10.2 Core Concepts: Forces, Energy, and Simple Machines

10.2 Core Concepts: Forces, Energy, and Simple Machines

The "force relationships, physical laws, simple machines" core of Physical Science is mostly mechanics. Master a short list of formulas and you can answer the bulk of the subtest in seconds.

Newton's three laws

1. First Law (inertia): an object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless a net external force acts on it.
2. Second Law: F = ma — net force equals mass times acceleration. Rearranged, a = F/m. A larger mass needs more force for the same acceleration.
3. Third Law: for every action there is an equal and opposite reaction. A rocket pushes exhaust down; the exhaust pushes the rocket up.

Weight vs mass is a classic trap. Mass (kilograms) is the amount of matter and never changes. Weight is a force, W = mg, and changes with gravity. An 80-kg airman weighs about 784 N on Earth (80 × 9.8) but only ~130 N on the Moon (80 × 1.62).

Energy, work, and power

The law of conservation of energy says energy is neither created nor destroyed, only transformed. A falling object trades gravitational PE for KE; a moving aircraft trading altitude for airspeed in a dive is the same exchange. Note that KE depends on velocity squared — doubling speed quadruples kinetic energy, which is why high-speed collisions are so destructive.

The six simple machines

Simple machines change the size or direction of a force; they trade distance for force but never reduce total work (ignoring friction). Mechanical advantage (MA) = output force ÷ input force.

• Lever — a bar pivoting on a fulcrum; a seesaw or crowbar. Longer effort arm = greater MA.
• Wheel and axle — a steering wheel or doorknob; a large wheel turns a small axle.
• Pulley — redirects force; multiple pulleys multiply MA.
• Inclined plane — a ramp; reduces force needed by increasing distance.
• Wedge — two inclined planes back-to-back; an axe or knife.
• Screw — an inclined plane wrapped around a cylinder; trades many turns for great force.

Worked example

A 50-N force lifts a load using a pulley system that requires pulling 4 m of rope to raise the load 1 m. What is the mechanical advantage? The rope distance is 4 times the load distance, so MA ≈ 4, meaning the system can lift a load up to ~200 N (50 × 4), minus friction losses.

Common traps

• Confusing mass (kg) with weight (N).
• Forgetting that g = 9.8 m/s² on Earth but only 1.62 m/s² on the Moon.
• Mixing units — a joule is N·m (energy), a watt is J/s (power); they are not interchangeable.
• Assuming a simple machine reduces total work — it only reduces the force by spreading it over more distance.

Momentum, friction, and circular motion

Beyond the headline formulas, a few secondary mechanics ideas show up. Momentum is mass times velocity (p = mv) and is conserved in collisions — a heavy, slow truck can carry the same momentum as a light, fast car. Friction is a force that opposes motion; it converts kinetic energy into heat, which is why brakes get hot. Static friction (before sliding starts) is generally larger than kinetic friction (while sliding). Centripetal force points toward the center of a circular path and keeps an object turning rather than flying off in a straight line; a banking aircraft and a car rounding a curve both rely on it.

Speed, velocity, and acceleration

The AFOQT distinguishes scalar and vector quantities. Speed is how fast (a scalar — magnitude only); velocity adds direction (a vector). Acceleration is any change in velocity — speeding up, slowing down, or turning. Average speed = distance ÷ time, so an aircraft covering 600 miles in 1.5 hours averages 400 mph. A worked one-step item: a car starts at rest and reaches 20 m/s in 4 seconds; what is its acceleration? a = Δv/t = 20/4 = 5 m/s². Recognizing that "starts from rest" means initial velocity is zero is half the battle on these stems.

Pressure and buoyancy

Pressure is force spread over area (P = F/A); a sharp knife cuts because a small edge area concentrates force into high pressure. Archimedes' principle says a submerged object feels an upward buoyant force equal to the weight of the fluid it displaces — objects less dense than the fluid float, denser ones sink. This connects to flight: an aircraft generates lift through pressure differences (Bernoulli's principle — faster air over the curved wing top creates lower pressure than the slower air below), which is why understanding pressure pays off across both Physical Science and Aviation Information items.