Find the extension of a steel wire with a diameter d = 1 mm

Find the elongation of a steel wire with diameter d = 1 mm

That digital product is a detailed solution to a physics problem. In it you will find information on how to find the elongation of a steel wire with a diameter d = 1 mm and a length of 7 m if it is stretched under the action of a load weighing 10 kg. Young's modulus of steel E = 200 GPa.

The solution to the problem is based on Hooke's law, which establishes a linear dependence of the deformation of an elongated body on the force applied to it. The text describes the necessary formulas for finding the stress, relative strain and elongation of the wire. The text is provided with a beautiful html design, which makes it pleasant to read and allows you to quickly find the information you need.

This product will be useful to schoolchildren, students and physics teachers, as well as anyone interested in mechanics and materials science. By accessing this digital product, you can easily solve similar problems and learn a lot about physics.

This digital product contains a detailed solution to a physics problem, which involves finding the elongation of a steel wire with a diameter of d = 1 mm and a length of 7 m under the influence of a load weighing 10 kg. Young's modulus of steel E = 200 GPa. The solution to the problem is based on Hooke's law, which establishes a linear dependence of the deformation of an elongated body on the force applied to it. The text presents the necessary formulas for finding the stress, relative strain and elongation of the wire. The text is designed in a beautiful html format, which makes it easy to read and quickly find the necessary information. This product will be useful to schoolchildren, students and physics teachers, as well as anyone interested in mechanics and materials science. By accessing this digital product, you can easily solve similar problems and learn a lot about physics.

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In order to find the elongation of a steel wire with a diameter d = 1 mm, it is necessary to know its length and the elastic modulus of the material. Wire elongation can be calculated using the formula: Δl = F * L / (E * S), where Δl is the elongation of the wire, F is the force acting on the wire, L is the length of the wire, E is the elastic modulus of the material and S is the cross-sectional area of ​​the wire, which is equal to π * d^2 / 4 for a round wire.

For a wire with a diameter of d = 1 mm, the cross-sectional area will be equal to π * (1 mm)^2 / 4 = 0.785 mm^2. The modulus of elasticity for steel is approximately 200 GPa (gigapascal).

Thus, the elongation of a steel wire with a diameter of 1 mm under the influence of a force can be calculated by knowing its length and the magnitude of the force. However, without this data, the exact value of wire elongation cannot be determined.

To find the elongation of a steel wire, it is necessary to use Hooke's law, which establishes proportionality between the elongation of the wire and the force applied to it:

F = k * deltaL,

where F is the force applied to the wire, k is the proportionality coefficient, deltaL is the elongation of the wire.

The proportionality coefficient k, in turn, is related to the Young’s modulus of the steel E and the cross-sectional area of ​​the wire S:

k = (S * E) / L,

where L is the original length of the wire.

Thus, the elongation of the wire can be expressed as:

deltaL = F * L / (S * E).

In our case, the diameter of the wire is d = 1 mm, therefore, its cross-sectional area is S = (pi * d^2) / 4 = (3.14 * 0.001^2) / 4 = 7.85 * 10^-7 m^2.

The initial length of the wire is L = 7 m, the mass of the load applied to the wire is 10 kg, therefore, the force acting on the wire is equal to F = m * g, where g is the acceleration of gravity, taken equal to 9.8 m/s^2. We get:

F = 10 * 9.8 = 98 N.

Young's modulus of steel E = 200 GPa = 200 * 10^9 Pa.

Substituting the data into the formula for wire elongation, we get:

deltaL = F * L / (S * E) = 98 * 7 / (7.85 * 10^-7 * 200 * 10^9) = 0.005 m = 5 mm.

Thus, the elongation of a steel wire with a diameter d = 1 mm and a length of 7 m under the influence of a load weighing 10 kg and the Young’s modulus of steel E = 200 GPa is 5 mm.

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