Unit 1 High-Yield Topics | Flowxiom<\/title>\n<meta name=\"description\" content=\"Unit 1 High-Yield Topics \u2014 Edexcel A-level Physics WPH. Question types: Inclined plane force analysis, rope tension equilibrium, magnitude and direction of r...\">\n<link rel=\"canonical\" href=\"https:\/\/flowxiom.com\/edexcel-physics-unit-1-high-yield-topics\/\">\n<script type=\"application\/ld+json\">\n{\n \"@context\": \"https:\/\/schema.org\",\n \"@type\": \"FAQPage\",\n \"mainEntity\": [\n {\n \"@type\": \"Question\",\n \"name\": \"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.\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"\\\\(A = \\\\pi(0.5\\\\times10^{-3})^2 = 7.85\\\\times10^{-7}\\\\ \\\\text{m}^2\\\\) \\n \\\\(\\\\sigma = 80 \/ 7.85\\\\times10^{-7} = 1.02\\\\times10^8\\\\ \\\\text{Pa}\\\\) \\n \\\\(\\\\varepsilon = 0.50\\\\times10^{-3} \/ 2.0 = 2.5\\\\times10^{-4}\\\\) \\n \\\\(E = \\\\sigma\/\\\\varepsilon = \\\\mathbf{4.1\\\\times10^{11}\\\\ \\\\text{Pa}}\\\\)\"\n }\n },\n {\n \"@type\": \"Question\",\n \"name\": \"Q2. A \\\\(5.0\\\\ \\\\text{N}\\\\) force acts at \\\\(37\u00b0\\\\) to the horizontal. Find the horizontal and vertical components. (\\\\(\\\\sin37\u00b0=0.60\\\\), \\\\(\\\\cos37\u00b0=0.80\\\\))\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"\\\\(F_x = 5.0\\\\cos37\u00b0 = \\\\mathbf{4.0\\\\ \\\\text{N}}\\\\) \\n \\\\(F_y = 5.0\\\\sin37\u00b0 = \\\\mathbf{3.0\\\\ \\\\text{N}}\\\\)\"\n }\n },\n {\n \"@type\": \"Question\",\n \"name\": \"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.\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"Acceleration = gradient \\\\(= (0-12)\/4 = \\\\mathbf{-3.0\\\\ \\\\text{m s}^{-2}}\\\\) (deceleration) \\n Displacement = area of triangle \\\\(= \\\\frac{1}{2}\\\\times4\\\\times12 = \\\\mathbf{24\\\\ \\\\text{m}}\\\\)\"\n }\n },\n {\n \"@type\": \"Question\",\n \"name\": \"Q4. A car brakes from \\\\(30\\\\ \\\\text{m\/s}\\\\) to rest with deceleration \\\\(5.0\\\\ \\\\text{m\/s}^2\\\\). Find the braking distance.\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"\\\\(v=0\\\\), \\\\(u=30\\\\), \\\\(a=-5.0\\\\). Use \\\\(v^2 = u^2 + 2as\\\\): \\n \\\\(0 = 900 + 2(-5.0)s \\\\Rightarrow s = \\\\mathbf{90\\\\ \\\\text{m}}\\\\)\"\n }\n },\n {\n \"@type\": \"Question\",\n \"name\": \"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}\\\\))\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"Vertical: \\\\(20 = \\\\frac{1}{2}(10)t^2 \\\\Rightarrow t = 2.0\\\\ \\\\text{s}\\\\) \\n Horizontal: \\\\(s_x = 6 \\\\times 2.0 = \\\\mathbf{12\\\\ \\\\text{m}}\\\\)\"\n }\n },\n {\n \"@type\": \"Question\",\n \"name\": \"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.\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"Taking initial direction as positive: \\n \\\\(\\\\Delta p = 0.2 \\\\times (-3-5) = -1.6\\\\ \\\\text{N s}\\\\) \\n Magnitude \\\\(= \\\\mathbf{1.6\\\\ \\\\text{N s}}\\\\)\"\n }\n }\n ]\n}\n<\/script>\n\n<script>\nMathJax = {\n tex: { inlineMath: [['\\\\(','\\\\)']], displayMath: [['\\\\[','\\\\]']] },\n svg: { fontCache: 'global' }\n};\n<\/script>\n<script async src=\"https:\/\/cdn.jsdelivr.net\/npm\/mathjax@3\/es5\/tex-svg.js\"><\/script>\n\n<style>\n:root{--accent:#2563eb;--warn-bg:#fef9c3;--warn-border:#ca8a04;--formula-bg:#eff6ff;--formula-border:#2563eb;}\nbody{font-family:system-ui,sans-serif;max-width:860px;margin:0 auto;padding:1.5rem;line-height:1.7;color:#1e293b;}\nh1{font-size:2rem;border-bottom:3px solid var(--accent);padding-bottom:.4rem;}\nh2{font-size:1.4rem;color:var(--accent);margin-top:2rem;}\nh3{font-size:1.1rem;margin-top:1.4rem;}\ntable{border-collapse:collapse;width:100%;margin:1rem 0;}\nth,td{border:1px solid #cbd5e1;padding:.5rem .75rem;text-align:left;}\nth{background:#e2e8f0;}\npre,code{background:#f1f5f9;border-radius:4px;}\npre{padding:1rem;overflow-x:auto;}\ncode{padding:.1rem .3rem;font-size:.9em;}\n.seo-warning-box{background:var(--warn-bg);border-left:4px