# Mechanics (Edexcel IAL Physics Unit 1 WPH11) > Edexcel International A-Level Physics · 2018 Edexcel IAL Physics Unit 1 (WPH11) > Source: https://www.owlsprep.com/study/edexcel-ial-physics-u1-mechanics/ This guide covers all Edexcel IAL Unit 1 (WPH11) Mechanics content, from 1D motion and vectors to forces, momentum, energy, moments, and Core Practical 1, with exam-aligned worked examples and mistake avoidance tips. **Prerequisites:** Basic SI unit conversions and arithmetic; Rearranging algebraic equations; Right-angled triangle trigonometry (sin, cos, tan) ## Learning objectives - Use suvat equations to solve 1D uniformly accelerated motion problems - Interpret and draw displacement/velocity/acceleration graphs for uniform and non-uniform motion - Resolve vectors into perpendicular components and calculate coplanar resultant vectors - Solve projectile motion problems using independent horizontal and vertical motion - Draw free-body diagrams and apply Newton's laws of motion to force problems - Apply conservation of linear momentum to 1D collision and explosion scenarios - Use the principle of moments and centre of gravity to solve equilibrium problems - Calculate work, kinetic energy, gravitational potential energy, power and efficiency using conservation of energy - Describe Core Practical 1 for measuring the acceleration of a freely falling object ## 1. Kinematics: Uniform Motion and Motion Graphs **Uniformly Accelerated Motion** — Motion where acceleration is constant over time, allowing use of the four suvat equations to calculate unknown quantities. For 1D uniformly accelerated motion, use the suvat equations, where $s$ = displacement, $u$ = initial velocity, $v$ = final velocity, $a$ = acceleration, $t$ = time taken. All equations are provided on your exam data sheet, so select the equation that excludes the unknown quantity you do not need to calculate. **Worked example:** A car accelerates uniformly from rest to 18 m s⁻¹ over a displacement of 100 m. Calculate the acceleration of the car. 1. List known values: $u = 0 \text{ m s}^{-1}$, $v = 18 \text{ m s}^{-1}$, $s = 100 \text{ m}$, $a = ?$ 2. Select suvat equation with no $t$ term: $v^2 = u^2 + 2as$ 3. Rearrange for $a$: $a = \frac{v^2 - u^2}{2s}$ 4. Substitute values: $a = \frac{18^2 - 0}{2 \times 100} = 1.62 \text{ m s}^{-2}$ (3 sf) For motion graphs: For non-uniform acceleration, estimate area using the trapezium rule or counting squares, and calculate gradients using tangents to the curve. > **Core Practical 1: Measuring g by Free Fall** > > Use an electromagnet and trapdoor to measure time taken for a ball bearing to fall a measured distance. Plot a graph of $s$ against $t^2$: gradient = $g/2$, so $g = 2 \times \text{gradient}$. Common errors include air resistance, reaction time for manual timing, and uncertainty in distance measurements. > **Exam tip:** Always label graph axes with units when drawing motion graphs, and clearly draw tangent lines on curves when calculating instantaneous gradients to gain full marks. *Calculator:* allowed ## 2. Vectors and Projectile Motion **Vector Resolution** — The process of splitting a single vector into two perpendicular components, which can be treated independently in calculations. Resolve any vector $V$ at angle $\theta$ to the horizontal into components: horizontal $V_x = V \cos\theta$, vertical $V_y = V \sin\theta$. For two perpendicular vectors, find the resultant magnitude using Pythagoras' theorem and direction using arctangent. For non-perpendicular coplanar vectors, use scale drawing to find the resultant. **Worked example:** A ball is kicked with an initial velocity of 15 m s⁻¹ at an angle of 30° above the horizontal. Calculate the horizontal and vertical components of the initial velocity. 