Vector and Scalar Quantities

Think of vectors as quantities that need both size and direction to make sense - like telling someone to walk "10 metres north". Scalars only need size, like saying "I weigh 60kg".

The magnitude simply means the size of any physical quantity. Speed, distance, mass, time, and energy are all scalar quantities because direction doesn't matter for them.

Velocity, acceleration, force, momentum, and displacement are vectors because they need direction to be meaningful. For example, saying a car has 50 mph velocity tells you nothing useful - but 50 mph eastward does!

Quick tip: If you can ask "which direction?" about a quantity, it's probably a vector.

What Are Forces?

A force is simply a push or pull acting on an object when it interacts with something else. Every force needs two objects to exist - you can't have a force without something causing it and something receiving it.

Contact forces happen when objects physically touch each other. Think friction when you rub your hands together, tension in a rope you're pulling, or air resistance slowing down a cyclist.

Non-contact forces work across empty space without touching. Gravity pulls you towards Earth, magnetic forces attract or repel magnets, and electrostatic forces make your hair stick to a balloon after rubbing it.

We show forces using free body diagrams - simple drawings with arrows pointing in the direction each force acts.

Remember: Every force has a cause - there's always something creating that push or pull!

Free Body Diagrams and Gravity

Free body diagrams use arrows to show forces acting on objects. Each arrow must be labelled with the force's magnitude (size) and type. You can draw the object as either a square or circle - both work perfectly.

Gravity exists because all matter attracts all other matter. The larger the mass, the stronger the gravitational field, which means greater attraction between objects.

Weight is the force acting on an object due to gravity. It's measured in newtons using a newton meter and always acts downward towards Earth's centre. Earth's gravitational field strength is 9.8 N/kg.

Weight acts through a single point called the centre of mass, which can be inside or outside an object. As mass increases, weight increases proportionally.

Key equation: Weight = mass × gravitational field strength $W = mg$

Weight Calculations and Work Done

Weight and mass are directly proportional - double the mass, double the weight. Use the equation: weight = mass × gravitational field strength. Remember: weight is in newtons, mass in kilograms, gravitational field strength in N/kg.

Work done happens when a force causes an object to move. It's the energy transferred when applying a force over a distance. The equation is: work done = force × distance.

Work done is measured in joules, force in newtons, and distance in metres. Don't convert metres to centimetres - keep everything in standard units for easier calculations.

The bigger the force or the further the distance, the more work gets done. Think about pushing a heavy box across a room - more force or a longer distance means more energy used.

Essential: Work done only happens when there's movement in the direction of the force!

Vector Diagrams and Resultant Forces

Vector diagrams help you find the combined effect of multiple forces. Draw vectors to scale $like 1 cm = 2 N$, then draw the resultant vector as a diagonal arrow from start to finish.

Measure the resultant's length and angle using a ruler and protractor. Accurate measurements and clear labelling are crucial for getting the right answer in exams.

The resultant force is the sum of all forces acting on an object. It's like having one single force that produces the same effect as all the individual forces combined.

When forces are unbalanced, there's a resultant force acting on the object, which causes changes in motion. Balanced forces mean no resultant force and no change in motion.

Exam tip: Always use a ruler and protractor for vector diagrams - freehand drawings won't get you marks!

Newton's Three Laws of Motion

Newton's second law connects force, mass, and acceleration: resultant force = mass × acceleration. A bigger resultant force means greater acceleration, while heavier objects accelerate less with the same force.

Newton's first law explains that objects only change velocity when a force is applied. Moving objects keep moving at constant velocity unless a resultant force acts on them. Stationary objects stay put unless pushed or pulled.

This applies whether something's moving or still - without a resultant force, nothing changes. Your bike keeps rolling at steady speed on flat ground because the forces are balanced.

Newton's third law states that forces always come in pairs. When two objects interact, they exert equal and opposite forces on each other. When you push a wall, it pushes back with equal force.

Remember: Every action has an equal and opposite reaction - forces are always mutual!

Stretching and Hooke's Law

Forces can stretch, bend, or compress objects, but this only happens when multiple forces act on stationary objects. Think about pulling a spring or squashing a sponge.

Elastic deformation means objects return to their original shape when the force stops - like a rubber band. Inelastic deformation means permanent change - like bending a paperclip too far.

Hooke's law describes how springs behave. The extension-load graph shows force on the y-axis and extension on the x-axis. At low forces, you get a straight line through the origin.

The line stays straight until reaching the limit of proportionality, where the spring can't stretch proportionally anymore and the line curves.

Key equation: Force = spring constant × extension $F = kx$

Investigating Hooke's Law

To investigate Hooke's law, measure the spring's original length first. Then hang different masses and measure how much longer it gets. The extension equals the loaded length minus the original length.

Plot a graph with extension on the x-axis and force on the y-axis. You'll get a straight line through the origin until reaching the limit of proportionality.

Add masses gradually to increase the downward force. Each measurement gives you another point for your graph. The slope of the straight section gives you the spring constant.

Extension = length of loaded spring - natural length of spring. This simple equation helps you calculate exactly how much the spring has stretched under each load.

Lab tip: Take several readings for each mass to improve accuracy and spot any anomalies!

Elastic Potential Energy and Motion

When forces stretch or compress objects, they transfer energy into an elastic potential energy store. This energy gets stored unless the object deforms inelastically and can't spring back.

The energy stored equals the area under the force-extension graph, or use: elastic potential energy = ½ × force × extension.

Distance is how far an object moves (scalar quantity), while displacement is the distance and direction of a straight line from start to finish (vector quantity).

Think about walking around a circular track - your distance might be 400m, but your displacement could be zero if you end up back where you started.

Important distinction: Distance is the total journey length; displacement is the direct route from start to finish!