Difference between force and stress

One of the key point that shows force and stress differ from each other is that the force is responsible for the deformation in the object while stress shows a measure of resistance to the deformation developed by the object.

Before moving toward our main topic, let’s know about the force and stress in brief.

Force:

Force is a push or pull action that can create motion in the object or resist the motion of the object.
Force is a vector quantity and it is denoted by the symbol ‘F’.

The force can arise due to the acceleration into the mass, gravitational or magnetic action, etc.

Example: As shown in the figure, the force acting on the ball provides acceleration to the ball which is equivalent to the product of its mass and acceleration.

force acting on ball

Thus the force acting on the ball is given by,

F = ma

Stress:

Stress is the internal resistance per unit resisting area developed by the object to resist the deformation. It is given by the ratio of internal resisting force to the area of cross-section.

The stress is not a scalar nor a vector quantity as it is considered as tensor quantity.

Example: As shown in the below figure, the man is stretching the rubber by applying the force ‘F’. To resist the deformation, the rubber is also developing the resistance force and this resistance force per unit cross-sectional area is the stress developed into the rubber.

stress developed in rubber

`\sigma` = `\frac{\text{Resistance force} (F_{R})}{\text{Cross sectional area} (A)}` = `\frac{F}{A}` ——(∵`F = F_{R}`)

Difference between force and stress:

Sr. No.ForceStress
1Force is the push or the pull action that can cause motion in the body or opposes the motion of the body.Stress is the internal resistance force per unit cross-sectional area developed by the object to resist the deformation.
2The force is applied externally.Stress is developed internally.
3The force is the change in the momentum of the body.Stress shows the internal resistance developed by the body against deformation.
4The force can cause stress in the body.Stress never creates force.
5The force can create motion into the object.The stress never creates any motion in the object.
6The force arises due to the acceleration of the mass, gravity, magnetism, etc.The stress is developed due to the application of force or due to uneven temperature changes.
7The force is generally denoted by the symbol ‘F’.The term stress can be denoted by the symbol ‘σ’.
8It can be calculated as F = m x a.It is calculated as, Stress = `\frac{\text{Internal resistance}}{\text{Cross sectional area}}`
9The SI unit of the force is the newton (N) or Kg.m/s².The SI unit for the stress is N/m².
10The dimensional formula of the force is [M¹L¹T⁻²].The dimensional formula of the stress is [M¹L⁻¹T⁻²].
11Force is a vector quantity.It is considered as a tensor quantity.
The above table indicates the difference between force and stress.

FAQs:

  1. Are stress and force same?

    No, stress and force are different terms.

  2. How is stress related to force?

    The relation between the stress and force is given by the following formula.
    Stress = (Force) / (Resisting area)

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