Forces and motion, and momentum (HT only)

Introduction to Forces and Motion

In this chapter, we look at how and why things move. Whether it’s a car braking, a skydiver falling, or two bumper cars colliding, the same rules of physics apply. We will explore the relationship between forces, acceleration, and a special property called momentum. Don't worry if it seems like there are many formulas; we will break them down step-by-step!

1. Describing Motion

To understand motion, we need to distinguish between how far something has traveled and its direction.

Distance vs. Displacement

Distance is a scalar quantity. it only tells us how far an object has moved (e.g., 50 meters).
Displacement is a vector quantity. It includes both the distance and the direction in a straight line from the start to the end point (e.g., 50 meters North).

Speed and Velocity

Just like distance and displacement, speed and velocity are different:
1. Speed is scalar (how fast you are going).
2. Velocity is a vector (speed in a specific direction).

The formula for distance traveled is:
\( s = v t \)
Where \( s \) is distance (m), \( v \) is speed (m/s), and \( t \) is time (s).

Acceleration

Acceleration is the rate at which velocity changes. If an object speeds up, slows down, or changes direction, it is accelerating.
The formula for acceleration is:
\( a = \frac{\Delta v}{t} \)
Where \( a \) is acceleration (\( m/s^2 \)), \( \Delta v \) is the change in velocity (m/s), and \( t \) is time (s).

The Equation Sheet Special: There is another formula you will be given for objects with constant acceleration:
\( v^2 - u^2 = 2 a s \)
Where \( v \) is final velocity, \( u \) is initial velocity, \( a \) is acceleration, and \( s \) is distance.

Quick Review: Scalar quantities only have size (magnitude). Vector quantities have both magnitude and direction.

2. Newton’s Laws of Motion

Sir Isaac Newton described three laws that explain how forces affect motion.

Newton’s First Law (Inertia)

If the resultant force acting on an object is zero:
- A stationary object will stay stationary.
- A moving object will continue to move at the same speed and in the same direction (constant velocity).

Newton’s Second Law

The acceleration of an object is proportional to the resultant force acting on it, and inversely proportional to its mass.
The famous formula is:
\( F = m a \)
Where \( F \) is resultant force (N), \( m \) is mass (kg), and \( a \) is acceleration (\( m/s^2 \)).

Newton’s Third Law

Whenever two objects interact, the forces they exert on each other are equal and opposite. For example, if you push on a wall, the wall pushes back on you with the exact same amount of force.

Common Mistake: Students often think objects only move if there is a force "pushing" them. Newton's First Law reminds us that if an object is already moving, it doesn't need a force to keep moving—it only needs a force to change its motion.

3. Terminal Velocity

When an object starts falling through a fluid (like air or water), it doesn't keep speeding up forever. It eventually reaches a steady speed called terminal velocity.

Stages of Falling:

1. Initial Fall: The object accelerates because the force of gravity (weight) is much larger than the air resistance.
2. Increasing Speed: As the object gets faster, the air resistance increases.
3. Terminal Velocity: Eventually, the air resistance increases until it exactly balances the weight. The resultant force is now zero, so the acceleration stops. The object falls at a constant speed.

4. Forces and Braking

The stopping distance of a vehicle is the total distance it travels from the moment the driver sees a hazard to the moment the car completely stops.

Stopping Distance = Thinking Distance + Braking Distance

Thinking Distance

This is the distance traveled during the driver's reaction time.
Affected by: Speed, tiredness, drugs, alcohol, and distractions (like mobile phones).

Braking Distance

This is the distance traveled once the brakes are applied.
Affected by: Speed, adverse road conditions (ice/wet), and the condition of the vehicle (worn brakes or tires).

Key Fact: When the brakes are applied, work is done by friction between the brakes and the wheels. This transfers kinetic energy from the car into thermal energy (heat) in the brakes, causing them to get hot.

5. Momentum (Higher Tier Only)

Momentum is a property that all moving objects have. It depends on the mass and the velocity of the object.

The formula for momentum is:
\( p = m v \)
Where \( p \) is momentum (kg m/s), \( m \) is mass (kg), and \( v \) is velocity (m/s).

Conservation of Momentum

In a closed system, the total momentum before an event is equal to the total momentum after the event. An "event" is usually a collision or an explosion.

Example: If a moving trolley hits a stationary one and they stick together, their combined mass will move slower than the original trolley to keep the total momentum the same.

Step-by-Step Momentum Calculation:
1. Calculate the momentum of object A (\( m \times v \)).
2. Calculate the momentum of object B.
3. Add them together to get the total "Before" momentum.
4. Set this equal to the "After" momentum to find a missing mass or velocity.

Required Practical 19: Force and Acceleration

In this practical, you investigate how changing the force or the mass affects the acceleration of a trolley.

The setup: A trolley is pulled by a string over a pulley, with masses hanging on the end to provide the force (\( F = m g \)).
To vary force: Move masses from the trolley onto the hanging hook (this keeps the total mass of the system constant while changing the pulling force).
To vary mass: Add masses onto the trolley but keep the hanging weight the same.
Result: You should find that acceleration is directly proportional to force (\( a \propto F \)).

Summary: Key Takeaways

1. Vectors: Velocity, displacement, acceleration, and force are vectors; they have direction.
2. Newton’s 2nd Law: \( F = m a \) is the most important equation for calculating how forces change motion.
3. Terminal Velocity: Occurs when air resistance equals weight, resulting in zero acceleration.
4. Stopping Distance: Higher speeds significantly increase both thinking and braking distances.
5. Momentum (HT): Momentum is always conserved in collisions; use \( p = m v \) to solve these problems.