solid var(--warn-border);padding:.75rem 1rem;margin:1rem 0;border-radius:0 6px 6px 0;}\n.seo-note-box{background:#f0fdf4;border-left:4px solid #16a34a;padding:.75rem 1rem;margin:1rem 0;border-radius:0 6px 6px 0;}\nsection.formula-card{background:var(--formula-bg);border:1px solid var(--formula-border);border-radius:8px;padding:1rem 1.25rem;margin:1.5rem 0;}\ndetails{border:1px solid #e2e8f0;border-radius:6px;padding:.5rem 1rem;margin:.75rem 0;}\nsummary{cursor:pointer;font-weight:600;}\n.answer-block{margin-top:.5rem;padding-top:.5rem;border-top:1px solid #e2e8f0;overflow-x:auto;}\n.answer-block p{margin:.25rem 0;}\n.numbered-step{padding-left:1.5rem;position:relative;}\nhr{border:none;border-top:1px solid #e2e8f0;margin:2rem 0;}\n.toc{background:#f8fafc;border:1px solid #e2e8f0;border-radius:8px;padding:1rem 1.5rem;margin-bottom:2rem;}\n.toc h2{margin-top:0;font-size:1.1rem;}\n.toc ul{margin:0;padding-left:1.2rem;}\n.toc a{color:var(--accent);text-decoration:none;}\n.site-footer{margin-top:3rem;padding-top:1rem;border-top:2px solid var(--accent);font-size:.9rem;color:#64748b;}\n<\/style>\n<\/head>\n<body>\n<nav class=\"toc\"><h2>Contents<\/h2><ul>\n <li><a href=\"#topic-1-vector-resolution-and-resultant-forces\">Topic 1: Vector Resolution and Resultant Forces<\/a><\/li>\n <li><a href=\"#topic-2-motion-graphs\">Topic 2: Motion Graphs<\/a><\/li>\n <li><a href=\"#topic-3-suvat-equations\">Topic 3: SUVAT Equations<\/a><\/li>\n <li><a href=\"#topic-4-projectile-motion\">Topic 4: Projectile Motion<\/a><\/li>\n <li><a href=\"#topic-5-momentum-and-impulse\">Topic 5: Momentum and Impulse<\/a><\/li>\n <li><a href=\"#topic-6-work-energy-and-power\">Topic 6: Work, Energy and Power<\/a><\/li>\n <li><a href=\"#topic-7-newtons-laws-and-moments\">Topic 7: Newton’s Laws and Moments<\/a><\/li>\n <li><a href=\"#topic-8-solid-materials-and-young-modulus\">Topic 8: Solid Materials and Young Modulus<\/a><\/li>\n <li><a href=\"#practice-questions\">Practice Questions<\/a><\/li>\n<\/ul><\/nav>\n<h1>Unit 1 High-Yield Topics<\/h1>\n<p><strong>Free resource by <a href=\"https:\/\/flowxiom.com\">Flowxiom<\/a> \u2014 Edexcel A-level Physics<\/strong><\/p>\n<p><em>Not everything. Just what’s on the paper. High-frequency topics only \u2014 covering ~80% of exam marks.<\/em><\/p>\n<p>Edexcel A-level Physics | Mechanics & Materials | WPH11 & WPH12<\/p>\n<hr>\n<h2 id=\"topic-1-vector-resolution-and-resultant-forces\">Topic 1: Vector Resolution and Resultant Forces<\/h2>\n<p><strong>Question types:<\/strong> Inclined plane force analysis, rope tension equilibrium, magnitude and direction of resultant.<\/p>\n<h3 id=\"key-formulae-resolving-a-force\">Key Formulae \u2014 Resolving a Force<\/h3>\n<p>For force \\(F\\) at angle \\(\\theta\\) from horizontal:<\/p>\n<p>\\[F_x = F\\cos\\theta \\qquad F_y = F\\sin\\theta\\]<\/p>\n<div class=\"seo-note-box\">\n<p>Adjacent side uses <strong>cos<\/strong>, opposite side uses <strong>sin<\/strong> (\u03b8 measured from horizontal)<\/p>\n<\/div>\n<h3 id=\"fourstep-method-for-resultant\">Four-Step Method for Resultant<\/h3>\n<p class=\"numbered-step\">Resolve all forces into horizontal and vertical components \u2014 right\/up positive<\/p>\n<p class=\"numbered-step\">Sum horizontal: \\(R_x = \\sum F_x\\); sum vertical: \\(R_y = \\sum F_y\\)<\/p>\n<p class=\"numbered-step\">Magnitude: \\(F_R = \\sqrt{R_x^2 + R_y^2}\\)<\/p>\n<p class=\"numbered-step\">Direction: \\(\\tan\\alpha = \\dfrac{|R_y|}{|R_x|}\\) \u2014 state as angle from horizontal<\/p>\n<h3 id=\"equilibrium-condition\">Equilibrium Condition<\/h3>\n<p>For three forces in equilibrium: they must be concurrent and form a closed triangle.