Question

Длина проволоки увеличилась на 0,60 мм, когда груз массой 5, 10 кг был подвешен на вертикальной проволоке длиной 5 м и площадью поперечного сечения 2 мм2. Найти модуль Юнга для материала проволоки

Answer 1

Ответ:

Объяснение:

Дано:

ΔL = 0,60 мм = 0,60·10⁻³ м

m = 5,10 кг

L = 5 м

S = 5 мм² = 5·10⁻⁶ м²

____________________

E - ?

1)

Механическое напряжение:

σ = F / S = m·g / S = 5,10·10 / (5·10⁻⁶) ≈ 1,02·10⁷ Па

2)

Относительное удлинение:

ε = ΔL / L = 0,60·10⁻³ / 5 = 0,12·10⁻³

Закон Гука:

σ = ε·E

Отсюда:

E = σ / ε

E = 1,02·10⁷ / (0,12·10⁻³) ≈ 8,5·10¹⁰ Па

Answer 2

#### Finding the Young's modulus for the wire To find the Young's modulus for the material of the wire, we need to use the given information about the change in length and the applied load. The formula for Young's modulus is: **Young's modulus (E) = (stress / strain)** Where: - Stress is the force applied per unit area (F/A) - Strain is the change in length per unit length (ΔL/L) In this case, the change in length (ΔL) is given as 0.60 mm, and the length of the wire (L) is given as 5 m. The area of the cross-section (A) is given as 2 mm². Let's calculate the stress and strain first: **Stress (σ) = Force (F) / Area (A)** The force (F) can be calculated using the mass (m) and acceleration due to gravity (g): **Force (F) = mass (m) * acceleration due to gravity (g)** Given that the mass is either 5 kg or 10 kg, we can calculate the force. For a mass of 5 kg: **Force (F) = 5 kg * 9.8 m/s²** For a mass of 10 kg: **Force (F) = 10 kg * 9.8 m/s²** Now, let's calculate the stress: **Stress (σ) = Force (F) / Area (A)** Next, we need to calculate the strain: **Strain (ε) = Change in length (ΔL) / Original length (L)** Now, we can calculate the Young's modulus: **Young's modulus (E) = Stress (σ) / Strain (ε)** Let's calculate the Young's modulus for both cases (mass of 5 kg and mass of 10 kg). For a mass of 5 kg: - Calculate the force (F) using the formula above. - Calculate the stress (σ) using the formula above. - Calculate the strain (ε) using the formula above. - Calculate the Young's modulus (E) using the formula above. For a mass of 10 kg: - Calculate the force (F) using the formula above. - Calculate the stress (σ) using the formula above. - Calculate the strain (ε) using the formula above. - Calculate the Young's modulus (E) using the formula above. #### Calculation for a mass of 5 kg: **Force (F) = 5 kg * 9.8 m/s²** **Stress (σ) = Force (F) / Area (A)** **Strain (ε) = Change in length (ΔL) / Original length (L)** **Young's modulus (E) = Stress (σ) / Strain (ε)** #### Calculation for a mass of 10 kg: **Force (F) = 10 kg * 9.8 m/s²** **Stress (σ) = Force (F) / Area (A)** **Strain (ε) = Change in length (ΔL) / Original length (L)** **Young's modulus (E) = Stress (σ) / Strain (ε)** Please provide the mass of the object so that we can calculate the Young's modulus for the wire.