Question

Жесткость стального провода равна 10000 Н/м. на сколько удлинится трос, если к нему подвесить груз массой 20 кг.

Answer 1

Calculation of Wire Elongation

To calculate the elongation of a wire when a load is applied, we can use Hooke's Law, which states that the elongation of an object is directly proportional to the force applied to it, as long as the elastic limit of the material is not exceeded.

In this case, we are given that the stiffness of the steel wire is 10,000 N/m. This stiffness, also known as the spring constant, represents the force required to stretch the wire by 1 meter.

We can use the formula for Hooke's Law to calculate the elongation of the wire:

Elongation = Force / Stiffness

The force applied to the wire is equal to the weight of the mass suspended from it. The weight can be calculated using the formula:

Weight = Mass x Acceleration due to gravity

In this case, the mass is given as 20 kg. The acceleration due to gravity is approximately 9.8 m/s^2.

Let's calculate the elongation of the wire:

Weight = 20 kg x 9.8 m/s^2 = 196 N

Elongation = 196 N / 10,000 N/m = 0.0196 m

Therefore, the wire will elongate by approximately 0.0196 meters when a 20 kg mass is suspended from it.

Please note that this calculation assumes that the wire is perfectly elastic and obeys Hooke's Law. In reality, there may be other factors that can affect the elongation of the wire, such as the material properties and the presence of any defects or imperfections.