P2 Forces
Scalars and vectors
A scalar has magnitude only. A vector has both magnitude and direction.
| Scalars | Vectors |
|---|---|
| Speed, distance, mass, energy, time, temperature | Velocity, displacement, force, acceleration, momentum, weight |
Vectors are represented by arrows: length shows magnitude, direction shows direction. To add vectors not in line, draw a scale diagram or use a right-angled triangle + Pythagoras.
Resolving vectors (Higher): split a vector into horizontal and vertical components.
- F_x = F cos θ (horizontal component)
- F_y = F sin θ (vertical component)
Forces and Newton's laws
Newton's 1st Law: An object remains at rest or moves at constant velocity unless acted on by a resultant force.
Newton's 2nd Law:
F = ma
where F = resultant force (N), m = mass (kg), a = acceleration (m/s²).
Weight: W = mg where g = 10 N/kg (or 9.8 N/kg if specified).
Newton's 3rd Law: When object A exerts a force on object B, object B exerts an equal and opposite force on object A (same type, same line of action, but opposite direction).
Free body diagrams
Draw a dot representing the object. Draw all forces as arrows from the dot, labelled with magnitude and direction. Check whether the resultant is zero (equilibrium) or non-zero (acceleration).
Terminal velocity: when drag = driving force, resultant = 0, acceleration = 0, constant velocity is reached.
Momentum
Momentum (p) = mass × velocity:
p = mv (kg m/s)
Conservation of momentum: in a closed system (no external forces), total momentum before a collision = total momentum after.
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Impulse (Higher):
Impulse = FΔt = Δp (change in momentum)
Larger impact time → smaller force for same Δp (crumple zones, air bags).
Newton's 2nd law in terms of momentum (Higher):
F = Δp / Δt = m(v − u) / t = ma
Stopping distances
- Thinking distance = speed × reaction time (affected by: tiredness, alcohol, drugs, distraction).
- Braking distance = depends on speed², road condition, tyre condition, brake condition (PAG P2.1 — ruler drop for reaction time).
- Stopping distance = thinking + braking.
Braking distance ∝ v² because KE = ½mv² — doubling speed quadruples KE, so quadruples braking distance.
Force-extension (Hooke's law)
F = ke
where F = force (N), k = spring constant (N/m), e = extension (m).
This applies up to the limit of proportionality. Beyond the elastic limit, the spring does not return to its original length.
Work done stretching a spring (elastic potential energy):
Eₑ = ½ke²
PAG P2.2: Investigate the relationship between force and extension for a spring. Plot F vs e; gradient = k. Identify the limit of proportionality.
Weight and gravitational field
W = mg
On Earth, g ≈ 10 N/kg. Weight is a force (vector); mass is a scalar.
⚠Common mistakes
- Confusing mass and weight: mass is in kg, weight is in Newtons.
- Newton's 3rd law pairs: forces must be same type (both contact, both gravitational etc.), on different objects.
- Thinking distance vs braking distance: thinking ∝ v; braking ∝ v².
- Momentum direction: always assign + and − directions before calculating.
- Hooke's law — extension not length: measure extension (change in length), not total length.
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