Key Concepts

Habari Mwanafunzi! Let's Stretch Our Minds with Hooke's Law!

Have you ever wondered what makes a rubber band snap back? Or how the suspension on a matatu makes a bumpy ride on a marram road feel a little smoother? The secret lies in a brilliant piece of physics called Hooke's Law. Today, we're going to break down the key ideas behind it. By the end of this lesson, you'll see this law in action everywhere, from the pen in your hand to the bridges you cross!

1. Elasticity: The "Bounce Back" Power

First things first, let's talk about being 'elastic'. In physics, elasticity is the ability of a material to return to its original shape and size after a stretching or squashing force is removed. Think about it!

• A rubber band (or mpira) you use for a catapult (manati). You stretch it, and it goes back.
• The spring inside a ballpoint pen. You click it, and the spring compresses and expands.
• A mattress spring. You lie on it, and it returns to its shape when you get up (hopefully!).

Materials that do this are called elastic materials. The opposite is a plastic material, which stays deformed, like when you mould a piece of udongo (clay).

Kenyan Example: Imagine a boda boda rider hitting a pothole. The shock absorbers (which contain powerful springs) compress to absorb the shock and then extend back to their original length. Without elasticity, that ride would be very, very painful!

2. Force and Extension: A Perfect Partnership

When you hang a weight on a spring, two things are happening:

1. You are applying a Force (F). This is the load or weight pulling the spring downwards. We measure it in Newtons (N).
2. The spring gets longer. This increase in length is called the Extension (e). We measure it in metres (m).

The main idea is simple: the more force you apply, the more the spring extends. They are directly proportional!

   +----         +----
   |             |
   |             | } L₀ (Original Length)
   |             |
   +----         +----
  (Before)       | W |  } e (Extension)
                 +---+
                (After)

To calculate extension (e):
e = New Length (L) - Original Length (L₀)

3. Hooke's Law: The Golden Rule

A brilliant scientist named Robert Hooke studied this relationship and came up with a law. It's the star of our show!

Hooke's Law states that: Provided the elastic limit is not exceeded, the extension of a spring is directly proportional to the applied force.

In the language of mathematics, we write it like this:

F ∝ e

Which becomes the famous equation:

F = ke

• F is the Applied Force (in Newtons, N).
• e is the Extension (in metres, m).
• k is the Spring Constant (in Newtons per metre, N/m).

4. The Spring Constant (k): A Measure of Stiffness

So, what is this 'k' value? The spring constant (k) tells us how stiff a spring is. It's a measure of how much force is needed to stretch a spring by one metre.

• A high 'k' value means the spring is very stiff. It needs a LOT of force to stretch it even a little bit. (Think of a huge truck's suspension spring).
• A low 'k' value means the spring is weak or soft. A small force will cause a large extension. (Think of the spring in a clothes peg).

Image Suggestion:

A side-by-side comparison. On the left, a massive, thick suspension spring from a lorry, labeled 'High Spring Constant (k) - Very Stiff'. On the right, a small, thin spring from a ballpoint pen, labeled 'Low Spring Constant (k) - Very Soft'. The style should be a clear, educational diagram with bold labels.

5. The Elastic Limit: The Point of No Return

Every elastic material has its limit! The elastic limit is the maximum force that can be applied to a spring after which it will NOT return to its original length. It becomes permanently damaged or deformed.

Have you ever over-stretched a rubber band and found it's now loose and useless? You pushed it past its elastic limit. The same happens to the springs in an old sofa at home that begins to sag – they have been overloaded for too long!

      Force (N)
        ^
        |
        |      /
        |     /
        |    / ............ Elastic Limit
        |   /
        |  /  <-- Straight line (Obeys Hooke's Law)
        | /
        +----------------> Extension (m)

Let's Do Some Maths! (Worked Example)

Time to put our knowledge to the test. Let's calculate a spring constant.

Problem: A light spring has an original length of 12 cm. When a 300 g mass is hung from its end, it stretches to a new length of 18 cm. Calculate the spring constant (k) of the spring. (Assume g = 10 N/kg).

Step 1: Write down what you know.
Original Length (L₀) = 12 cm
New Length (L) = 18 cm
Mass (m) = 300 g

Step 2: Convert everything to SI units.
L₀ = 12 cm = 0.12 m
L = 18 cm = 0.18 m
m = 300 g = 0.3 kg

Step 3: Calculate the Extension (e).
e = L - L₀
e = 0.18 m - 0.12 m
e = 0.06 m

Step 4: Calculate the Force (F). The force is the weight of the mass.
F = mass × acceleration due to gravity (mg)
F = 0.3 kg × 10 N/kg
F = 3 N

Step 5: Use Hooke's Law to find the spring constant (k).
F = ke
So, k = F / e
k = 3 N / 0.06 m
k = 50 N/m

Answer: The spring constant is 50 N/m.

See? Not so hard! You just need to be systematic. Well done for following through. Now you understand the physics behind everything that stretches and springs. Keep observing the world around you; physics is everywhere!