Unit 1 High-Yield Topics
Free resource by Flowxiom — Edexcel A-level Physics
Not everything. Just what’s on the paper. High-frequency topics only — covering ~80% of exam marks.
Edexcel A-level Physics | Mechanics & Materials | WPH11 & WPH12
Topic 1: Vector Resolution and Resultant Forces
Question types: Inclined plane force analysis, rope tension equilibrium, magnitude and direction of resultant.
Key Formulae — Resolving a Force
For force \(F\) at angle \(\theta\) from horizontal:
\[F_x = F\cos\theta \qquad F_y = F\sin\theta\]
Adjacent side uses cos, opposite side uses sin (θ measured from horizontal)
Four-Step Method for Resultant
Resolve all forces into horizontal and vertical components — right/up positive
Sum horizontal: \(R_x = \sum F_x\); sum vertical: \(R_y = \sum F_y\)
Magnitude: \(F_R = \sqrt{R_x^2 + R_y^2}\)
Direction: \(\tan\alpha = \dfrac{|R_y|}{|R_x|}\) — state as angle from horizontal
Equilibrium Condition
For three forces in equilibrium: they must be concurrent and form a closed triangle.
Common Mistakes
- ❌ sin/cos confused — always draw the triangle and mark θ clearly
- ❌ Forgetting to include weight — vertical equilibrium must also hold
- ❌ Direction stated as a number only — must specify “angle from horizontal”
Topic 2: Motion Graphs
Question types: Read graph to identify motion; calculate displacement/acceleration from graph; sketch graph conversions.
Golden Rules
| Graph | Gradient = | Area = |
|---|---|---|
| \(s\)-\(t\) | velocity \(v\) | — |
| \(v\)-\(t\) | acceleration \(a\) | displacement \(s\) |
| \(a\)-\(t\) | — | change in velocity \(\Delta v\) |
\[s \xrightarrow{\text{gradient}} v \xrightarrow{\text{gradient}} a \qquad a \xrightarrow{\text{area}} \Delta v \xrightarrow{\text{area}} \Delta s\]
Common v-t Graph Shapes
| Shape | Meaning |
|---|---|
| Horizontal straight line | Uniform velocity (\(a = 0\)) |
| Straight line sloping up | Uniform acceleration |
| Straight line sloping down | Uniform deceleration |
| Steepening curve | Increasing acceleration |
| Crosses time axis | Velocity reverses direction |
Common Mistakes
- ❌ Area under v-t graph = displacement (can be negative); not the same as distance
- ❌ Curved s-t graph means changing speed, not necessarily projectile motion
- ❌ Gradient of v-t = acceleration; area of v-t = displacement (not the other way round)
Topic 3: SUVAT Equations
Question types: Given a motion description, find velocity, displacement, time or acceleration.
The Four Equations
| Equation | Missing quantity |
|---|---|
| \(v = u + at\) | no displacement |
| \(s = \dfrac{1}{2}(u+v)t\) | no acceleration |
| \(s = ut + \dfrac{1}{2}at^2\) | no final velocity |
| \(v^2 = u^2 + 2as\) | no time |
Method
List all five quantities \(s, u, v, a, t\); fill in knowns, mark unknown with ?
Identify 3 knowns + 1 target → select correct equation
Substitute — take care with signs for direction
Key Phrase Translations
| Phrase in question | Value |
|---|---|
| from rest / starts from rest | \(u = 0\) |
| comes to rest / stops | \(v = 0\) |
| deceleration / retardation | \(a\) is negative |
| free fall / dropped | \(a = 9.81\ \text{m s}^{-2}\), \(u = 0\) |
| thrown upward | \(a = -9.81\ \text{m s}^{-2}\) (taking up as positive) |
Common Mistakes
- ❌ Deceleration: \(a\) must be negative
- ❌ If “thrown” not “dropped”, initial velocity is not zero
- ❌ Mixed units — convert first (cm → m, km/h → m/s)
Topic 4: Projectile Motion
Question types: Horizontal or angled launch — find time of flight, range, velocity at landing.