<\/p>\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c sin\/cos confused \u2014 always draw the triangle and mark \u03b8 clearly<\/li>\n<li>\u274c Forgetting to include weight \u2014 vertical equilibrium must also hold<\/li>\n<li>\u274c Direction stated as a number only \u2014 must specify “angle from horizontal”<\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"topic-2-motion-graphs\">Topic 2: Motion Graphs<\/h2>\n<p><strong>Question types:<\/strong> Read graph to identify motion; calculate displacement\/acceleration from graph; sketch graph conversions.<\/p>\n<h3 id=\"golden-rules\">Golden Rules<\/h3>\n<table>\n<thead><tr><th>Graph<\/th><th>Gradient =<\/th><th>Area =<\/th><\/tr><\/thead>\n<tr><td>\\(s\\)-\\(t\\)<\/td><td>velocity \\(v\\)<\/td><td>\u2014<\/td><\/tr>\n<tr><td>\\(v\\)-\\(t\\)<\/td><td>acceleration \\(a\\)<\/td><td>displacement \\(s\\)<\/td><\/tr>\n<tr><td>\\(a\\)-\\(t\\)<\/td><td>\u2014<\/td><td>change in velocity \\(\\Delta v\\)<\/td><\/tr>\n<\/table>\n\n<p>\\[s \\xrightarrow{\\text{gradient}} v \\xrightarrow{\\text{gradient}} a \\qquad a \\xrightarrow{\\text{area}} \\Delta v \\xrightarrow{\\text{area}} \\Delta s\\]<\/p>\n<h3 id=\"common-vt-graph-shapes\">Common v-t Graph Shapes<\/h3>\n<table>\n<thead><tr><th>Shape<\/th><th>Meaning<\/th><\/tr><\/thead>\n<tr><td>Horizontal straight line<\/td><td>Uniform velocity (\\(a = 0\\))<\/td><\/tr>\n<tr><td>Straight line sloping up<\/td><td>Uniform acceleration<\/td><\/tr>\n<tr><td>Straight line sloping down<\/td><td>Uniform deceleration<\/td><\/tr>\n<tr><td>Steepening curve<\/td><td>Increasing acceleration<\/td><\/tr>\n<tr><td>Crosses time axis<\/td><td>Velocity reverses direction<\/td><\/tr>\n<\/table>\n\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c Area under v-t graph = displacement (can be negative); not the same as distance<\/li>\n<li>\u274c Curved s-t graph means changing speed, not necessarily projectile motion<\/li>\n<li>\u274c Gradient of v-t = acceleration; area of v-t = displacement (not the other way round)<\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"topic-3-suvat-equations\">Topic 3: SUVAT Equations<\/h2>\n<p><strong>Question types:<\/strong> Given a motion description, find velocity, displacement, time or acceleration.<\/p>\n<h3 id=\"the-four-equations\">The Four Equations<\/h3>\n<table>\n<thead><tr><th>Equation<\/th><th>Missing quantity<\/th><\/tr><\/thead>\n<tr><td>\\(v = u + at\\)<\/td><td>no displacement<\/td><\/tr>\n<tr><td>\\(s = \\dfrac{1}{2}(u+v)t\\)<\/td><td>no acceleration<\/td><\/tr>\n<tr><td>\\(s = ut + \\dfrac{1}{2}at^2\\)<\/td><td>no final velocity<\/td><\/tr>\n<tr><td>\\(v^2 = u^2 + 2as\\)<\/td><td>no time<\/td><\/tr>\n<\/table>\n\n<h3 id=\"method\">Method<\/h3>\n<p class=\"numbered-step\">List all five quantities \\(s, u, v, a, t\\); fill in knowns, mark unknown with ?<\/p>\n<p class=\"numbered-step\">Identify 3 knowns + 1 target \u2192 select correct equation<\/p>\n<p class=\"numbered-step\">Substitute \u2014 take care with signs for direction<\/p>\n<h3 id=\"key-phrase-translations\">Key Phrase Translations<\/h3>\n<table>\n<thead><tr><th>Phrase in question<\/th><th>Value<\/th><\/tr><\/thead>\n<tr><td>from rest \/ starts from rest<\/td><td>\\(u = 0\\)<\/td><\/tr>\n<tr><td>comes to rest \/ stops<\/td><td>\\(v = 0\\)<\/td><\/tr>\n<tr><td>deceleration \/ retardation<\/td><td>\\(a\\) is negative<\/td><\/tr>\n<tr><td>free fall \/ dropped<\/td><td>\\(a = 9.81\\ \\text{m s}^{-2}\\), \\(u = 0\\)<\/td><\/tr>\n<tr><td>thrown upward<\/td><td>\\(a = -9.81\\ \\text{m s}^{-2}\\) (taking up as positive)<\/td><\/tr>\n<\/table>\n\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c Deceleration: \\(a\\) must be negative<\/li>\n<li>\u274c If “thrown” not “dropped”, initial velocity is not zero<\/li>\n<li>\u274c Mixed units \u2014 convert first (cm \u2192 m, km\/h \u2192 m\/s)<\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"topic-4-projectile-motion\">Topic 4: Projectile Motion<\/h2>\n<p><strong>Question types:<\/strong> Horizontal or angled launch \u2014 find time of flight, range, velocity at landing.