The top point
false
You don't. An equation with two variables can be graphed as a line or a curve on x-y coordinates. When you do that, EVERY point on the line or curve satisfies the equation. You can't 'solve' it ... i.e. come up with unique values for 'x' and 'y' ... until you have another equation. It represents another line or curve on the graph, and the 'solution' represents the point (or points) where the graphs of the two equations intersect.
In simple language, derivative is rate of change of something and integral represents the area of a curve whose equation is known.
x2 + y2 = r2 Where "x" and "y" represent the co-ordinates of any point on the curve relative to it's center point, and "r" represents it's radius. If you want to specify a curve that goes around a specific point (we'll call it {a, b}), then that can be expressed as: (x - a)2 + (y - b)2 = r2
The linear portion of the stress-strain curve represents the elastic deformation of a material. This is where the material behaves elastically and will return to its original shape once the applied stress is removed.
I assume you mean the curve of length against applied force (or mass) for a wire. The beginning part of the curve should be a straight line, and this is where the deformation is elastic. When the substance passes its elastic limit, the line starts to curve up.
A stress-strain curve typically has two segments because the material first deforms elastically before transitioning to plastic deformation. The initial linear region represents elastic deformation, where the material can return to its original shape after the stress is removed. The second region shows plastic deformation, where the material undergoes permanent deformation due to interatomic sliding or dislocation motion.
The toe region of a curve represents the initial low-velocity, elastic deformation phase where stress and strain are directly proportional. It is the beginning segment of the stress-strain curve when a material starts to deform under load but before significant plastic deformation occurs. The toe region is where the material's structure begins to reorganize and align, allowing for further plastic deformation.
the curve elastrate different, processes that are taking place with the deformation of the material,there is the elastic region the after plastic region which is followed by material being broken
Hooke's law describes the relationship between the force applied to a spring and the resulting extension or compression of the spring, as long as the material remains in the elastic deformation range of the stress-strain curve. Beyond the elastic limit, the material may exhibit plastic deformation, and Hooke's law may not apply.
Young Modulus is the slope of the stress-strain diagram in the linear elastic region. This is the most common use of modulus. As the material goes non-linear in the stress strain curve, thre slope will get increasingly lower. In this case one connects the end points of the stress strain diagram at the point of interest with a straight line. The slope of that straight line is the secant modulus.
Plastic behavior refers to the irreversible deformation of a material when subjected to an external load beyond its elastic limit. This results in a permanent change in shape even after the load is removed. Plastic deformation occurs due to dislocation movement within the material's atomic structure.
There are a lot of test to be performed to get enough data for the research. Tensile test, hardness test, etc. Discovering the Yield Point, the Elastic and Plastic Deformation and the Fail Points on the Stress-Strain Curve. All the data is carefully collected and analyzed...
It is false that the steeper the demand curve the less elastic the demand curve. The steeper line is used in economics to indicate the inelastic demand curve.
Brittle materials such as ceramics do not have a yield point. For these materials the rupture strength and the ultimate strength are the same, therefore the stress-strain curve would consist of only the elastic region, followed by a failure of the material.
When an object undergoes a deformation that does not cause it to break or permanently deform, the change in length can be equal to the original length if the deformation is elastic. This means that the object returns to its original length once the deforming force is removed, exhibiting a linear relationship between stress and strain. This behavior is described by Hooke's Law in the elastic region of a material's stress-strain curve.