) is the stress divided by the elastic modulus:

ε = σ / E = 2.82 * 10^8 N/m² / 7.00 * 10^10 N/m² = 0.00403

Finally, the change in length (ΔL) is the strain times the original length (L):

ΔL = ε * L = 0.00403 * 12.00 m = 0.0484 m or 48.4 mm

So, the increase in length of the wire is 48.4 mm.

Question

To solve this problem, we need to use the formula for stress and strain. Stress is the force per unit area, and strain is the change in length divided by the original length. The elastic modulus (E) is the ratio of stress to strain.

First, we need to calculate the cross-sectional area of the wire. The diameter is given as 1.50 mm, so the radius is 0.75 mm or 0.00075 m. The area (A) of a circle is given by the formula πr², so:

A = π * (0.00075 m)² = 1.77 * 10^-6 m²

Next, we calculate the stress (σ) in the wire, which is the force (F) divided by the area (A):

σ = F / A = 500 N / 1.77 * 10^-6 m² = 2.82 * 10^8 N/m²

The strain (ε) is the stress divided by the elastic modulus:

ε = σ / E = 2.82 * 10^8 N/m² / 7.00 * 10^10 N/m² = 0.00403

Finally, the change in length (ΔL) is the strain times the original length (L):

ΔL = ε * L = 0.00403 * 12.00 m = 0.0484 m or 48.4 mm

So, the increase in length of the wire is 48.4 mm.

Knowee AI · Accepted Answer

To solve this problem, we need to use the formula for stress and strain. Stress is the force per unit area, and strain is the change in length divided by the original length. The elastic modulus (E) is the ratio of stress to strain.

First, we need to calculate the cross-sectional area of the wire. The diameter is given as 1.50 mm, so the radius is 0.75 mm or 0.00075 m. The area (A) of a circle is given by the formula πr², so:

A = π * (0.00075 m)² = 1.77 * 10^-6 m²

Next, we calculate the stress (σ) in the wire, which is the force (F) divided by the area (A):

σ = F / A = 500 N / 1.77 * 10^-6 m² = 2.82 * 10^8 N/m²

The strain (ε) is the stress divided by the elastic modulus:

ε = σ / E = 2.82 * 10^8 N/m² / 7.00 * 10^10 N/m² = 0.00403

Finally, the change in length (ΔL) is the strain times the original length (L):

ΔL = ε * L = 0.00403 * 12.00 m = 0.0484 m or 48.4 mm

So, the increase in length of the wire is 48.4 mm.

A wire is 12.00 m long and has a diameter of 1.50 mm. The elastic modulus of the wire is 7.00 × 1010 N/m2. If a force of 500 N is applied to end of the wire, then the increase in length of the wire is

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