In the context of physics, resilience denotes the capacity of a material or system to withstand stress, deformation or damage, while still retaining its structural integrity and ability to function as intended. This means that a physical entity that is resilient can withstand external forces and bounce back to its original state or level of performance. For instance, Rubber bands, bungee cords, and springs are all examples of resilient materials that can stretch and bounce back to their original shape.
Table of Contents
Resilience in Physics-Examples
| Material | Formula for Resilience | Example | Calculation |
| Rubber | (1/2) * stress * strain | A rubber band is stretched by 5 cm under a force of 10 N, giving a resilience of 0.25 J | (1/2) * 10 N * 0.05 m = 0.25 J |
| Steel | (1/2) * yield strength * strain^2 | A steel beam with a yield strength of 250 MPa undergoes a deformation of 0.05%, giving a resilience of 0.0625 J | (1/2) * 250 MPa * (0.0005)^2 = 0.0625 J |
| Glass | (1/2) * fracture toughness * (thickness)^2 | A sheet of tempered glass with a fracture toughness of 1.5 MPa*m^(1/2) and a thickness of 3 mm has a resilience of 6.75 x 10^-6 J | (1/2) * 1.5 MPa*m^(1/2) * (0.003 m)^2 = 6.75 x 10^-6 J |
Daily Life Examples of Resilience
- Car bumpers absorb collision impact and return to shape using plastic, rubber, or composite materials.
- Trampolines stretch and deform when jumped on, then return to shape due to springs’ elasticity.
- Basketball balls bounce due to their material’s resilience and elasticity, typically rubber or composite materials.
- Shoes’ soles absorb impact shock when walking or running and return to shape using materials such as rubber, foam, and gel.
- Springs are used in many applications, their resilience is determined by material properties such as stiffness, strength, and yield strength.
Simple Definition of Resilience
Resilience in physics is the ability of an object or material to bounce back to its original shape or position after being stretched or squeezed.
A rubber band is a good example of something that is resilient. When you stretch a rubber band, it gets longer and thinner, but when you release it, it bounces back to its original length and thickness.
Difference between Resilience and Toughness
Toughness and resilience are two terms often used interchangeably, but they actually refer to different properties of materials or systems.
| Property | Toughness | Resilience |
| Definition | A material’s ability to resist cracking, breaking, or fracturing | A material’s ability to return to its original shape or form after being deformed |
| Measurement | Amount of energy required to break the material | Ability to withstand repeated loading and unloading without deforming or breaking |
| Application | Used in applications where subjected to significant stress or impact | Used in applications where subjected to cyclic loading, such as springs or shock absorbers |
| Examples | – Steel has a toughness of 200 J/cm^3, meaning it can absorb 200 joules of energy per cubic centimeter before breaking. | – Rubber has a high resilience, as it can stretch up to five times its original length and return to its original shape. |
| – Carbon fiber reinforced plastic has a toughness of 35 J/cm^3, making it ideal for use in aircraft and other high-stress applications. | – The metal alloy used in watch springs has high resilience, as it can be compressed and released millions of times without deforming. | |
| – Tempered glass has a toughness of 67 J/cm^3, which allows it to resist cracking and breaking when subjected to impacts. | – Beryllium copper has high resilience, as it can be bent and shaped without breaking or deforming. |
Calculating the resilience of a material
To calculate resilience, you need to measure how much energy a material can absorb before it becomes permanently deformed.
To do this, you can calculate the area under the stress-strain curve of the material up to its yield point, which represents the amount of elastic strain energy stored in the material. Then, you divide this value by the strain energy density of the material, which is calculated using its elastic modulus and yield strength.
The resilience of a material can be calculated using the formula:
Resilience = (1/2) × σ × ε
where: σ is the stress (force per unit area) and ε is the strain (change in length per unit length) of the material under elastic deformation.
Another way to calculate resilience is to use the modulus of resilience, which is defined as the maximum amount of energy that a material can absorb without undergoing plastic deformation. The modulus of resilience is given by:
Modulus of resilience = (1/2) × σ^2 / E
where E is the Young’s modulus of the material.
In both formulas, the units of resilience are joules per cubic meter (J/m^3) or joules per square meter (J/m^2), depending on the units used for stress and strain.
Summary
- Resilience is the ability to recover from adversity or stress.
- Resilience can be observed in various contexts, including materials, ecosystems, and human psychology.
- Materials such as rubber bands exhibit resilience when they can return to their original shape after being stretched.
More Links
SI Unit of Work| Definition, Formula, and Examples
Uniform Circular Motion| Real-Life Examples
Linear Motion or Rectilinear Motion| Daily Life Examples
Kinematic Equations| Sample Problems and Solutions
Linear Acceleration
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