Definition
Elasticity: Elasticity is the ability of a material or object to return to its original size and shape after a force has stretched or squeezed it. Imagine you are playing with a rubber band: when you pull it and then let go, it snaps back to the way it was before. That “snap back” is what elasticity means. The object remembers its original form and goes back to it.
Elastic Object: An elastic object is any object that can be deformed (changed in shape or size) by a force, but once the force is gone, it goes back to how it was. For example, if you stretch a spring or squash a sponge, it will go back to its normal form if it is elastic.
Key Concepts
Deforming Force: A deforming force is any kind of push or pull that causes an object to change its shape or size. For instance, pulling on a spring makes it longer, while pressing on a sponge makes it shorter or flatter.
Original Shape: This is the shape or size an object had before any force acted on it. It’s like saying, “This is what the object looked like before we touched it or applied any pressure.”
Return to Shape: Elastic materials are special because they can go back to their original shape after the force that changed them is removed. But if you stretch or squeeze them too much, they might not return to normal. That means they’ve gone beyond their elastic limit and are now permanently deformed.
Hooke's Law
Law Statement: Hooke’s Law explains how a spring (or similar elastic object) behaves when a force is applied. It says that the amount a spring stretches or compresses is directly linked to the force you use—but only if the spring is not overstretched. If you double the force, the extension doubles too, as long as you stay within the elastic limit.
Formula:
F = kx
This formula shows that the force (F) applied to a spring is equal to the spring constant (k) multiplied by the extension or compression (x).
Spring Constant (k): The spring constant is a number that tells you how stiff the spring is. If the number is big, the spring is very stiff and harder to stretch. If it’s small, the spring is more flexible and easier to stretch.
Unit of k: The unit for the spring constant is Newton per metre, written as N/m. This tells us how many newtons of force are needed to stretch the spring by one metre.
Elastic Potential Energy
Definition: When you stretch or compress an elastic object, like a spring or rubber band, you are giving it energy and that energy gets stored inside the object. This stored energy is called elastic potential energy.
Formulas:
- Eₚ = ½ F x — This means that the energy stored is half the product of the force and the extension.
- Eₚ = ½ k x² — This means the energy is also half the product of the spring constant and the square of the extension.
Work Done: The work done on the spring (the effort used to stretch it) is not wasted — it gets stored as energy. You can measure how much energy is stored by looking at the area under the force-extension graph.
Force-Extension Graph
Force-Extension Graph: In the beginning, when you start to pull or push on a spring by applying force, the spring stretches or compresses in a way that follows a straight-line pattern. This means if you make a graph where the x-axis shows how much the spring stretches (extension) and the y-axis shows how much force you are using, the line goes straight upward like a diagonal. This shows the spring is following Hooke’s Law, which says that the extension is directly proportional to the force applied—as long as you don’t stretch it too far.
Slope of Graph: The steepness, or how slanted the line is on the graph, is called the slope. This slope represents the spring constant, known as “k.” If the line is very steep, that means the spring is very hard to stretch—it is stiff and has a high spring constant. A flatter line would mean the spring is easier to stretch.
Area Under Graph: If you look at the space under the line on this graph, that shaded area represents how much elastic potential energy is stored inside the spring. The more you stretch the spring, the bigger the area becomes, which means more energy is stored that can be released when the spring goes back to its original shape.
Elastic Limit: The elastic limit is a very important point. It is the maximum amount you can stretch the spring while it still obeys Hooke’s Law. If you stretch it more than this limit, the spring won’t go back to its normal shape. It becomes permanently stretched or even damaged, and it won’t work properly anymore.
Factors Affecting Spring Constant (k)
Material Type: The kind of material that the spring is made from changes how stiff it is. For example, steel is stronger and harder to stretch than copper. That means a steel spring will have a higher spring constant than a copper one because it resists stretching more.
Spring Length: A short spring is usually stiffer than a long spring. So, it’s harder to stretch a short spring, and that means it will have a bigger value of k. A longer spring is easier to pull or push.
Coil Diameter: The diameter means how wide each loop or coil of the spring is. If the coils are very small, the spring becomes tighter and harder to stretch. That means the spring constant will be higher when the diameter is smaller.
Wire Thickness: The thickness of the wire that makes up the spring also matters. If the wire is thick, it takes more force to stretch the spring, so the spring constant increases. Thinner wires are easier to stretch and have a smaller value of k.
Other Factors: There are other things too that can affect the spring constant. For example, if the spring is very hot or cold, its stiffness can change. Also, the shape or design of the spring, like how tightly or loosely it’s coiled, can make it easier or harder to stretch.
Spring Systems
Series Connection:
- When you join several springs one after another in a line, like a chain, it’s called a series connection.
- In this setup, every spring feels the same amount of force when you pull or push.
- The total amount the whole system stretches is just the total of how much each spring stretches by itself.
- The system becomes easier to stretch because the springs share the job of stretching. That means the overall spring constant is smaller than any single spring by itself.
Parallel Connection:
- If you place springs side-by-side so they work together at the same time, it’s called a parallel connection.
- In this setup, the total force is divided between the springs. Each one only feels part of the total force.
- Even though the force is shared, all the springs stretch by the same amount.
- The whole system becomes harder to stretch because the springs are working together and resisting the force. So, the overall spring constant is larger.
Applications of Elasticity
Springs: Springs are used in many places because of their elastic properties. In cars, they are used in the suspension system to absorb bumps and shocks from the road. In weighing machines, they help measure how heavy something is by how much the spring stretches. In mechanical clocks, they store energy and help the moving parts run smoothly.
Rubber Bands: A rubber band is a stretchy loop made from elastic material. When you pull it, it stretches and stores energy. When you let go, it quickly snaps back to its original shape, releasing all that energy.
Bungee Cords: Bungee cords are strong, stretchy ropes used in adventurous sports like bungee jumping or for safety in rescues. When a person falls, the cord stretches to slow them down gently instead of letting them hit the ground suddenly. It absorbs the energy of the fall to keep the person safe.
Sports Equipment: In sports, elasticity is used in trampolines to help people bounce high, in bows for archery to store and release energy when shooting an arrow, and in pole vaulting poles that bend and help athletes fly over tall bars. These tools store energy when bent or stretched and release it when returning to their original shape.
Structures: Engineers use materials that are elastic when they build big structures like bridges and tall buildings. These materials can bend a little without breaking, which helps the structure handle things like strong winds, heavy traffic, or even earthquakes.
Key Terms and Concepts
Extension: This means making something longer. When you pull on an object like a spring, it stretches and becomes longer than it was before. The difference between the new length and the original length is called the extension.
Compression: This means making something shorter. When you push on an object, like squashing a spring or a sponge, it gets shorter. That shortening is called compression.
Elastic Limit: This is the most you can stretch or compress something before it won’t go back to normal. If you pass this limit, the object becomes permanently changed and won’t return to its original shape.
Spring Constant (k): This is a number that tells us how difficult it is to stretch or compress a spring. A large k means the spring is very stiff and hard to stretch. A small k means it’s soft and easy to stretch.
Potential Energy: This is stored energy. For example, when you stretch a spring, it holds energy inside it because it’s out of its normal shape. When you let go, the spring snaps back and releases that stored energy.