1. Known values: $V = 15 \text{ m s}^{-1}$, $\theta = 30^\circ$ 2. Horizontal component: $V_x = 15 \cos 30^\circ = 13.0 \text{ m s}^{-1}$ (3 sf) 3. Vertical component: $V_y = 15 \sin 30^\circ = 7.5 \text{ m s}^{-1}$ Projectile motion treats horizontal and vertical motion as fully independent: horizontal velocity is constant (no air resistance, no horizontal force), while vertical motion is uniformly accelerated by gravity at $9.81 \text{ m s}^{-2}$ downwards. Calculate time of flight using vertical motion first, then use constant horizontal velocity to find horizontal distance travelled. > **Exam tip:** Always assign a positive direction (e.g. upwards = positive) for vertical motion, so gravitational acceleration is written as $-9.81 \text{ m s}^{-2}$ for upward motion calculations. *Calculator:* allowed ## 3. Forces and Newton's Laws of Motion **Free-Body Diagram** — A simplified diagram showing all forces acting on a single isolated object, with force arrows drawn to scale in the correct direction and clearly labelled. Key laws of motion: Weight of an object is $W = mg$, where $g = 9.81 \text{ m s}^{-2}$. Terminal velocity occurs when drag force equals the weight of a falling object, so resultant force is zero and speed is constant. **Worked example:** A 2.5 kg box is pushed across a flat floor with a horizontal force of 12 N, facing a constant frictional force of 4.5 N. Calculate the acceleration of the box. 1. Calculate resultant horizontal force: $\sum F = 12 - 4.5 = 7.5 \text{ N}$ 2. Rearrange $\sum F = ma$ for acceleration: $a = \frac{\sum F}{m}$ 3. Substitute values: $a = \frac{7.5}{2.5} = 3.0 \text{ m s}^{-2}$ > **Exam tip:** Always identify all forces acting on the object (weight, normal reaction, friction, drag, applied force, tension) before calculating resultant force to avoid missing terms. *Calculator:* allowed ## 4. 1D Linear Momentum and Conservation **Linear Momentum** — Momentum $p = mv$, where $m$ = mass, $v$ = velocity, units $\text{kg m s}^{-1}$. It is a vector quantity, so direction must be included in calculations. Conservation of linear momentum states that the total momentum of a closed system remains constant if no external resultant force acts on it. This applies to all 1D collisions and explosions, and is derived directly from Newton's Second and Third Laws of motion. **Worked example:** A 2 kg trolley moving at 3 m s⁻¹ right collides with a stationary 1 kg trolley. After collision, the 2 kg trolley moves at 1 m s⁻¹ right. Calculate the velocity of the 1 kg trolley after collision. 1. Total momentum before collision: $(2 \times 3) + (1 \times 0) = 6 \text{ kg m s}^{-1}$ (right = positive) 2. Total momentum after collision: $(2 \times 1) + (1 \times v) = 2 + v$ 3. Equate total momentum before and after: $6 = 2 + v$ → $v = 4 \text{ m s}^{-1}$ (right direction) > **Exam tip:** Always assign a positive direction at the start of 1D momentum calculations, and use negative values for velocities in the opposite direction to avoid sign errors. *Calculator:* allowed ## 5. Moments and Equilibrium **Moment of a Force** — Moment = force × perpendicular distance from the pivot to the line of action of the force, units $\text{N m}$. Moments can be clockwise or anticlockwise. Centre of gravity is the point where the entire weight of an object can be considered to act. For an object in equilibrium: For uniform objects, weight acts at the midpoint of the object. **Worked example:** A uniform 1 m long see-saw of weight 50 N is pivoted at its centre. A 300 N child sits 0.3 m left of the pivot. How far right of the pivot must a 200 N child sit to balance the see-saw? 1. Anticlockwise moment from 300 N child: $300 \times 0.3 = 90 \text{ N m}$ 2. Clockwise moment from 200 N child: $200 \times d$ 3. Equate moments for equilibrium: $200d = 90$ → $d = 0.45 \text{ m}$ right of pivot > **Exam tip:** Always include the moment from the weight of a uniform object if the pivot is not at its midpoint, as this is a common missed term in equilibrium questions. *Calculator:* allowed ## 6. Work, Energy, Power and Efficiency **Work Done** — Work done $\Delta W = F \Delta s \cos\theta$, where $\theta$ is the angle between force $F$ and displacement $\Delta s$, units Joules (J). If force is aligned with displacement, $\cos\theta = 1$ so $\Delta W = F\Delta s$. Key energy formulae: Conservation of energy states energy cannot be created or destroyed, only converted between forms. Power $P = \frac{\text{work done}}{\text{time taken}} = \frac{\text{energy transferred}}{\text{time taken}}$, units Watts (W). Efficiency = $\frac{\text{useful energy output}}{\text{total energy input}} = \frac{\text{useful power output}}{\text{total power input}}$, often expressed as a percentage. **Worked example:** A 50 kg student climbs 2.5 m up stairs in 3.2 s. Calculate the useful power output of the student. 