IP Physics Notes (Upper Secondary, Year 3-4): 3) Forces

Quick recap -- Treat force as a vector, link weight to gravitational field strength, capture all pushes/pulls in a free-body diagram, and let Newton's laws plus vector resolution tell you whether motion changes.

Force Fundamentals

• A force is a push or pull arising from interaction between bodies. It can change an object's speed, direction, or shape.
• Forces are vectors: they need both magnitude and direction. The SI unit is the newton \( \pu{N} \).
• Typical families you must recognise: weight (gravity), normal contact, friction, tension, upthrust, and applied pulls/pushes.

Mass, Weight & Gravitational Fields

• Mass measures the amount of matter and inertia an object has. It stays constant wherever you go.
• Weight is the gravitational force on that mass. Close to Earth, \( W = mg \).
• Near Earth's surface, use \( g \approx \pu{9.81 m.s-2} \) (round to \( \pu{10 m.s-2} \) for IP estimates).
• Gravitational field strength \( g \) is the force per unit mass \( \left( g = \dfrac{W}{m} \right) \). Its unit \( \pu{N.kg-1} \) is equivalent to \( \pu{m.s-2} \).

Density & Upthrust

• Density links mass and volume: \( \rho = \dfrac{m}{V} \) with \( \rho \) in \( \pu{kg.m-3} \).
• Regular solids: use calipers/rules to measure dimensions, compute volume, and substitute. Irregular solids: submerge in water and take the displaced volume.
• Upthrust equals the weight of displaced fluid. Floating objects adjust until \( \text{weight} = \text{upthrust} \); sinking objects have \( \text{weight} > \text{upthrust} \).

Friction, Drag & Terminal Velocity

• Friction opposes relative motion between surfaces. It arises from microscopic surface roughness.
• Static friction builds up to a limiting value, matching the applied force until motion begins. Kinetic friction remains roughly constant while sliding.
• Air resistance and viscous drag rise with speed. A falling object accelerates until drag equals weight; net force becomes zero and the object travels at terminal velocity.
• Reduce unwanted friction with lubrication, streamlining, or smoother surfaces; increase useful friction with textured materials (e.g., shoe soles, brake pads).

Drawing Free-Body Diagrams

1. Isolate the body of interest with a simple outline or dot.
2. Mark all external forces as arrows starting on the body. Label each force clearly.
3. Show weight vertically downward from the centre of mass.
4. Include normal contact forces perpendicular to surfaces, friction along the surface, tension along strings, and thrust along propulsion axes.
5. Use separate diagrams for interacting bodies when applying Newton's third law.

Balanced vs Unbalanced Forces

• Equilibrium: vector sum of forces is zero. The object stays at rest or moves at constant velocity (no acceleration).
• Unbalanced forces: resultant \( \neq 0 \), so the object accelerates in the resultant's direction.
• Check equilibrium by resolving forces into perpendicular components (horizontal/vertical or parallel/perpendicular to a slope) and ensuring each component sums to zero.

Newton's Laws Refresher

First Law: Inertia

• An object maintains its state of rest or uniform motion unless acted on by a resultant force.
• Inertia quantifies resistance to changes in motion; more mass means more inertia.

Second Law: Resultant Force

• Resultant force equals mass x acceleration: \( \sum \vec{F} = m \vec{a} \).
• In one dimension, apply the signed form \( F_\text{resultant} = ma \). On slopes, resolve along and perpendicular to the plane before substituting.
• Weight provides a classic proof: \( W = mg \) emerges from this law when the only force causing vertical acceleration is gravity.

Third Law: Action-Reaction Pairs

• For every force object A exerts on object B, object B exerts an equal and opposite force of the same type on object A.
• Action-reaction forces act on different objects. Do not pair weight and normal contact force--they act on one object and balance via equilibrium, not Newton's third law.

Worked Example: Sled with Friction

A ( \pu{12 kg} ) sled is pulled on level ground by a rope at ( 30^\circ ) above the horizontal with a tension of ( \pu{55 N} ). The kinetic friction coefficient is 0.15.

1. Resolve tension: horizontal ( T_x = \pu{55 N} \cos 30^\circ = \pu{47.6 N} ), vertical ( T_y = \pu{55 N} \sin 30^\circ = \pu{27.5 N} ).
2. Normal reaction: ( R = mg - T_y = \pu{12 kg} \times \pu{9.81 m.s-2} - \pu{27.5 N} \approx \pu{90.2 N} ).
3. Friction: ( F_f = 0.15 \times R \approx \pu{13.5 N} ).
4. Resultant horizontal force: ( F = T_x - F_f \approx \pu{34.1 N} ).
5. Acceleration: ( a = \dfrac{F}{m} \approx \dfrac{34.1}{12} \approx \pu{2.84 m.s-2} ).

Vector Addition & Resolution

• Combine forces graphically (head-to-tail) or analytically via components.
• For perpendicular components \( F_x \) and \( F_y \), the magnitude of the resultant is \( F = \sqrt{F_x^2 + F_y^2} \) and its direction is \( \tan \theta = \dfrac{F_y}{F_x} \).
• Resolving a single force \( F \) at angle \( \theta \) gives \( F_x = F \cos \theta \) and \( F_y = F \sin \theta \). Use this to simplify slope problems and tension networks.

Key Takeaways

• Always start with a free-body diagram and clear force labels.
• Use \( W = mg \) and \( \rho = \dfrac{m}{V} \) to switch between gravitational and density language.
• Decide if forces balance (equilibrium) or not before jumping into \( F = ma \).
• When in doubt, resolve forces into perpendicular components and check that you obey Newton's third-law pairings across bodies, not within a single diagram.