Forces and motion

Welcome to Forces and Motion!

Ever wondered why you lurch forward when a bus brakes suddenly, or why it’s harder to stop a fast-moving bicycle than a slow one? This chapter is all about the rules that govern how things move. We will look at speed, acceleration, and the famous laws of Sir Isaac Newton. Don't worry if this seems like a lot of math at first—we'll break it down into simple, real-world steps!

1. Speed and Velocity: What’s the Difference?

In everyday life, we use these words to mean the same thing, but in science, they are very different!

Scalars vs. Vectors

To understand motion, we need to know two types of measurements:

1. Scalar quantities: These only have a magnitude (size).
Example: Distance (how far you’ve walked) and Speed (how fast you're going).

2. Vector quantities: These have both magnitude (size) AND a direction.
Example: Displacement (how far you are from your start point in a straight line) and Velocity (speed in a specific direction).

Typical Speeds to Remember

You should have a rough idea of how fast things move in the real world:

• Walking: ~1.5 m/s
• Running: ~3 m/s
• Cycling: ~6 m/s
• Sound in air: ~330 m/s

Did you know? The speed of sound can change depending on the temperature of the air!

Quick Review: If a car travels at 20 m/s around a circular track, its speed is constant, but its velocity is constantly changing because its direction is changing!

Key Takeaway: Vectors care about direction; scalars do not.

2. Calculating Motion

We use a simple formula to link distance, speed, and time when an object moves at a constant speed:

\( \text{distance travelled} = \text{speed} \times \text{time} \)

Symbolically: \( s = v t \)

• \( s \) = distance (metres, m)
• \( v \) = speed (metres per second, m/s)
• \( t \) = time (seconds, s)

Distance-Time Graphs

You can tell a lot about a journey by looking at a graph:

• The Gradient (slope): Represents the speed. A steeper line means a higher speed.
• A Flat horizontal line: The object is stationary (not moving).
• (HT only) Tangents: If the line is curved, the object is accelerating. You find the speed at a specific point by drawing a tangent to the curve and calculating its gradient.

Key Takeaway: Steep slope = Fast; Flat line = Stopped.

3. Acceleration and Free Fall

Acceleration is the rate at which velocity changes. If you speed up, slow down, or change direction, you are accelerating!

The formula for acceleration is:

\( a = \frac{\Delta v}{t} \)

• \( a \) = acceleration (\( m/s^2 \))
• \( \Delta v \) = change in velocity (m/s)
• \( t \) = time (s)

Common Mistake: Forgetting that slowing down is also acceleration (often called deceleration or negative acceleration).

The "Big" Equation

When an object moves with constant acceleration, we use this formula (don't panic, it's on your equation sheet!):

\( v^2 - u^2 = 2 a s \)

• \( v \) = final velocity
• \( u \) = initial velocity
• \( a \) = acceleration
• \( s \) = distance

Gravity and Terminal Velocity

Near the Earth’s surface, any object falling freely has an acceleration of about 9.8 \( m/s^2 \).

When an object falls through a fluid (like air), it initially speeds up. Eventually, the friction (air resistance) equals the weight of the object. The resultant force becomes zero, and the object stops speeding up. This is called terminal velocity.

Key Takeaway: Falling objects speed up at 9.8 \( m/s^2 \) until air resistance balances them out.

4. Newton’s Laws of Motion

Sir Isaac Newton came up with three rules that everything in the universe follows.

Newton’s First Law (The Law of Inertia)

If the resultant force on an object is zero:

• If it's stationary, it stays stationary.
• If it's moving, it keeps moving at the same speed and in the same direction.

Newton’s Second Law (The "Push" Law)

The acceleration of an object is proportional to the force applied and inversely proportional to its mass.

\( F = m a \)

• \( F \) = Resultant force (Newtons, N)
• \( m \) = Mass (kg)
• \( a \) = Acceleration (\( m/s^2 \))

(HT only) Inertial Mass: This is just a measure of how difficult it is to change the velocity of an object. It's defined as the ratio of Force over Acceleration (\( m = F/a \)).

Newton’s Third Law (The "Pair" Law)

Whenever two objects interact, the forces they exert on each other are equal and opposite.

Example: If you push on a wall, the wall pushes back on you with the exact same amount of force.

Key Takeaway: No resultant force = No change in motion. \( F = ma \) is the golden rule.

5. Momentum, Energy, and Work

Momentum (HT Only)

Momentum is a property of moving objects. Think of it as how much "oomph" an object has.

\( p = m v \)

In a closed system, the total momentum before an event (like a crash) is the same as the total momentum after. This is called the conservation of momentum.

Kinetic Energy

Anything that moves has kinetic energy. The amount depends on mass and speed:

\( E_k = \frac{1}{2} m v^2 \)

Important Point: Because the velocity is squared, doubling your speed actually quadruples your kinetic energy! This is why fast cars are so dangerous.

Work Done

When a force moves an object, "work is done" and energy is transferred.

\( W = F s \)

One Joule of work is done when a force of 1 Newton moves an object 1 metre.

Key Takeaway: More speed = way more energy. Work is just energy being used by a force.

6. Stopping Distances

This is a vital topic for road safety. The Total Stopping Distance of a car is made of two parts:

Stopping Distance = Thinking Distance + Braking Distance

1. Thinking Distance

The distance the car travels while the driver reacts. It is affected by:

• Speed: The faster you go, the further you travel while reacting.
• Reaction Time: Affected by tiredness, drugs, alcohol, or distractions (like mobile phones).

2. Braking Distance

The distance the car travels after the brakes are applied. It is affected by:

• Speed: Higher speed = much longer braking distance.
• Road conditions: Wet or icy roads reduce friction.
• Vehicle condition: Worn brakes or bald tyres.

The Danger of Large Decelerations

When you brake hard, the friction between the brakes and the wheels does work. This transfers kinetic energy into thermal energy (heat). If the deceleration is too large, the brakes can overheat or the driver can lose control.

Memory Aid: Thinking is in your Head (Reaction factors). Braking is in the Car (Mechanical/Road factors).

Key Takeaway: Double the speed doesn't just double the stopping distance—it increases it significantly because of the \( v^2 \) in the kinetic energy formula!

Quick Review Box

• Vector: Magnitude + Direction.
• \( F = ma \): Force = Mass x Acceleration.
• Resultant Force = 0: Constant velocity or stationary.
• Stopping Distance: Thinking + Braking.