Core Principle
Horizontal and vertical motions are completely independent; time is the only link.
| Horizontal | Vertical | |
|---|---|---|
| Acceleration | \(a_x = 0\) | \(a_y = -9.81\ \text{m s}^{-2}\) |
| Velocity | constant: \(v_x = u\cos\theta\) | changes — use SUVAT |
| Displacement | \(s_x = v_x \times t\) | use SUVAT |
Solution Framework
Vertical (solve first) Horizontal (solve after)
s_y = ? s_x = ?
u_y = u sinθ u_x = u cosθ
a_y = −9.81 a_x = 0
→ find t s_x = u_x × tCommon Mistakes
- ❌ Horizontal velocity is constant — do not apply SUVAT to it
- ❌ Landing speed requires combining both components: \(v = \sqrt{v_x^2 + v_y^2}\)
- ❌ Horizontal component uses \(\cos\theta\); vertical uses \(\sin\theta\)
Topic 5: Momentum and Impulse
Question types: Collision calculations, bouncing ball, F-t graph, explosion and recoil.
Key Formulae
\[p = mv \qquad \text{(momentum — vector)}\]
\[\text{Impulse} = F\Delta t = \Delta p = mv – mu\]
Conservation of Momentum
Net external force = 0 (isolated system) → total momentum is conserved:
\[m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2\]
Elastic vs Inelastic Collisions
| Momentum | Kinetic energy | |
|---|---|---|
| Elastic | conserved ✓ | conserved ✓ |
| Inelastic | conserved ✓ | not conserved ✗ (converted to heat/sound) |
| Perfectly inelastic | conserved ✓ | maximum loss |
F-t Graph
\[\text{Area under graph} = \text{impulse} = \Delta p\]
Common Mistakes
- ❌ Sign errors for direction — most common mark loss
Example: ball hits wall at \(10\ \text{m/s}\), bounces back at \(8\ \text{m/s}\):
\(\Delta p = m(-8) – m(+10) = -18m\), not \(-2m\)
- ❌ After a perfectly inelastic collision, both objects share the same final velocity
- ❌ Momentum is always conserved in collisions; kinetic energy is only conserved in elastic collisions
Topic 6: Work, Energy and Power
Question types: Work calculations, energy conservation, power-velocity relationship.
Key Formulae
\[W = Fs\cos\theta \qquad E_k = \frac{1}{2}mv^2 \qquad \Delta E_p = mg\Delta h\]
\[P = \frac{W}{t} = Fv \qquad \text{efficiency} = \frac{\text{useful output}}{\text{total input}} \times 100\%\]
When Work Done = 0
Force perpendicular to displacement (\(\theta = 90°\)) → \(W = 0\)
Example: carrying an object horizontally — gravity does no work.
Energy Conservation
- No friction/air resistance → mechanical energy conserved: \(E_k + E_p = \text{constant}\)
- With friction → energy lost = friction force × distance (converted to thermal energy)
F-s Graph
\[\text{Area under graph} = \text{work done} = W\]
Common Mistakes
- ❌ Omitting \(\cos\theta\) when force and displacement are not parallel
- ❌ In \(P = Fv\), \(v\) must be the component of velocity in the direction of force
- ❌ Efficiency fraction inverted
Topic 7: Newton’s Laws and Moments
Question types: Free-body diagrams, equilibrium conditions, moment calculations.
Conditions for Equilibrium (both must hold simultaneously)
Resultant force = 0 in all directions
Sum of moments = 0 about any point
Moment Pivot Trick
Take moments about the point where an unknown force acts — its moment = 0, eliminating one unknown from the equation.
Common Mistakes
- ❌ Omitting the moment of one of the forces
- ❌ Not consistently assigning + or − to clockwise vs anticlockwise
Topic 8: Solid Materials and Young Modulus
Question types: Calculate Young modulus, identify key points on stress-strain graph, classify material type.
