Welcome to Forces and Elasticity!
Ever wondered why a trampoline bounces back after you jump on it, or why a bungee cord stretches but doesn't snap? In this chapter, we are going to explore how forces can change the shape of an object. Usually, we think of forces as things that make objects move, but they can also squash, stretch, and twist them!
1. Changing Shape: Stretching, Bending, and Compressing
To change the shape of an object, you need to apply a force. There are three main ways we talk about changing shape:
• Stretching: Pulling the ends of an object further apart (like a rubber band).
• Bending: Applying force to the middle of an object while holding the ends (like a plastic ruler).
• Compressing: Squashing or pushing the ends of an object together (like a sponge).
The "Two-Force" Rule
Don't worry if this seems tricky at first, but here is a very important rule: to stretch, bend, or compress a stationary object, you must apply more than one force.
Example: If you pull on one end of a spring that isn't attached to anything, the whole spring will just move through the air. To actually stretch it, you need to hold the other end (applying a second force) or pull in opposite directions.
Quick Review: You always need at least two forces acting on a stationary object to change its shape. If you only use one, the object will just move!
2. Elastic vs. Inelastic Deformation
When you take the forces away, does the object go back to its original shape? This is how we tell the difference between elastic and inelastic behavior.
Elastic Deformation: The object returns to its original shape and size once the forces are removed.
Example: A hair tie or a metal slinky.
Inelastic (Plastic) Deformation: The object stays in its new shape. It does NOT go back to how it was before.
Example: Squashing a piece of blue-tack or modeling clay.
Key Takeaway: Elastic = Bounces back. Inelastic = Stays changed.
3. Hooke’s Law: The Physics of Springs
For many objects, especially metal springs, there is a special relationship between the force you apply and how much they stretch. We call the amount of stretch the extension.
The Rule: The extension of an elastic object is directly proportional to the force applied. This means if you double the force, you double the extension!
The Equation
We can write this as a simple formula:
\( F = k e \)
• \( F \) is the force applied (measured in Newtons, N).
• \( k \) is the spring constant (measured in Newtons per metre, N/m).
• \( e \) is the extension (measured in metres, m).
Memory Trick: Think of the spring constant (k) as the "stiffness" of the spring. A high k means the spring is very stiff and hard to stretch. A low k means it’s loose and easy to stretch.
Did you know? This equation also works for compression! In that case, \( e \) stands for the amount the object was squashed.
4. The Limit of Proportionality
Even the best springs have a breaking point. If you pull a spring too hard, it will eventually stop following Hooke's Law. This point is called the limit of proportionality.
• Before this point: The graph of Force vs. Extension is a straight line through the origin (linear).
• After this point: The graph starts to curve (non-linear). This means the spring is permanently damaged and won't return to its original shape.
Common Mistake: Students often forget that extension is the increase in length, not the total length.
Extension = New Length - Original Length.
5. Storing Energy (Work Done)
When you stretch a spring, you are doing work. This energy doesn't just disappear; it gets stored as elastic potential energy inside the spring.
As long as the spring hasn't reached its limit of proportionality, the work done on the spring is exactly equal to the elastic potential energy stored in it.
The Energy Equation
You can calculate this stored energy using this formula:
\( E_e = 0.5 \times k \times e^2 \)
• \( E_e \) is the elastic potential energy (Joules, J).
• \( k \) is the spring constant (N/m).
• \( e \) is the extension (m).
Watch out! In exams, students often forget to square the extension (\( e^2 \)). Always remember to multiply the extension by itself before doing the rest of the math!
6. Summary and Key Points
Quick Review Box:
• You need two forces to stretch, bend, or squash a stationary object.
• Elastic means it goes back to its original shape; Inelastic means it doesn't.
• Hooke's Law: \( F = k e \). Force and extension are directly proportional until the limit is reached.
• Linear graphs are straight lines; Non-linear graphs are curved.
• Energy stored is called Elastic Potential Energy (\( E_e = 0.5 k e^2 \)).
Top Tip for Practicals: When doing the "Investigate the relationship between force and extension" experiment (Required Practical 6), always measure the natural length of the spring before adding any weights, and measure from the same point on the spring every time!