Question

при какой наибольшим диаметре поперечно сечения стальная проволока под действием силы в 7840 H разорвется? предел прочности стали 4*10^8 Па

Answer 1

Для неподвижной проволоки (по умолчанию) сила, действующая на проволоку, и сила упругости, возникающая при ее деформации, равны, т.е. F = Fupr. Условия разрыва проволоки σpr ≤ σ, где σpr = 500 МПа = 5,00∙108 Па – предел прочности стали,  σpr=FuprS ,  S=14π⋅d2 , Fupr = F = 7850 Н. Тогда  σ=4Fπ⋅d2;σpr≤4Fπ⋅d2;d≤4Fπ⋅σpr−−−−√;dmax=4Fπ⋅σpr−−−−√ , dmax ≈ 4,47∙10-3 м.

Answer 2

Steel Wire Breaking Strength Calculation

To calculate the breaking strength of a steel wire with a given diameter under a force of 7840 H (Hertz), we can use the formula for stress:

Stress (σ) = Force (F) / Area (A)

The area of the cross-section of the wire can be calculated using the formula for the area of a circle:

Area (A) = π * (Diameter/2)^2

Given that the diameter of the wire is the largest, we can use the maximum diameter to calculate the area and then the stress.

Using the provided information, we can calculate the breaking strength of the steel wire.

Calculation

The formula for stress can be used to calculate the breaking strength of the steel wire:

Stress (σ) = Force (F) / Area (A)

Given: - Force (F) = 7840 H - Diameter of the wire = 4.4 mm

We can calculate the area and then the stress using the above formulas.

Area Calculation

The area of the cross-section of the wire can be calculated using the formula for the area of a circle:

Area (A) = π * (Diameter/2)^2

Substituting the given diameter:

Area (A) = π * (4.4/2)^2

Area (A) ≈ 15.21 mm^2

Stress Calculation

Now, we can calculate the stress using the formula:

Stress (σ) = Force (F) / Area (A)

Substituting the given force and calculated area:

Stress (σ) = 7840 H / 15.21 mm^2

Stress (σ) ≈ 515.29 H/mm^2

Conclusion

The breaking strength of the steel wire with a diameter of 4.4 mm under a force of 7840 H is approximately 515.29 H/mm^2.

This calculation is based on the provided information and the formulas for stress and area of a circle.