Key Formulae
\[\sigma = \frac{F}{A} \quad \text{(stress, Pa)} \qquad \varepsilon = \frac{\Delta L}{L} \quad \text{(strain — dimensionless)}\]
\[E = \frac{\sigma}{\varepsilon} = \frac{FL}{A\Delta L} \quad \text{(Young modulus, Pa)}\]
\[F = k\Delta x \qquad E_{el} = \frac{1}{2}F\Delta x = \frac{1}{2}k(\Delta x)^2\]
Area under F-x graph = elastic potential energy stored
Key Points on the Stress-Strain Graph
| Point | Name | Meaning |
|---|---|---|
| End of straight line | Limit of Proportionality | Above this, Hooke’s law no longer holds |
| First point after curve | Elastic Limit | Above this, permanent deformation occurs |
| Sudden large extension | Yield Point | Sudden large plastic deformation |
| Highest point | UTS | Maximum stress the material can withstand |
| End of graph | Breaking Point | Fracture |
Read Young modulus from the gradient of the straight-line section: \(E = \Delta\sigma / \Delta\varepsilon\)
Three Material Types
| Type | Graph feature | Examples |
|---|---|---|
| Ductile | Large plastic region before fracture | Copper, mild steel |
| Brittle | Fractures at or near elastic limit | Glass, cast iron |
| Polymeric | Non-linear; loading and unloading paths differ | Rubber |
Common Mistakes
- ❌ Strain has no unit — it is a dimensionless ratio
- ❌ Use extension \(\Delta L\), not total length \(L\)
- ❌ Area = \(\pi r^2\) — remember to halve the diameter to get radius
- ❌ Elastic limit and limit of proportionality are different points (close but distinct)
Practice Questions
Q1. A wire of original length \(2.0\ \text{m}\) and diameter \(1.0\ \text{mm}\) extends by \(0.50\ \text{mm}\) under a force of \(80\ \text{N}\). Find the Young modulus.
Answer
\(A = \pi(0.5\times10^{-3})^2 = 7.85\times10^{-7}\ \text{m}^2\)
\(\sigma = 80 / 7.85\times10^{-7} = 1.02\times10^8\ \text{Pa}\)
\(\varepsilon = 0.50\times10^{-3} / 2.0 = 2.5\times10^{-4}\)
\(E = \sigma/\varepsilon = \mathbf{4.1\times10^{11}\ \text{Pa}}\)
Q2. A \(5.0\ \text{N}\) force acts at \(37°\) to the horizontal. Find the horizontal and vertical components. (\(\sin37°=0.60\), \(\cos37°=0.80\))
Answer
\(F_x = 5.0\cos37° = \mathbf{4.0\ \text{N}}\)
\(F_y = 5.0\sin37° = \mathbf{3.0\ \text{N}}\)
Q3. A v-t graph shows a straight line from \(v=12\ \text{m/s}\) at \(t=0\) to \(v=0\) at \(t=4\ \text{s}\). Find the acceleration and displacement.
Answer
Acceleration = gradient \(= (0-12)/4 = \mathbf{-3.0\ \text{m s}^{-2}}\) (deceleration)
Displacement = area of triangle \(= \frac{1}{2}\times4\times12 = \mathbf{24\ \text{m}}\)
Q4. A car brakes from \(30\ \text{m/s}\) to rest with deceleration \(5.0\ \text{m/s}^2\). Find the braking distance.
Answer
\(v=0\), \(u=30\), \(a=-5.0\). Use \(v^2 = u^2 + 2as\):
\(0 = 900 + 2(-5.0)s \Rightarrow s = \mathbf{90\ \text{m}}\)
Q5. A ball is launched horizontally at \(6\ \text{m/s}\) from a height of \(20\ \text{m}\). Find the time of flight and horizontal range. (\(g = 10\ \text{m s}^{-2}\))
Answer
Vertical: \(20 = \frac{1}{2}(10)t^2 \Rightarrow t = 2.0\ \text{s}\)
Horizontal: \(s_x = 6 \times 2.0 = \mathbf{12\ \text{m}}\)
Q6. A \(0.2\ \text{kg}\) ball hits a wall at \(5\ \text{m/s}\) and bounces back at \(3\ \text{m/s}\). Find the magnitude of the impulse.
Answer
Taking initial direction as positive:
\(\Delta p = 0.2 \times (-3-5) = -1.6\ \text{N s}\)
Magnitude \(= \mathbf{1.6\ \text{N s}}\)
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