Science (Double Award) | Forces and motion

Welcome to Forces and Motion!

Hello future physicists! This chapter is the foundation of all movement you see around you, from a planet orbiting the Sun to you cycling to school. Understanding Forces and Motion is crucial because it explains why things move and how we can predict that movement.

Don't worry if some of the formulas look challenging at first. We will break down every concept into small, easy-to-understand steps, using everyday examples to make the physics stick! Let's get moving!

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Section 1: Describing Movement (Kinematics)

1.1 Scalars and Vectors

In physics, we classify quantities based on whether they involve direction. This is a very important distinction!

• Scalar Quantity: Only has a magnitude (size).
  Examples: Distance, Speed, Mass, Time, Energy.
• Vector Quantity: Has both magnitude and direction.
  Examples: Displacement, Velocity, Force, Acceleration, Momentum.

Distance vs. Displacement

This is a classic tricky pair!

Distance (Scalar): The total path length travelled. If you walk 5m north and then 5m south, your total distance is 10m.

Displacement (Vector): The shortest path from the start point to the end point, including direction. If you walk 5m north and 5m south, your final displacement is 0m.

1.2 Speed and Velocity

Most people use these words interchangeably, but in physics, they are different!

Speed (Scalar) is the rate of change of distance.
$$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$$ $$v = \frac{d}{t}$$

Velocity (Vector) is the rate of change of displacement. It is speed in a specific direction.

1.3 Acceleration

Acceleration is about changing velocity. You accelerate when you speed up, slow down, or change direction.

Acceleration (Vector) is the rate of change of velocity.

• Units: metres per second squared ($m/s^2$).
• When you slow down, this is sometimes called deceleration (which is just negative acceleration).

$$\text{Acceleration} = \frac{\text{Change in Velocity}}{\text{Time Taken}}$$ $$a = \frac{v - u}{t}$$

Where:
$a$ = acceleration ($m/s^2$)
$v$ = final velocity ($m/s$)
$u$ = initial velocity ($m/s$)
$t$ = time taken ($s$)

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Section 2: Analysing Motion with Graphs

2.1 Distance-Time Graphs

These graphs show how far an object has moved from its starting point over time.

What the graph tells you:

• Gradient (Steepness): The gradient of a distance-time graph represents the Speed.
• Horizontal Line (Zero Gradient): The object is Stationary (not moving).
• Straight Line (Constant Gradient): The object is moving at a Constant Speed.
• Curving Upwards (Increasing Gradient): The object is Accelerating (getting faster).

2.2 Velocity-Time Graphs

These graphs are powerful because they show not only speed but also acceleration and the total distance travelled!

What the graph tells you:

• Gradient: The gradient of a velocity-time graph represents the Acceleration.
  • Positive gradient = Acceleration.
  • Zero gradient (horizontal line) = Constant Velocity (Zero acceleration).
  • Negative gradient = Deceleration (Slowing down).
• Area under the Graph: The area under the line on a velocity-time graph represents the Distance Travelled (or displacement).

Don't worry if finding the area seems tricky. If the area is a rectangle or a trapezium (trapezoid), you use simple geometry formulas to calculate it!

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Section 3: Forces and Newton's Laws

3.1 Understanding Force

A Force is simply a push or a pull. Forces are measured in Newtons (N). Since a force must act in a specific direction, force is a Vector Quantity.

Common forces we deal with:

• Gravity (Weight): Pulling things down.
• Friction: Opposes motion when two surfaces rub.
• Air Resistance (Drag): Opposes motion through the air.
• Tension: Pulling force in ropes or cables.
• Reaction Force (Normal Contact Force): The force exerted by a surface perpendicular to the object resting on it.

3.2 Resultant Force

The Resultant Force (or net force) is the single force that could replace all the forces acting on an object and have the same effect.

• If forces act in the same direction, you add them.
• If forces act in opposite directions, you subtract them.
• If the resultant force is Zero, the forces are Balanced.

Example: If a car engine pushes with 500 N and air resistance pulls back with 100 N, the resultant force is $500 - 100 = 400 N$ (in the direction of motion).

3.3 Newton's Laws of Motion

1. Newton’s First Law (The Law of Inertia)

Statement: An object will remain at rest, or continue to move at a constant velocity, unless acted upon by a Resultant Force.

In simpler terms: If the forces are balanced (Resultant Force = 0 N), the object is either standing still OR moving at a perfectly steady speed in a straight line. You need an unbalanced force to change motion (to accelerate).

Inertia is the tendency of an object to resist changes in its motion. The more mass an object has, the more inertia it has.

2. Newton’s Second Law (\(F = ma\))

This is the most important equation in this section. It links force, mass, and acceleration.

