Define the 'Spring Constant' ($k$).

The spring constant is the force required per unit extension of a material, representing its stiffness. It is measured in Newtons per meter ($N\,m^{-1}$).

State Hooke's Law in words and symbols.

Hooke's Law states that extension is directly proportional to the applied force, provided the limit of proportionality is not exceeded. It is written as $F = kx$.

What is 'Natural Length'?

Natural length is the original length of an object (such as a spring or wire) when no external tensile or compressive forces are acting upon it.

What is the fundamental difference between tensile and compressive forces?

Tensile forces act in opposite directions to stretch an object, increasing its length. Compressive forces act toward each other to squeeze an object, decreasing its length.

How does elastic deformation differ from plastic deformation?

Elastic deformation is reversible; the object returns to its original shape when the force is removed. Plastic deformation is permanent; the object remains deformed even after the force is removed.

What is the difference between the 'limit of proportionality' and the 'elastic limit'?

The limit of proportionality is the point where the linear relationship ($F \propto x$) ends. The elastic limit is the point beyond which the material will no longer return to its original shape; these points are often very close but conceptually distinct.

What common error occurs when using the 'length' of a spring in Hooke's Law calculations?

Students often use the total length ($L$) instead of the extension ($x$). Hooke's Law requires the change in length ($x = L - L_0$), so the natural length must be subtracted first.

Why is it a mistake to calculate the spring constant as $k = \text{gradient}$ on an Extension-Force graph?

On an Extension ($y$) vs. Force ($x$) graph, the gradient is $\frac{x}{F}$, which is $\frac{1}{k}$. To find $k$, you must take the reciprocal of the gradient.

What happens to the energy calculation if you forget to convert extension from cm to m?

Since energy is measured in Joules ($N\,m$), using cm will result in a value that is 100 times too large (for $F=kx$) or 10,000 times too large (for $E = \frac{1}{2}kx^2$) because the unit is squared.

How is the work done to stretch a spring represented on a Force-Extension graph?

The work done is represented by the area under the curve. For a material obeying Hooke's Law, this is the area of the triangle: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2}Fx$.

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Physics

6. Deformation of Solids

Extension & Compression

Summary

Extension and compression describe the physical deformation of objects when subjected to external forces. This field of study focuses on the relationship between applied force and the resulting change in length, governed primarily by Hooke's Law within a material's elastic limit.

1. Definition & Core Concepts

2. Hooke's Law & The Spring Constant

3. Elastic vs. Plastic Deformation

Elastic Deformation is a temporary change in shape. When the applied force is removed, the material returns exactly to its original natural length.
Plastic Deformation occurs when the material is stretched beyond its elastic limit. In this state, the material undergoes permanent structural changes and will not return to its original length once the force is removed.
The Limit of Proportionality is the specific point on a force-extension graph where the linear relationship between force and extension ends. Beyond this point, Hooke's Law no longer applies.
Understanding these limits is critical in engineering to ensure structures can withstand loads without suffering permanent damage or failure.

4. Force-Extension Graphs

Force-Extension graph showing the linear Hooke's Law region, the limit of proportionality, and the shaded area representing elastic potential energy.

5. Exam Strategy & Tips