1. Calculate gravitational potential energy gained: $\Delta E_{grav} = 50 \times 9.81 \times 2.5 = 1226.25 \text{ J}$ 2. Calculate power: $P = \frac{E}{t} = \frac{1226.25}{3.2} = 383 \text{ W}$ (3 sf) > **Exam tip:** Efficiency is always less than 1 (or 100%) because some energy is always lost as heat, sound or other waste forms, so answers above 100% are always incorrect. *Calculator:* allowed ## Common pitfalls - **Wrong:** Forgetting to assign direction for vectors (velocity, force, momentum) in calculations - Why it fails: Vectors have direction, so opposite directions require negative values to get correct results - Correct: Define a positive direction at the start of all vector calculations, use negative values for opposite directions - **Wrong:** Using calculus (differentiation/integration) for non-uniform acceleration problems - Why it fails: Calculus is not permitted in Unit 1, you will lose marks even if your final answer is correct - Correct: Use tangent gradients for instantaneous rates and area under graphs for displacement/change in velocity - **Wrong:** Treating horizontal velocity of a projectile as accelerating - Why it fails: There is no horizontal force acting on a projectile (ignoring air resistance), so horizontal velocity is constant - Correct: Use constant velocity $s=vt$ for horizontal projectile motion, use suvat equations only for vertical motion - **Wrong:** Omitting the weight of a uniform object in moment calculations when the pivot is not at its centre - Why it fails: The weight of the object acts at its centre of mass, so it exerts a moment around the pivot if not aligned - Correct: Always include the moment from the object's weight if the pivot is not at its midpoint - **Wrong:** Using $g = 10 \text{ m s}^{-2}$ instead of $9.81 \text{ m s}^{-2}$ - Why it fails: The exam data sheet specifies $g=9.81 \text{ m s}^{-2}$, so using 10 leads to rounding errors and lost marks - Correct: Always use $g = 9.81 \text{ m s}^{-2}$ unless explicitly told otherwise in the question ## Cheatsheet | Concept | Key Formula/Rule | Exam Reminder | | --- | --- | --- | | SUVAT Equations | $s=(u+v)t/2$, $v=u+at$, $s=ut+½at²$, $v²=u²+2as$ | Choose equation that excludes the unneeded unknown value | | Motion Graphs | $s$-$t$ gradient = velocity, $v$-$t$ gradient = acceleration, $v$-$t$ area = displacement | Use tangents for non-uniform motion gradients | | Vectors | $V_x=V\cos\theta$, $V_y=V\sin\theta$, resultant = $\sqrt{V_x^2 + V_y^2}$ | Assign positive direction for all vector calculations | | Projectiles | Horizontal v constant, vertical $a=9.81 \text{ m s}^{-2}$ downwards | Calculate time of flight using vertical motion first | | Newton's Laws | $\sum F=ma$, $W=mg$ | Draw free-body diagrams to identify all forces first | | 1D Momentum | $p=mv$, total $p$ before = total $p$ after | Use negative signs for opposite direction velocities | | Moments | Moment = $F \times$ perpendicular distance, sum clockwise = sum anticlockwise | Include uniform object weight at its midpoint | | Work/Energy/Power | $\Delta W=F\Delta s\cos\theta$, $E_k=½mv²$, $P=E/t$, efficiency = useful/total | Efficiency is always less than 100% | ## What's next Now you have mastered the core Mechanics content for Edexcel IAL Physics Unit 1 WPH11, you can move on to the second part of Unit 1: Materials, which covers Hooke's law, stress, strain, density and viscosity. You should also practice past paper questions specifically for Mechanics to reinforce your understanding, paying close attention to command terms and mark scheme requirements. Make sure you can carry out calculations for Core Practical 1 and explain sources of error for free fall experiments, as these are commonly tested in both multiple choice and structured questions. --- From [OwlsPrep](https://www.owlsprep.com) — free study guides for A-Level, IB, AP and IGCSE, written against the official syllabus. Canonical page: https://www.owlsprep.com/study/edexcel-ial-physics-u1-mechanics/