Forces and matter

Welcome to Forces and Matter!

In this chapter, we are going to explore what happens when we use forces to change the shape of objects. Whether you are stretching a bungee cord, squashing a foam ball, or bending a plastic ruler, you are seeing physics in action! This topic is a key part of Paper 6 (Physics 2). We will look at why some things "snap back" to normal while others stay broken, and we will learn how to calculate the energy stored in a stretched spring. Don't worry if physics usually feels like a lot of math—we will break it down step-by-step!

1. Changing Shapes: It Takes Two!

Have you ever tried to stretch a rubber band by only pulling on one side? It doesn't work! The rubber band just moves through the air. To change the shape of an object (like stretching, bending, or compressing it), you actually need more than one force acting on it.

Why?
If you only apply one force, the object will simply accelerate in that direction (remember Newton's Laws?). To change its shape, you need opposite forces to pull it apart or push it together. This could be you pulling both ends of a spring, or one end of a spring being tied to a wall while you pull the other.

Quick Review: Three ways to change shape
1. Stretching: Pulling the ends apart.
2. Bending: Applying force to the middle while the ends are supported.
3. Compressing: Pushing the ends together (squashing).

Key Takeaway: You must have at least two forces acting on an object to stretch, bend, or compress it.

2. Elastic vs. Inelastic Distortion

When you take a force away from an object you’ve been squashing or stretching, one of two things will happen. Scientists call this distortion (which just means changing shape).

Elastic Distortion

This is "stretchy" behavior. If an object returns to its original shape after you remove the forces, it is elastically distorted.
Example: A rubber band or a Slinky.

Inelastic (Plastic) Distortion

This is "permanent" behavior. If an object stays in its new shape even after you stop pushing or pulling it, it is inelastically distorted.
Example: Pushing your finger into a piece of modeling clay or crushing an empty soda can.

Did you know?

Even a steel spring has a "limit." if you pull it too hard, it will stop being elastic and stay stretched out forever! This is called its limit of proportionality.

Key Takeaway: Elastic means it goes back to normal; Inelastic means the change is permanent.

3. Hooke’s Law: The Math of Stretching

For many objects (especially springs), there is a simple relationship between the force you apply and how much the object stretches. This is known as Hooke's Law.

The Equation

\( force \ exerted \ on \ a \ spring \ (N) = spring \ constant \ (N/m) \times extension \ (m) \)

In symbols: \( F = k \times x \)

Breaking down the terms:
- Force (\( F \)): Measured in Newtons (N). This is how hard you are pulling.
- Spring Constant (\( k \)): Measured in Newtons per metre (N/m). This tells you how "stiff" the spring is. A high \( k \) means a very stiff spring (like on a car's suspension).
- Extension (\( x \)): Measured in metres (m). This is the increase in length, not the total length!

Common Mistake Alert!

Students often use the total length of the spring in calculations. Don't do this! Extension is the New Length minus the Original Length. If a 10cm spring is stretched to 12cm, the extension is 2cm (which you would convert to 0.02m).

Key Takeaway: The harder you pull, the more it stretches. The "stiffness" of the spring is the spring constant.

4. Linear vs. Non-Linear Relationships

If you were to draw a graph of Force (on the y-axis) against Extension (on the x-axis):

1. Linear Relationship: The graph is a straight line through the origin \((0,0)\). This means the extension is directly proportional to the force. Most springs are linear... at first!
2. Non-Linear Relationship: The graph is a curve. This happens when the object doesn't follow Hooke's Law. Rubber bands are often non-linear—they might be easy to stretch at first and then get much stiffer.

Quick Review Box:
- Straight line graph? It's a linear relationship (\( F=kx \) works).
- Curved line graph? It's a non-linear relationship.

5. Energy Stored in a Spring (Work Done)

When you stretch a spring, you are doing work. This energy doesn't just disappear; it gets stored in the spring as elastic potential energy. You can calculate exactly how much energy is stored using this formula:

The Equation

\( energy \ transferred \ in \ stretching \ (J) = 0.5 \times spring \ constant \ (N/m) \times (extension \ (m))^2 \)

In symbols: \( E = \frac{1}{2} \times k \times x^2 \)

Step-by-Step Example:

If a spring with a constant (\( k \)) of 100 N/m is stretched by 0.1 m, how much energy is stored?
1. Square the extension: \( 0.1 \times 0.1 = 0.01 \)
2. Multiply by the spring constant: \( 100 \times 0.01 = 1 \)
3. Multiply by 0.5: \( 0.5 \times 1 = 0.5 \)
Answer: \( 0.5 \ Joules \)

Key Takeaway: Stretching a spring stores energy. Because the extension is squared in the formula, doubling the stretch actually quadruples the energy stored!

6. Core Practical: Investigating Force and Extension

You will likely do this experiment in class! The goal is to see the relationship between force and extension for a spring.

The Process:

1. Secure a spring to a clamp stand and measure its original length with a ruler.
2. Add a 100g mass (this is a force of about 1 Newton).
3. Measure the new length of the spring.
4. Calculate the extension (New length - Original length).
5. Repeat by adding more masses one by one.
6. Plot a graph of Force (y-axis) vs Extension (x-axis).

Safety First!

Always wear safety goggles. If a spring is stretched too far, it can snap or fly off and hit you in the eye!

What the results show:
The gradient (steepness) of your straight-line graph is equal to the spring constant (\( k \)). The steeper the line, the stiffer the spring!

Key Takeaway: Hanging weights on a spring lets us prove Hooke's Law and calculate the spring's stiffness.