Forces and Gravity

Every push, pull, or twist you experience is a force - and they come in two main types. Contact forces happen when objects touch (like friction when you rub your hands together), whilst non-contact forces work at a distance (like gravity pulling objects downward).

Here's what makes forces special: they're vector quantities, meaning they have both strength and direction. This is crucial because a 10N force pushing left has a completely different effect than 10N pushing right.

Weight is simply gravity's pull on your mass, calculated as weight = mass × gravitational field strength $9.8 N/kg on Earth$. Your mass stays the same everywhere, but your weight would be different on the Moon because gravity is weaker there.

Quick Check: Your bathroom scales actually measure your weight, not your mass - they just convert it to show kilograms!

When multiple forces act on an object, we can replace them with a single resultant force that has the same overall effect. Work happens when forces cause movement: work done = force × distance moved.

Elasticity and Hooke's Law

Springs and elastic bands follow a surprisingly predictable pattern called Hooke's Law: the force needed to stretch them is directly proportional to how much you extend them. Think of it as "double the force, double the stretch."

This relationship works perfectly until you reach the limit of proportionality. Beyond this point, you've overstretched the material and it won't return to its original shape - that's inelastic deformation.

The key equation is: force = spring constant × extension. The spring constant tells you how stiff the spring is - a higher value means you need more force to stretch it the same distance.

Real-world Connection: Car suspension systems use springs within their elastic limits to absorb bumps whilst returning to their original position.

When you stretch a spring, you're storing elastic potential energy (0.5 × spring constant × extension²). This energy gets released when the spring returns to its original length, which is why catapults and trampolines work so effectively.

Moments, Levers and Gears

Moments are the turning effects of forces - they're what make spanners work and doors swing open. The moment equals force × perpendicular distance from the pivot, measured in newton-metres.

For any balanced object, clockwise moments exactly equal anticlockwise moments around the pivot. This principle explains why seesaws balance and why you can use a long spanner to loosen tight bolts with less effort.

Levers are brilliant force multipliers. By applying a small force over a long distance from the pivot, you can move heavy loads with much less effort. Crowbars, scissors, and bottle openers all work on this principle.

Gears transfer rotational motion between wheels. When a small gear drives a larger one, you get more turning force (moment) but slower rotation. When a large gear drives a smaller one, you get faster rotation but less turning force.

Remember: Gears that touch each other always rotate in opposite directions - this is crucial for understanding gear systems.

Pressure and Fluids

Pressure measures how much force spreads over an area: pressure = force ÷ area. This explains why sharp knives cut easily (small area, high pressure) whilst lying on a bed of nails doesn't hurt much (large area, low pressure).

In liquids, pressure increases with depth because there's more liquid pressing down from above. The equation is: pressure = height × density × gravitational field strength. This is why your ears pop when swimming deep underwater.

Upthrust is the upward force that makes things float. When an object is submerged, the pressure is greater on the bottom surface than the top, creating a net upward force. Whether something floats depends on whether upthrust equals or exceeds the object's weight.

Density Matters: Objects less dense than the fluid they're in will float, whilst denser objects sink - this is why ice floats on water.

Atmospheric pressure decreases with altitude because there's less air pressing down from above. This is why mountaineers need oxygen masks and why your ears pop on planes.

Motion Basics

Distance and displacement might sound similar, but they're quite different. Distance is simply how far you've travelled (a scalar), whilst displacement includes direction and measures the straight-line distance from start to finish (a vector).

Speed tells you how fast something moves without considering direction, making it a scalar quantity. Typical walking speed is 1.5 m/s, running is about 3 m/s, and cycling averages 6 m/s. Sound travels at roughly 330 m/s through air.

For constant speed, use: distance = speed × time. This simple equation helps you calculate journey times or work out how fast you were moving.

Velocity is speed with direction included, making it a vector quantity. This distinction becomes crucial when analysing motion in physics problems.

Pro Tip: On distance-time graphs, the steeper the line, the faster the object is moving - the gradient equals the speed.

Velocity and Acceleration

Velocity combines speed and direction, so an object changing direction (even at constant speed) has changing velocity. This vector nature makes velocity calculations more complex but much more useful for real-world applications.

Acceleration measures how quickly velocity changes: acceleration = change in velocity ÷ time. Objects can accelerate by speeding up, slowing down, or changing direction. Slowing down is called deceleration.

On velocity-time graphs, the gradient gives you acceleration, whilst the area under the curve shows distance travelled. These graphs are incredibly useful for analysing motion.

The key equation for uniform acceleration is: v² - u² = 2as, where v is final velocity, u is initial velocity, a is acceleration, and s is distance.

Gravity Facts: Near Earth's surface, all objects fall with the same acceleration of 9.8 m/s² (ignoring air resistance).

Terminal velocity occurs when falling objects stop accelerating because air resistance balances gravitational force. Parachutes work by dramatically increasing air resistance to reduce terminal velocity.

Forces and Braking

Stopping distance combines two parts: thinking distance (how far you travel whilst reacting) plus braking distance (how far you travel whilst stopping). Both increase significantly with speed, making speeding extremely dangerous.

Reaction times typically range from 0.2 to 0.9 seconds, but tiredness, alcohol, drugs, and distractions can dramatically increase this. Even small delays have huge consequences at high speeds.

Braking distance depends on road conditions, weather, and vehicle condition. Wet or icy roads, worn tyres, or faulty brakes all increase stopping distances dangerously.

When you brake, friction converts the vehicle's kinetic energy into heat energy, warming the brakes. Harder braking means more heat, which can cause brake failure if they overheat.

Critical Point: Stopping distance increases with the square of speed - double the speed means roughly four times the stopping distance.

Higher speeds require much greater braking forces to stop in the same distance. Excessive braking forces can cause skidding, loss of control, or brake failure.

Momentum

Momentum equals mass × velocity, giving us a measure of how much "oomph" a moving object has. Heavy objects and fast objects both have high momentum, making them harder to stop.

The conservation of momentum principle states that in collisions, total momentum before equals total momentum after. This fundamental law helps us analyse crashes and explosions.

Force relates to momentum through: F = change in momentum ÷ time. This explains why safety features work by extending collision times rather than preventing them entirely.

Airbags inflate during crashes to increase the time over which passengers slow down, reducing the average force on their bodies. This significantly decreases injury risk.

Safety Connection: Seatbelts, crash mats, helmets, and playground surfaces all work by extending the time taken to change momentum.

Crumple zones in cars deliberately deform during crashes, extending collision time and absorbing energy. This protects passengers by reducing the forces acting on them during the impact.

Newton's Laws of Motion

Newton's First Law states that objects keep doing what they're doing unless a resultant force acts. Stationary objects stay still, moving objects maintain constant velocity. This tendency to resist change is called inertia.

When vehicles travel at steady speed, driving forces exactly balance resistive forces like friction and air resistance. Only unbalanced forces cause acceleration.

Newton's Second Law gives us: resultant force = mass × acceleration. This fundamental equation shows that heavier objects need more force to achieve the same acceleration.

Inertial mass measures how difficult it is to change an object's velocity. More massive objects have greater inertia and resist acceleration more strongly.

Law Connection: All three of Newton's laws work together to explain every aspect of motion you observe daily.

Newton's Third Law states that forces always come in equal and opposite pairs. When you walk, you push backward on the ground, and it pushes forward on you with equal force.