<\/p>\n<h3 id=\"core-principle\">Core Principle<\/h3>\n<p>Horizontal and vertical motions are completely independent; <strong>time is the only link<\/strong>.<\/p>\n<table>\n<thead><tr><th><\/th><th>Horizontal<\/th><th>Vertical<\/th><\/tr><\/thead>\n<tr><td>Acceleration<\/td><td>\\(a_x = 0\\)<\/td><td>\\(a_y = -9.81\\ \\text{m s}^{-2}\\)<\/td><\/tr>\n<tr><td>Velocity<\/td><td>constant: \\(v_x = u\\cos\\theta\\)<\/td><td>changes \u2014 use SUVAT<\/td><\/tr>\n<tr><td>Displacement<\/td><td>\\(s_x = v_x \\times t\\)<\/td><td>use SUVAT<\/td><\/tr>\n<\/table>\n\n<h3 id=\"solution-framework\">Solution Framework<\/h3>\n<pre><code>Vertical (solve first) Horizontal (solve after)\ns_y = ? s_x = ?\nu_y = u sin\u03b8 u_x = u cos\u03b8\na_y = \u22129.81 a_x = 0\n\u2192 find t s_x = u_x \u00d7 t<\/code><\/pre>\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c Horizontal velocity is constant \u2014 do not apply SUVAT to it<\/li>\n<li>\u274c Landing speed requires combining both components: \\(v = \\sqrt{v_x^2 + v_y^2}\\)<\/li>\n<li>\u274c Horizontal component uses \\(\\cos\\theta\\); vertical uses \\(\\sin\\theta\\)<\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"topic-5-momentum-and-impulse\">Topic 5: Momentum and Impulse<\/h2>\n<p><strong>Question types:<\/strong> Collision calculations, bouncing ball, F-t graph, explosion and recoil.<\/p>\n<h3 id=\"key-formulae\">Key Formulae<\/h3>\n<p>\\[p = mv \\qquad \\text{(momentum \u2014 vector)}\\]<\/p>\n<p>\\[\\text{Impulse} = F\\Delta t = \\Delta p = mv – mu\\]<\/p>\n<h3 id=\"conservation-of-momentum\">Conservation of Momentum<\/h3>\n<p>Net external force = 0 (isolated system) \u2192 total momentum is conserved:<\/p>\n<p>\\[m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2\\]<\/p>\n<h3 id=\"elastic-vs-inelastic-collisions\">Elastic vs Inelastic Collisions<\/h3>\n<table>\n<thead><tr><th><\/th><th>Momentum<\/th><th>Kinetic energy<\/th><\/tr><\/thead>\n<tr><td>Elastic<\/td><td>conserved \u2713<\/td><td>conserved \u2713<\/td><\/tr>\n<tr><td>Inelastic<\/td><td>conserved \u2713<\/td><td><strong>not conserved<\/strong> \u2717 (converted to heat\/sound)<\/td><\/tr>\n<tr><td>Perfectly inelastic<\/td><td>conserved \u2713<\/td><td>maximum loss<\/td><\/tr>\n<\/table>\n\n<h3 id=\"ft-graph\">F-t Graph<\/h3>\n<p>\\[\\text{Area under graph} = \\text{impulse} = \\Delta p\\]<\/p>\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c <strong>Sign errors for direction<\/strong> \u2014 most common mark loss<\/li>\n<\/ul>\n<p>Example: ball hits wall at \\(10\\ \\text{m\/s}\\), bounces back at \\(8\\ \\text{m\/s}\\):<\/p>\n<p>\\(\\Delta p = m(-8) – m(+10) = -18m\\), <strong>not<\/strong> \\(-2m\\)<\/p>\n<ul>\n<li>\u274c After a perfectly inelastic collision, both objects share the same final velocity<\/li>\n<li>\u274c Momentum is always conserved in collisions; kinetic energy is only conserved in elastic collisions<\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"topic-6-work-energy-and-power\">Topic 6: Work, Energy and Power<\/h2>\n<p><strong>Question types:<\/strong> Work calculations, energy conservation, power-velocity relationship.<\/p>\n<h3 id=\"key-formulae\">Key Formulae<\/h3>\n<p>\\[W = Fs\\cos\\theta \\qquad E_k = \\frac{1}{2}mv^2 \\qquad \\Delta E_p = mg\\Delta h\\]<\/p>\n<p>\\[P = \\frac{W}{t} = Fv \\qquad \\text{efficiency} = \\frac{\\text{useful output}}{\\text{total input}} \\times 100\\%\\]<\/p>\n<h3 id=\"when-work-done-0\">When Work Done = 0<\/h3>\n<p>Force perpendicular to displacement (\\(\\theta = 90\u00b0\\)) \u2192 \\(W = 0\\)<\/p>\n<p>Example: carrying an object horizontally \u2014 gravity does no work.