What is the reason behind the stress being zero when stretching a rod?

In summary, when a body is in equilibrium, the internal stress is equal to the external force applied divided by the area. In the case of stretching a rod with equal and opposite forces, the net external force is zero, resulting in zero internal stress. This is because the internal forces within the rod, such as the force on the cut end, also cancel out and do not contribute to the overall stress. This is in line with Newton's First Law, which states that a body at rest will remain at rest unless acted upon by an external force.
  • #1
ajayguhan
153
1
I know that I'm wrong but couldn't find where I'm

Stress=internal force /area

When the body is in equilibrium, force applied equals internal force.therefore stress=force applied/area
Let us stretch a rod by two equal and opposite force.,say f and -f...thus total force is zero

Stress= force applied/area
Stress=0 , since total force applied is zero

When we stretch a rod, there is a stress. How come it came zero for me...?



Thanks in advance.
 
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  • #2
The net external force acting on the rod is zero, therefore, the rod is in equilibrium and is not moving (or moving at constant velocity), in accordance with Newton's First Law.

Now draw a Free Body Diagram of a piece of the rod, by pictorially cutting it say down the middle and examining the force acting on the cut end. Since the piece of the rod is also not moving, the net force on that cut piece must also be zero, and thus the force on the cut end must also be F, again in accordance with Newton's first law. This is an internal force, producing an internal stress F/A on that cut section, or any section of the rod.
 

1. What is the difference between stress and strain?

Stress is the force applied to an object per unit area, while strain is the resulting deformation or change in shape of the object. In other words, stress measures the external forces acting on an object, while strain measures the object's response to those forces.

2. How is work done related to stress and strain?

Work done is a measure of the energy transferred to an object as a result of a force acting on it. In the context of stress and strain, work done can be thought of as the energy required to deform an object. The more stress and strain an object experiences, the more work is done on it.

3. What are the units for stress, strain, and work done?

Stress is typically measured in units of force per unit area, such as pounds per square inch (psi) or newtons per square meter (N/m^2). Strain is a dimensionless quantity, often expressed as a percentage or decimal. Work done is measured in units of energy, such as joules (J) or foot-pounds (ft-lb).

4. How does stress and strain affect the behavior of materials?

The relationship between stress and strain can vary depending on the material being tested. Some materials, like metals, have a linear relationship between stress and strain, meaning that the amount of strain is directly proportional to the amount of stress applied. Other materials, like polymers, may exhibit non-linear behavior, with strain increasing at a faster rate than stress.

5. How do scientists measure stress and strain?

Stress and strain can be measured using a variety of techniques, including tensile testing, compression testing, and shear testing. These methods involve applying controlled forces to a material and measuring the resulting deformation. Advanced techniques such as x-ray diffraction and atomic force microscopy can also be used to study the atomic-level stress and strain in materials.

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