Forces and Energy
Newton's Three Laws of Motion
First Law: An object remains at rest or moves with constant velocity unless acted upon by a resultant (unbalanced) force. Inertia is the tendency to resist changes in motion.
Second Law: The resultant force equals mass times acceleration: F = ma. A larger force → larger acceleration; a larger mass → smaller acceleration for the same force.
Third Law: For every action there is an equal and opposite reaction. Forces always come in pairs acting on different objects. Example: a book rests on a table — the book exerts a downward force on the table; the table exerts an equal upward force (normal reaction) on the book.
Weight and Mass
Weight = mass × gravitational field strength: W = mg (N = kg × N/kg). On Earth, g = 10 N/kg. Weight is a force (vector, in newtons); mass is a scalar (in kg).
Momentum
Momentum (p) = mass × velocity: p = mv (kg m/s).
Impulse = change in momentum = force × time: FΔt = Δp = mv − mu.
Conservation of momentum: in a closed system (no external forces), total momentum before a collision = total momentum after. This applies to all collisions.
Elastic collision: kinetic energy is conserved. Inelastic collision: some KE is converted to heat/sound (most real collisions).
Work Done, KE and GPE
Work done = force × distance in direction of force: W = Fd (joules = newtons × metres).
Kinetic energy: KE = ½mv²
Gravitational potential energy: GPE = mgh
Work-energy theorem: work done on an object equals its change in KE (if no friction): W = ΔKE.
Hooke's Law and Force-Extension
A spring obeys Hooke's law when extension is proportional to force: F = ke, where k is the spring constant (N/m) and e is extension (m). This holds up to the limit of proportionality.
Elastic potential energy stored in a stretched spring: E = ½ke² (or E = ½Fe).
Beyond the elastic limit, the spring deforms permanently and does not return to its original length.
WJEC Required Practical: Force-Extension
Hang known masses on a spring, measure extension each time, plot F (y-axis) vs e (x-axis). The gradient = spring constant k. Mark where the line deviates from straight (limit of proportionality).
⚠Common mistakes
- Newton's Third Law pairs must act on different objects: weight (Earth pulls object) and normal reaction (surface pushes object) are a Newton's Third Law pair only if they are equal — if the object is accelerating, they are unequal.
- Confusing mass and weight: mass is measured in kg (constant everywhere); weight is measured in N (changes with g).
- Momentum is a vector: direction matters. Objects moving in opposite directions have momenta that partially cancel.
- Hooke's law extension vs length: extension is the added length (x = L − L₀), not the total length.
AI-generated · claude-opus-4-7 · v3-wjec-physics