<\/p>\n<h3 id=\"energy-conservation\">Energy Conservation<\/h3>\n<ul>\n<li>No friction\/air resistance \u2192 mechanical energy conserved: \\(E_k + E_p = \\text{constant}\\)<\/li>\n<li>With friction \u2192 energy lost = friction force \u00d7 distance (converted to thermal energy)<\/li>\n<\/ul>\n<h3 id=\"fs-graph\">F-s Graph<\/h3>\n<p>\\[\\text{Area under graph} = \\text{work done} = W\\]<\/p>\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c Omitting \\(\\cos\\theta\\) when force and displacement are not parallel<\/li>\n<li>\u274c In \\(P = Fv\\), \\(v\\) must be the component of velocity in the direction of force<\/li>\n<li>\u274c Efficiency fraction inverted<\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"topic-7-newtons-laws-and-moments\">Topic 7: Newton’s Laws and Moments<\/h2>\n<p><strong>Question types:<\/strong> Free-body diagrams, equilibrium conditions, moment calculations.<\/p>\n<h3 id=\"conditions-for-equilibrium-both-must-hold-simultaneously\">Conditions for Equilibrium (both must hold simultaneously)<\/h3>\n<p class=\"numbered-step\">Resultant force = 0 in all directions<\/p>\n<p class=\"numbered-step\">Sum of moments = 0 about any point<\/p>\n<h3 id=\"moment-pivot-trick\">Moment Pivot Trick<\/h3>\n<div class=\"seo-note-box\">\n<p>Take moments about the point where an unknown force acts \u2014 its moment = 0, eliminating one unknown from the equation.<\/p>\n<\/div>\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c Omitting the moment of one of the forces<\/li>\n<li>\u274c Not consistently assigning + or \u2212 to clockwise vs anticlockwise<\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"topic-8-solid-materials-and-young-modulus\">Topic 8: Solid Materials and Young Modulus<\/h2>\n<p><strong>Question types:<\/strong> Calculate Young modulus, identify key points on stress-strain graph, classify material type.<\/p>\n<h3 id=\"key-formulae\">Key Formulae<\/h3>\n<p>\\[\\sigma = \\frac{F}{A} \\quad \\text{(stress, Pa)} \\qquad \\varepsilon = \\frac{\\Delta L}{L} \\quad \\text{(strain \u2014 dimensionless)}\\]<\/p>\n<p>\\[E = \\frac{\\sigma}{\\varepsilon} = \\frac{FL}{A\\Delta L} \\quad \\text{(Young modulus, Pa)}\\]<\/p>\n<p>\\[F = k\\Delta x \\qquad E_{el} = \\frac{1}{2}F\\Delta x = \\frac{1}{2}k(\\Delta x)^2\\]<\/p>\n<div class=\"seo-note-box\">\n<p>Area under F-x graph = elastic potential energy stored<\/p>\n<\/div>\n<h3 id=\"key-points-on-the-stressstrain-graph\">Key Points on the Stress-Strain Graph<\/h3>\n<table>\n<thead><tr><th>Point<\/th><th>Name<\/th><th>Meaning<\/th><\/tr><\/thead>\n<tr><td>End of straight line<\/td><td>Limit of Proportionality<\/td><td>Above this, Hooke’s law no longer holds<\/td><\/tr>\n<tr><td>First point after curve<\/td><td>Elastic Limit<\/td><td>Above this, permanent deformation occurs<\/td><\/tr>\n<tr><td>Sudden large extension<\/td><td>Yield Point<\/td><td>Sudden large plastic deformation<\/td><\/tr>\n<tr><td>Highest point<\/td><td>UTS<\/td><td>Maximum stress the material can withstand<\/td><\/tr>\n<tr><td>End of graph<\/td><td>Breaking Point<\/td><td>Fracture<\/td><\/tr>\n<\/table>\n\n<div class=\"seo-note-box\">\n<p>Read Young modulus from the <strong>gradient of the straight-line section<\/strong>: \\(E = \\Delta\\sigma \/ \\Delta\\varepsilon\\)<\/p>\n<\/div>\n<h3 id=\"three-material-types\">Three Material Types<\/h3>\n<table>\n<thead><tr><th>Type<\/th><th>Graph feature<\/th><th>Examples<\/th><\/tr><\/thead>\n<tr><td>Ductile<\/td><td>Large plastic region before fracture<\/td><td>Copper, mild steel<\/td><\/tr>\n<tr><td>Brittle<\/td><td>Fractures at or near elastic limit<\/td><td>Glass, cast iron<\/td><\/tr>\n<tr><td>Polymeric<\/td><td>Non-linear; loading and unloading paths differ<\/td><td>Rubber<\/td><\/tr>\n<\/table>\n\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c Strain has no unit \u2014 it is a dimensionless ratio<\/li>\n<li>\u274c Use extension \\(\\Delta L\\), not total length \\(L\\)<\/li>\n<li>\u274c Area = \\(\\pi r^2\\) \u2014 remember to halve the diameter to get radius<\/li>\n<li>\u274c Elastic limit and limit of proportionality are different points (close but distinct)<\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"practice-questions\">Practice Questions<\/h2>\n<p><strong>Q1.