Resultant Forces and Newton's First Law

Ever wondered why a book stays put on your desk until you push it? It's all about resultant force - the overall force acting on an object after you add up all the individual forces.

When forces are balanced $resultant force = 0$, objects either stay still or keep moving at the same speed in the same direction. This is Newton's First Law in action. Think of a car cruising at constant speed on a motorway - the driving force equals the air resistance and friction.

When forces are unbalanced, you get movement or a change in motion. The object will accelerate in the direction of the larger force. Work done happens when a force moves an object through a distance, and it's measured using the formula W = Fs $work = force × distance$.

Quick Tip: You can break down any single force into horizontal and vertical parts using trigonometry - super useful for solving physics problems!

Forces and Elasticity

You actually need two forces to stretch, compress, or bend any object - otherwise it would just fly off in one direction! This is why springs and elastic bands work the way they do.

Elastic deformation means the material bounces back to its original shape (like a rubber band), whilst plastic deformation means it stays permanently changed (like bending a paperclip). When you stretch something, you're converting energy from kinetic to elastic potential energy.

Hooke's Law states that extension is directly proportional to the applied force - until you reach the limit where things get permanently stretched. The formula is F = Ke, where K is the spring constant (how stiff the spring is).

You can test this yourself by hanging masses from a spring and measuring how much it stretches. Plot force against extension and you'll get a straight line through the origin - the gradient gives you the spring constant.

Real-world Connection: This principle is used in everything from car suspension systems to weighing scales!

Moments, Levers and Gears

A moment is simply the turning effect of a force - think about using a spanner to tighten a bolt or opening a heavy door. The formula is M = Fd $moment = force × perpendicular distance from the pivot$.

Levers are brilliant force multipliers that make our lives easier. Whether you're using scissors, a bicycle, or a door handle, you're applying the principle of moments: for any object in equilibrium, clockwise moments = anticlockwise moments.

The centre of mass is where an object's weight acts from. For symmetrical objects, it's where the lines of symmetry cross. For irregular shapes, you can find it by suspending the object from different points and seeing where the lines intersect.

Gears change the relationship between speed and turning force. A gear ratio of 4:1 means the driver gear turns 4 times for every 1 turn of the driven gear - giving you more force but less speed (perfect for cycling up hills!).

Try This: Notice how gears on bikes work - low gears give you more turning force for hills, high gears give you more speed on flat roads.

Pressure in Fluids

Pressure is force acting perpendicular to a surface per unit area, measured in pascals (Pa). The deeper you go in any liquid, the greater the pressure becomes because there's more mass of liquid pushing down above you.

The key formula is p = hρg $pressure = height × density × gravitational field strength$. This explains why your ears pop when diving deep into a swimming pool, or why dams are thicker at the bottom than the top.

Upthrust is the upward force that acts on anything submerged in a fluid. It happens because there's greater pressure (and therefore greater upward force) on the bottom surface than the downward force on the top surface.

Whether something floats or sinks depends on density. If an object is less dense than the fluid it's in, it will float. The upthrust equals the weight of fluid that gets displaced - this is why ships made of steel can still float on water.

Fun Fact: The same principles that make helium balloons float in air also make oil float on water!

Describing Motion Along a Line

Distance is how far you've travelled (scalar), whilst displacement is how far you are from your starting point in a straight line (vector). You could walk 5km around a track but have zero displacement if you end up where you started!

Speed is distance per second (scalar), but velocity includes direction (vector). You can have constant speed whilst changing velocity - like moving in a circle at constant speed but constantly changing direction.

Typical speeds you should know: walking $~1.5 m/s$, cycling $~6 m/s$, cars on motorways $~30 m/s$, sound $~330 m/s$. Use s = vt to calculate distance travelled.

Acceleration is the change in velocity per second, calculated using a = Δv/t. On distance-time graphs, the gradient gives you speed. On velocity-time graphs, the gradient gives you acceleration and the area under the line gives you distance travelled.

Memory Trick: Remember that acceleration can mean speeding up, slowing down, or changing direction!

Forces and Braking

Stopping distance is the total distance your car travels from when you first notice a hazard until you completely stop. It's made up of thinking distance (while you react) plus braking distance (while the brakes work).

Reaction time for humans is typically 0.2-0.9 seconds, but it increases with tiredness, alcohol, drugs, or distractions like mobile phones. During this time, you're still travelling at full speed - which is why it's so dangerous!

Key stopping distances to remember: 30 mph = 23m total, 70 mph = 100m total. Notice that doubling your speed roughly quadruples your stopping distance because kinetic energy increases with the square of velocity.

Braking distance increases with vehicle mass, poor brake/tyre condition, and slippery road surfaces. When brakes work, they convert kinetic energy to thermal energy, which is why brakes get hot and can overheat during heavy braking.

Safety Note: This is why speed limits exist and why you should never tailgate other vehicles!

Momentum and Collisions

Momentum is mass × velocity (p = mv) and it's a vector quantity, so direction matters. A large truck moving slowly can have the same momentum as a small car moving fast.

The law of conservation of momentum states that in a closed system (no external forces), momentum before an event equals momentum after. This applies to collisions, explosions, and even rockets launching into space.

For collisions where objects stick together: M₁u₁ + M₂u₂ = $M₁ + M₂$v. For explosions where objects start stationary: 0 = M₁v₁ + M₂v₂.

Force can also be calculated as F = mΔv/Δt - the rate of change of momentum. This explains why airbags and crumple zones work: they increase the impact time, which reduces the force for a given momentum change.

Real-world Application: This principle explains why shin pads protect footballers - they increase impact time, reducing the force of impact!