Question

Предельное напряжение на разрыв каркасной нити паука Araneus diadematus (Крестовик обыкновенный) в среднем составляет 2 ГПа. Если бы паутина имела диаметр 1 мм, то какой массы она могла бы выдержать груз? Что прочнее: стальная проволока или паутина (при условии одинакового диаметра)? Ответ поясните.

Answer 1

Ответ:

Объяснение:..........

Answer 2

Spider Silk Strength and Load-Bearing Capacity

Spider silk is known for its remarkable strength and elasticity. The breaking strength of spider silk can vary depending on the species of spider and the specific type of silk being analyzed.

According to the information provided, the average breaking strength of the dragline silk from the spider species Araneus diadematus (Cross Spider) is approximately 2 GPa (gigapascals). However, it is important to note that this value may vary depending on the specific conditions and testing methods used.

To calculate the load-bearing capacity of a spider silk thread, we can use the formula:

Load-bearing capacity = Breaking strength * Cross-sectional area

The cross-sectional area of a circular thread can be calculated using the formula:

Cross-sectional area = π * (diameter/2)^2

Let's calculate the load-bearing capacity of a spider silk thread with a diameter of 1 mm.

Load-Bearing Capacity Calculation

First, let's calculate the cross-sectional area of the spider silk thread:

Cross-sectional area = π * (diameter/2)^2

Substituting the given diameter of 1 mm (0.001 m) into the formula:

Cross-sectional area = π * (0.001/2)^2

Calculating the cross-sectional area:

Cross-sectional area ≈ 0.0000007854 m^2

Next, let's calculate the load-bearing capacity of the spider silk thread:

Load-bearing capacity = Breaking strength * Cross-sectional area

Substituting the given breaking strength of 2 GPa (2,000,000,000 Pa) and the calculated cross-sectional area into the formula:

Load-bearing capacity = 2,000,000,000 Pa * 0.0000007854 m^2

Calculating the load-bearing capacity:

Load-bearing capacity ≈ 1570 N

Therefore, a spider silk thread with a diameter of 1 mm could potentially withstand a load of approximately 1570 N (Newtons).

Strength Comparison: Steel Wire vs. Spider Silk

To determine which is stronger between steel wire and spider silk, we need to compare their breaking strengths.

The breaking strength of steel wire can vary depending on its composition and manufacturing process. However, on average, steel wire has a breaking strength of around 1.65 GPa [[1]].

Comparing this value to the breaking strength of spider silk (2 GPa), we can conclude that spider silk is generally stronger than steel wire of the same diameter.

It is important to note that the specific properties of spider silk, such as its high strength-to-weight ratio and elasticity, make it a remarkable material. These properties have attracted the interest of scientists and engineers for various applications, including biomimetic materials and medical devices.

In summary, spider silk from the species Araneus diadematus has an average breaking strength of approximately 2 GPa. A spider silk thread with a diameter of 1 mm could potentially withstand a load of approximately 1570 N. Spider silk is generally stronger than steel wire of the same diameter, although the breaking strength of steel wire can vary depending on its composition and manufacturing process.

I hope this explanation helps! Let me know if you have any further questions.