<\/strong> 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.<\/p>\n<details><summary>Answer<\/summary><div class=\"answer-block\"><p>\\(A = \\pi(0.5\\times10^{-3})^2 = 7.85\\times10^{-7}\\ \\text{m}^2\\)<\/p>\n<p>\\(\\sigma = 80 \/ 7.85\\times10^{-7} = 1.02\\times10^8\\ \\text{Pa}\\)<\/p>\n<p>\\(\\varepsilon = 0.50\\times10^{-3} \/ 2.0 = 2.5\\times10^{-4}\\)<\/p>\n<p>\\(E = \\sigma\/\\varepsilon = \\mathbf{4.1\\times10^{11}\\ \\text{Pa}}\\)<\/p><\/div><\/details>\n<hr>\n<p><strong>Q2.<\/strong> A \\(5.0\\ \\text{N}\\) force acts at \\(37\u00b0\\) to the horizontal. Find the horizontal and vertical components. (\\(\\sin37\u00b0=0.60\\), \\(\\cos37\u00b0=0.80\\))<\/p>\n<details><summary>Answer<\/summary><div class=\"answer-block\"><p>\\(F_x = 5.0\\cos37\u00b0 = \\mathbf{4.0\\ \\text{N}}\\)<\/p>\n<p>\\(F_y = 5.0\\sin37\u00b0 = \\mathbf{3.0\\ \\text{N}}\\)<\/p><\/div><\/details>\n<hr>\n<p><strong>Q3.<\/strong> 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.<\/p>\n<details><summary>Answer<\/summary><div class=\"answer-block\"><p>Acceleration = gradient \\(= (0-12)\/4 = \\mathbf{-3.0\\ \\text{m s}^{-2}}\\) (deceleration)<\/p>\n<p>Displacement = area of triangle \\(= \\frac{1}{2}\\times4\\times12 = \\mathbf{24\\ \\text{m}}\\)<\/p><\/div><\/details>\n<hr>\n<p><strong>Q4.<\/strong> A car brakes from \\(30\\ \\text{m\/s}\\) to rest with deceleration \\(5.0\\ \\text{m\/s}^2\\). Find the braking distance.<\/p>\n<details><summary>Answer<\/summary><div class=\"answer-block\"><p>\\(v=0\\), \\(u=30\\), \\(a=-5.0\\). Use \\(v^2 = u^2 + 2as\\):<\/p>\n<p>\\(0 = 900 + 2(-5.0)s \\Rightarrow s = \\mathbf{90\\ \\text{m}}\\)<\/p><\/div><\/details>\n<hr>\n<p><strong>Q5.<\/strong> 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}\\))<\/p>\n<details><summary>Answer<\/summary><div class=\"answer-block\"><p>Vertical: \\(20 = \\frac{1}{2}(10)t^2 \\Rightarrow t = 2.0\\ \\text{s}\\)<\/p>\n<p>Horizontal: \\(s_x = 6 \\times 2.0 = \\mathbf{12\\ \\text{m}}\\)<\/p><\/div><\/details>\n<hr>\n<p><strong>Q6.<\/strong> 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.<\/p>\n<details><summary>Answer<\/summary><div class=\"answer-block\"><p>Taking initial direction as positive:<\/p>\n<p>\\(\\Delta p = 0.2 \\times (-3-5) = -1.6\\ \\text{N s}\\)<\/p>\n<p>Magnitude \\(= \\mathbf{1.6\\ \\text{N s}}\\)<\/p><\/div><\/details>\n<hr>\n<p><em>Want more? Visit <a href=\"https:\/\/flowxiom.com\">flowxiom.com<\/a><\/em><\/p>\n<footer class=\"site-footer\">\n <p>Free resource by <a href=\"https:\/\/flowxiom.com\">Flowxiom<\/a> \u2014 Edexcel A-level Physics<br>\n High-frequency topics only, covering ~80% of exam marks.<\/p>\n<\/footer>\n<\/body>\n<\/html>\n\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This page is a “must-know” guide for Unit 1 Physics. It breaks down difficult concepts like projectile motion and energy conservation into simple steps. Key features include:<\/p>\n<p>Formula Breakdowns: Clear explanations of SUVAT, Momentum, and Young Modulus.<\/p>\n<p>Exam Tips: Specific advice on how to avoid losing marks on common errors.<\/p>\n<p>Graph Analysis: Simple rules for interpreting motion and stress-strain graphs.<\/p>\n<p>Practice: Worked examples to help you apply the theory to real exam questions.<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-34","post","type-post","status-publish","format-standard","hentry","category-exam-sprint-pack-physics-exam-sprint-pack"],"_links":{"self":[{"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/posts\/34","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/comments?post=34"}],"version-history":[{"count":3,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/posts\/34\/revisions"}],"predecessor-version":[{"id":41,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/posts\/34\/revisions\/41"}],"wp:attachment":[{"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/media?parent=34"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/categories?post=34"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/tags?post=34"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}

