Forces and motion

Welcome to Forces and Motion!

Ever wondered why you lurch forward when a bus slams on its brakes, or why it’s harder to stop a speeding car than a walking person? That’s exactly what we are going to explore! In this chapter, we’ll look at how things move and the rules (laws) they have to follow. Don’t worry if some of the math looks scary at first—we will break it down step-by-step.

1. Describing Motion

Before we can talk about forces, we need to know how to describe how things move. It’s all about distance, speed, and direction.

Distance vs. Displacement

These two sound the same, but they are very different in Physics!

• Distance is just how far you have travelled. It doesn't care about direction. This is a scalar quantity.
• Displacement is the straight-line distance from your start point to your finish point, plus the direction. This is a vector quantity.

Analogy: If you walk 10 meters away from your front door and then 10 meters back, your distance is 20m, but your displacement is 0m because you ended up exactly where you started!

Speed and Velocity

• Speed is how fast you are going (scalar).
• Velocity is speed in a given direction (vector).

Typical Speeds you need to remember:
• Walking: ~1.5 m/s
• Running: ~3 m/s
• Cycling: ~6 m/s
• Speed of sound in air: 330 m/s

The Main Equation:
For constant speed:
\( distance\ travelled = speed \times time \)
\( s = v \times t \)

Note: In physics, we use s for distance/displacement and v for speed/velocity.

Distance-Time Graphs

We use these to "see" motion:
• A straight, upwards line means constant speed.
• A flat horizontal line means the object is stationary (stopped).
• The slope (gradient) of the line tells you the speed.

Quick Review:
Scalar: Size only (e.g., speed, distance).
Vector: Size AND direction (e.g., velocity, displacement).

Acceleration

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

The Equation:
\( acceleration = \frac{change\ in\ velocity}{time\ taken} \)
\( a = \frac{\Delta v}{t} \)
(Measured in \( m/s^2 \))

Velocity-Time Graphs:
• Gradient: Tells you the acceleration.
• Flat line: Constant velocity (NOT stopped!).
• Area under the graph (HT only): Tells you the distance travelled.

Key Takeaway

Velocity includes direction; speed does not. To find speed from a distance-time graph, look at the slope.

2. Newton’s Laws of Motion

Isaac Newton figured out three rules that everything in the universe follows. These are the "rules of the game" for physics.

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 exact same velocity (same speed and direction).

Did you know? If you threw a ball in deep space, it would keep going in a straight line forever because there is no air resistance or gravity to stop it!

Newton’s Second Law (F = ma)

This is arguably the most important equation in Physics. It says that the acceleration of an object depends on the force applied and the mass of the object.

The Equation:
\( resultant\ force = mass \times acceleration \)
\( F = m \times a \)

What this means:
1. The more force you use, the more something accelerates.
2. The heavier (more mass) something is, the more force you need to make it accelerate.

Newton’s Third Law

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

Example: When you sit on a chair, you push down on the chair, and the chair pushes back up on you with the exact same force. If it didn't, you'd fall through it!

Common Mistake to Avoid:
Students often think Newton's Third Law forces cancel each other out. They don't! They act on different objects (the person and the chair).

Key Takeaway

Force equals mass times acceleration (\( F=ma \)). If forces are balanced, velocity doesn't change.

3. Forces and Braking

This section is vital for road safety and often appears in exams with real-world data.

Stopping Distance

The total distance it takes for a car to stop is made of two parts:
Stopping Distance = Thinking Distance + Braking Distance

1. Thinking Distance: How far the car travels while you react.
• Affected by: Speed, Tiredness, Alcohol/Drugs, Distractions (like phones).

2. Braking Distance: How far the car travels after you hit the brakes.
• Affected by: Speed, Weather (wet/icy roads), Vehicle condition (worn tires or brakes).

The Physics of Braking

When you press the brake pedal, the brake pads press against the wheels. This creates friction.
• Work is done by the brakes.
• Kinetic energy of the car is transferred into thermal (heat) energy in the brakes.
• This is why brakes get very hot after a long hill!

Danger: If a car is going twice as fast, it has four times the kinetic energy. This means the braking distance increases massively as you speed up.

Key Takeaway

Stopping distance depends on both the driver's reaction and the car's physical ability to grip the road. Speed affects both!

4. Momentum (Higher Tier Only)

Momentum is a property of all moving objects. It’s basically "mass in motion."

The Equation:
\( momentum = mass \times velocity \)
\( p = m \times v \)
(Measured in \( kg\ m/s \))

Conservation of Momentum

In a closed system (where no outside forces act), the total momentum before an event (like a collision) is the same as the total momentum after the event.

Example: If a moving trolley hits a stationary one and they stick together, they will move slower because the mass has increased, but the total momentum remains the same.

Safety Features

Airbags, seatbelts, and crumple zones save lives by increasing the time it takes for you to stop during a crash.
Since \( Force = \frac{change\ in\ momentum}{time} \), increasing the time reduces the force acting on your body!

Memory Trick:
To remember the safety rule: More Time = Less Force.

Key Takeaway

Momentum is always conserved in collisions. Safety features work by stretching out the time of an impact to lower the force.