Question

Проволока длиной 5 м и диаметром 0,4 мм под действием силы 50 Н удлинилась на 5 см. Каков модуль Юнга вещества, из которого сделана проволока?

Answer 1

F=50 H   Lo=5 м   ΔL=0.05 м   d=0.4*10^-3 м   Е=?

F=E*S*ΔL/Lo     S=π*d²/4

E=4*F*Lo/(π*d²*ΔL)=4*50*5/(3.14*0.16*10^-6*0.05)=40*10^9 Н/м²

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Answer 2

Calculating Young's Modulus

To calculate the Young's modulus of the material from which the wire is made, we can use the formula:

Young's Modulus (E) = (F * L) / (A * ΔL)

Where: - F = Force applied (in Newtons) - L = Original length of the wire (in meters) - A = Cross-sectional area of the wire (in square meters) - ΔL = Change in length of the wire (in meters)

Given: - F = 50 N - L = 5 m - ΔL = 0.05 m (5 cm) - d = 0.4 mm (0.0004 m)

First, we need to calculate the cross-sectional area A of the wire using the diameter d.

Calculating Cross-Sectional Area

The formula to calculate the cross-sectional area of a wire is:

A = π * (d/2)^2

Where: - π is the mathematical constant (approximately 3.14159) - d is the diameter of the wire

Substitute the value of d into the formula to find A.

Solution

Cross-Sectional Area (A) = π * (0.0004/2)^2

Cross-Sectional Area (A) = π * (0.0002)^2

Cross-Sectional Area (A) ≈ 3.14159 * 0.00004 ≈ 1.25664 x 10^-7 square meters

Now that we have the cross-sectional area, we can calculate the Young's modulus using the formula mentioned earlier.

Calculating Young's Modulus

Young's Modulus (E) = (50 * 5) / (1.25664 x 10^-7 * 0.05)

Young's Modulus (E) ≈ 500 / (6.2832 x 10^-9)

Young's Modulus (E) ≈ 7.946 x 10^10 N/m^2

Therefore, the modulus of elasticity (Young's modulus) of the material from which the wire is made is approximately 7.946 x 10^10 N/m^2.