{"id":34,"date":"2026-04-17T16:07:26","date_gmt":"2026-04-17T16:07:26","guid":{"rendered":"https:\/\/flowxiom.com\/?p=34"},"modified":"2026-04-17T16:16:50","modified_gmt":"2026-04-17T16:16:50","slug":"unit-1-high-yield-topics","status":"publish","type":"post","link":"https:\/\/flowxiom.com\/index.php\/2026\/04\/17\/unit-1-high-yield-topics\/","title":{"rendered":"Unit 1 High-Yield Topics"},"content":{"rendered":"\n\n\n\n\n\nUnit 1 High-Yield Topics | Flowxiom<\/title>\n<meta name=\"description\" content=\"Unit 1 High-Yield Topics \u2014 Edexcel A-level Physics WPH. Question types: Inclined plane force analysis, rope tension equilibrium, magnitude and direction of r...\">\n<link rel=\"canonical\" href=\"https:\/\/flowxiom.com\/edexcel-physics-unit-1-high-yield-topics\/\">\n<script type=\"application\/ld+json\">\n{\n \"@context\": \"https:\/\/schema.org\",\n \"@type\": \"FAQPage\",\n \"mainEntity\": [\n {\n \"@type\": \"Question\",\n \"name\": \"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.\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"\\\\(A = \\\\pi(0.5\\\\times10^{-3})^2 = 7.85\\\\times10^{-7}\\\\ \\\\text{m}^2\\\\) \\n \\\\(\\\\sigma = 80 \/ 7.85\\\\times10^{-7} = 1.02\\\\times10^8\\\\ \\\\text{Pa}\\\\) \\n \\\\(\\\\varepsilon = 0.50\\\\times10^{-3} \/ 2.0 = 2.5\\\\times10^{-4}\\\\) \\n \\\\(E = \\\\sigma\/\\\\varepsilon = \\\\mathbf{4.1\\\\times10^{11}\\\\ \\\\text{Pa}}\\\\)\"\n }\n },\n {\n \"@type\": \"Question\",\n \"name\": \"Q2. A \\\\(5.0\\\\ \\\\text{N}\\\\) force acts at \\\\(37\u00b0\\\\) to the horizontal. Find the horizontal and vertical components. (\\\\(\\\\sin37\u00b0=0.60\\\\), \\\\(\\\\cos37\u00b0=0.80\\\\))\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"\\\\(F_x = 5.0\\\\cos37\u00b0 = \\\\mathbf{4.0\\\\ \\\\text{N}}\\\\) \\n \\\\(F_y = 5.0\\\\sin37\u00b0 = \\\\mathbf{3.0\\\\ \\\\text{N}}\\\\)\"\n }\n },\n {\n \"@type\": \"Question\",\n \"name\": \"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.\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"Acceleration = gradient \\\\(= (0-12)\/4 = \\\\mathbf{-3.0\\\\ \\\\text{m s}^{-2}}\\\\) (deceleration) \\n Displacement = area of triangle \\\\(= \\\\frac{1}{2}\\\\times4\\\\times12 = \\\\mathbf{24\\\\ \\\\text{m}}\\\\)\"\n }\n },\n {\n \"@type\": \"Question\",\n \"name\": \"Q4. A car brakes from \\\\(30\\\\ \\\\text{m\/s}\\\\) to rest with deceleration \\\\(5.0\\\\ \\\\text{m\/s}^2\\\\). Find the braking distance.\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"\\\\(v=0\\\\), \\\\(u=30\\\\), \\\\(a=-5.0\\\\). Use \\\\(v^2 = u^2 + 2as\\\\): \\n \\\\(0 = 900 + 2(-5.0)s \\\\Rightarrow s = \\\\mathbf{90\\\\ \\\\text{m}}\\\\)\"\n }\n },\n {\n \"@type\": \"Question\",\n \"name\": \"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}\\\\))\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"Vertical: \\\\(20 = \\\\frac{1}{2}(10)t^2 \\\\Rightarrow t = 2.0\\\\ \\\\text{s}\\\\) \\n Horizontal: \\\\(s_x = 6 \\\\times 2.0 = \\\\mathbf{12\\\\ \\\\text{m}}\\\\)\"\n }\n },\n {\n \"@type\": \"Question\",\n \"name\": \"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.\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"Taking initial direction as positive: \\n \\\\(\\\\Delta p = 0.2 \\\\times (-3-5) = -1.6\\\\ \\\\text{N s}\\\\) \\n Magnitude \\\\(= \\\\mathbf{1.6\\\\ \\\\text{N s}}\\\\)\"\n }\n }\n ]\n}\n<\/script>\n\n<script>\nMathJax = {\n tex: { inlineMath: [['\\\\(','\\\\)']], displayMath: [['\\\\[','\\\\]']] },\n svg: { fontCache: 'global' }\n};\n<\/script>\n<script async src=\"https:\/\/cdn.jsdelivr.net\/npm\/mathjax@3\/es5\/tex-svg.js\"><\/script>\n\n<style>\n:root{--accent:#2563eb;--warn-bg:#fef9c3;--warn-border:#ca8a04;--formula-bg:#eff6ff;--formula-border:#2563eb;}\nbody{font-family:system-ui,sans-serif;max-width:860px;margin:0 