Sec 3 Physics Dynamics notes

A force is a push or a pull of one body on another, measured in newtons. Contact forces act where bodies touch: friction along a surface opposing sliding, air resistance (drag) opposing motion through air, tension pulling along a string or cable, and the normal force pushing perpendicular to a surface. Non-contact forces act across empty space: gravity, electrostatic forces between charges, and magnetic forces between magnets or currents.

Telling them apart is a real exam skill: a compressed spring, a stretched rope and a book pressing on a shelf are contact; a falling apple, a compass needle swinging and a rubbed ruler lifting paper are non-contact. Note that weight — the gravitational force on a body — is always present, even when nothing is touching the body, which is exactly why astronauts are weightless-feeling only while falling, not because gravity vanished.

Mass is the amount of matter in a body, measured in kilograms with a balance. It is also the body’s inertia: the property that resists changes of motion. A loaded tanker needs a long braking distance not because gravity cares, but because its large mass makes its velocity hard to change.

A gravitational field is a region in which a mass experiences a force due to gravitational attraction. The Earth’s field points towards the Earth’s centre, and its field strength g is defined as the gravitational force per unit mass: g = 10 N/kg near the Earth’s surface. Weight is that force: W = m g, in newtons, measured with a spring balance.

Newton’s ideas (you apply them; stating the laws verbatim is not required) come down to three working rules. First: with balanced forces (zero resultant) a body stays at rest or keeps moving at constant velocity — motion needs no force to sustain it, only to change it. Second: an unbalanced (resultant) force changes the motion, in proportion to the force and inversely to the mass: resultant force = mass × acceleration, F = ma. Third: forces come in pairs — if A pushes B, B pushes A equally and oppositely, and the two forces act on different bodies.

The F = ma calculation only ever uses the resultant — the single leftover force after all the forces on the body are combined. Subtract friction from a push, or weight from drag, before dividing by the mass. A positive answer’s direction follows the resultant’s direction, and a decelerating body still obeys F = ma: the resultant simply points against the motion.

For a static point mass under three forces (a lamp hung from two cords, a picture on a wire), the forces balance: the three arrows drawn tip-to-tail close into a triangle. Use the vector methods from Chapter 1 — scale drawing or a right-angle split — to find an unknown tension, then check with the fact that equal angles mean equal tensions.

A free-body diagram isolates a single body and shows every force acting on it as an arrow starting on the body, pointing the way the force pushes or pulls, labelled with its name and (ideally) drawn with lengths proportional to size. Forces the body exerts on other things are left out — they belong to the other body’s diagram.

1. 1Draw the body alone

   a simple box or dot; details do not matter.

2. 2Weight first

   an arrow straight down from the centre, labelled W = mg.

3. 3Add contact forces

   normal force perpendicular to each touching surface; friction along it, opposing sliding or attempted sliding.

4. 4Add strings and drag

   tension along the string away from the body; air resistance opposite the velocity.

5. 5Check balance or result

   equal opposite arrows → equilibrium; unequal → mark the resultant and set F = ma along that direction.

Friction opposes relative sliding between surfaces, and also the attempted sliding of a static object (that is what lets your shoes grip the floor). It can be useful or a nuisance: tyre grip and brakes are friction doing its job; engine losses and worn soles are friction billing you for it. Drag (air resistance) is friction against a fluid, and its key property is growth: the faster the body moves, the larger the drag.

That growth explains terminal velocity. A falling body starts with drag near zero, so the resultant is the full weight and the acceleration is g = 10 m/s². As speed builds, drag grows, the resultant (weight − drag) shrinks, and the acceleration falls — a non-uniform acceleration on the v–t graph. When drag equals the weight, the resultant is zero, the acceleration stops, and the body continues at a constant terminal velocity. A heavier body (same shape) needs more drag to balance, so it accelerates longer and its terminal velocity is higher.