Statement: The acceleration of an object is directly proportional to the resultant force acting on it, and inversely proportional to its mass.

$$F = m \times a$$ $$\text{Resultant Force (N)} = \text{Mass (kg)} \times \text{Acceleration} (m/s^2)$$

Memory Aid: If you push a small car (low mass) with a big force, it gets a big acceleration. If you push a truck (high mass) with the same force, it gets a small acceleration.

3. Newton’s Third Law

Statement: Whenever two objects interact, the forces they exert on each other are equal in magnitude and opposite in direction.

This is often simplified to: "For every action, there is an equal and opposite reaction."

Example: When you stand on the floor, your weight pushes down on the floor (Action force). The floor pushes back up on you with an equal and opposite Normal Contact Force (Reaction force).

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Section 4: Mass, Weight, and Gravitational Effects

4.1 Mass and Weight

These are often confused!

• Mass (m): The amount of matter in an object.
  • Scalar quantity.
  • Measured in kilograms (kg).
  • Mass stays the same wherever you are (Earth, Moon, or space).
• Weight (W): The force of gravity acting on an object.
  • Vector quantity (it always acts downwards).
  • Measured in Newtons (N).
  • Weight changes depending on the planet's gravity.

4.2 Calculating Weight

Weight is related to mass by the gravitational field strength ($g$).

$$W = m \times g$$ $$\text{Weight (N)} = \text{Mass (kg)} \times \text{Gravitational Field Strength (N/kg)}$$

On Earth, the gravitational field strength ($g$) is approximately $9.8 N/kg$ (often rounded to $10 N/kg$ for simple calculations).

4.3 Terminal Velocity

When an object falls through a fluid (like air or water), it experiences drag (air resistance). This drag increases as speed increases.

Let's look at the example of a skydiver:

1. Start: When the skydiver jumps, the only downward force is Weight. Air resistance is zero. Weight > Air Resistance, so the skydiver accelerates.
2. Increasing Speed: As speed increases, the air resistance force increases. Acceleration decreases, but the skydiver is still speeding up.
3. Terminal Velocity Reached: Eventually, the air resistance force becomes exactly equal to the weight of the skydiver. The forces are balanced (Resultant Force = 0 N). According to Newton’s First Law, the acceleration becomes zero, and the skydiver falls at a steady, maximum speed called the Terminal Velocity.

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Section 5: Momentum

5.1 Defining Momentum

Momentum (p) is the 'quantity of motion' an object possesses. It measures how difficult it is to stop a moving object.

Momentum is a Vector Quantity (it has direction).

Momentum depends on two factors: Mass (m) and Velocity (v).

$$p = m \times v$$ $$\text{Momentum} (kg\,m/s) = \text{Mass} (kg) \times \text{Velocity} (m/s)$$

Did You Know?

A large truck moving slowly can have far more momentum than a small bullet moving very fast! Mass is a massive factor.

5.2 Conservation of Momentum

This is one of the most fundamental laws of physics, especially important when studying collisions and explosions.

Law of Conservation of Momentum: In a closed system (where no external forces, like friction, act), the total momentum before a collision is equal to the total momentum after the collision.

$$(m_1 \times u_1) + (m_2 \times u_2) = (m_1 \times v_1) + (m_2 \times v_2)$$

(Where $u$ is initial velocity and $v$ is final velocity for objects 1 and 2.)

Key Takeaway for Conservation: Momentum is never lost, it is just transferred between objects. This is why when two snooker balls collide, one stops and the other moves away.

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Section 6: Forces in Action – Road Safety

6.1 Stopping Distance

The total distance a vehicle travels from the moment the driver decides to stop until the moment the vehicle is fully stationary is called the Stopping Distance.

$$\text{Stopping Distance} = \text{Thinking Distance} + \text{Braking Distance}$$

1. Thinking Distance

The distance travelled while the driver is reacting to the hazard and deciding to brake.

• Factors that increase Thinking Distance: Tiredness, alcohol/drugs, distraction (e.g., mobile phones), high speed.

2. Braking Distance

The distance travelled from the moment the brakes are applied until the vehicle stops.

• Factors that increase Braking Distance: High speed (crucially, braking distance increases much faster than speed—it is proportional to $v^2$), poor road conditions (ice, water), worn brakes or tires, greater mass/load of the vehicle.

6.2 Safety and Friction

Braking relies heavily on Friction between the tires and the road surface.

• If the friction is poor (wet, icy roads), the force available to slow the car down is reduced.
• According to $F=ma$, if the braking force ($F$) decreases, the deceleration ($a$) decreases, meaning it takes much longer (and therefore much further) to stop.