auto;padding:1.5rem;line-height:1.7;color:#1e293b;}\nh1{font-size:2rem;border-bottom:3px solid var(--accent);padding-bottom:.4rem;}\nh2{font-size:1.4rem;color:var(--accent);margin-top:2rem;}\nh3{font-size:1.1rem;margin-top:1.4rem;}\ntable{border-collapse:collapse;width:100%;margin:1rem 0;}\nth,td{border:1px solid #cbd5e1;padding:.5rem .75rem;text-align:left;}\nth{background:#e2e8f0;}\npre,code{background:#f1f5f9;border-radius:4px;}\npre{padding:1rem;overflow-x:auto;}\ncode{padding:.1rem .3rem;font-size:.9em;}\n.seo-warning-box{background:var(--warn-bg);border-left:4px solid var(--warn-border);padding:.75rem 1rem;margin:1rem 0;border-radius:0 6px 6px 0;}\n.seo-note-box{background:#f0fdf4;border-left:4px solid #16a34a;padding:.75rem 1rem;margin:1rem 0;border-radius:0 6px 6px 0;}\nsection.formula-card{background:var(--formula-bg);border:1px solid var(--formula-border);border-radius:8px;padding:1rem 1.25rem;margin:1.5rem 0;}\ndetails{border:1px solid #e2e8f0;border-radius:6px;padding:.5rem 1rem;margin:.75rem 0;}\nsummary{cursor:pointer;font-weight:600;}\n.answer-block{margin-top:.5rem;padding-top:.5rem;border-top:1px solid #e2e8f0;overflow-x:auto;}\n.answer-block p{margin:.25rem 0;}\n.numbered-step{padding-left:1.5rem;position:relative;}\nhr{border:none;border-top:1px solid #e2e8f0;margin:2rem 0;}\n.toc{background:#f8fafc;border:1px solid #e2e8f0;border-radius:8px;padding:1rem 1.5rem;margin-bottom:2rem;}\n.toc h2{margin-top:0;font-size:1.1rem;}\n.toc ul{margin:0;padding-left:1.2rem;}\n.toc a{color:var(--accent);text-decoration:none;}\n.site-footer{margin-top:3rem;padding-top:1rem;border-top:2px solid var(--accent);font-size:.9rem;color:#64748b;}\n<\/style>\n<\/head>\n<body>\n<nav class=\"toc\"><h2>Contents<\/h2><ul>\n <li><a href=\"#topic-1-vector-resolution-and-resultant-forces\">Topic 1: Vector Resolution and Resultant Forces<\/a><\/li>\n <li><a href=\"#topic-2-motion-graphs\">Topic 2: Motion Graphs<\/a><\/li>\n <li><a href=\"#topic-3-suvat-equations\">Topic 3: SUVAT Equations<\/a><\/li>\n <li><a href=\"#topic-4-projectile-motion\">Topic 4: Projectile Motion<\/a><\/li>\n <li><a href=\"#topic-5-momentum-and-impulse\">Topic 5: Momentum and Impulse<\/a><\/li>\n <li><a href=\"#topic-6-work-energy-and-power\">Topic 6: Work, Energy and Power<\/a><\/li>\n <li><a href=\"#topic-7-newtons-laws-and-moments\">Topic 7: Newton’s Laws and Moments<\/a><\/li>\n <li><a href=\"#topic-8-solid-materials-and-young-modulus\">Topic 8: Solid Materials and Young Modulus<\/a><\/li>\n <li><a href=\"#practice-questions\">Practice Questions<\/a><\/li>\n<\/ul><\/nav>\n<h1>Unit 1 High-Yield Topics<\/h1>\n<p><strong>Free resource by <a href=\"https:\/\/flowxiom.com\">Flowxiom<\/a> \u2014 Edexcel A-level Physics<\/strong><\/p>\n<p><em>Not everything. Just what’s on the paper. High-frequency topics only \u2014 covering ~80% of exam marks.<\/em><\/p>\n<p>Edexcel A-level Physics | Mechanics & Materials | WPH11 & WPH12<\/p>\n<hr>\n<h2 id=\"topic-1-vector-resolution-and-resultant-forces\">Topic 1: Vector Resolution and Resultant Forces<\/h2>\n<p><strong>Question types:<\/strong> Inclined plane force analysis, rope tension equilibrium, magnitude and direction of resultant.<\/p>\n<h3 id=\"key-formulae-resolving-a-force\">Key Formulae \u2014 Resolving a Force<\/h3>\n<p>For force \\(F\\) at angle \\(\\theta\\) from horizontal:<\/p>\n<p>\\[F_x = F\\cos\\theta \\qquad F_y = F\\sin\\theta\\]<\/p>\n<div class=\"seo-note-box\">\n<p>Adjacent side uses <strong>cos<\/strong>, opposite side uses <strong>sin<\/strong> (\u03b8 measured from horizontal)<\/p>\n<\/div>\n<h3 id=\"fourstep-method-for-resultant\">Four-Step Method for Resultant<\/h3>\n<p class=\"numbered-step\">Resolve all forces into horizontal and vertical components \u2014 right\/up positive<\/p>\n<p class=\"numbered-step\">Sum horizontal: \\(R_x = \\sum F_x\\); sum vertical: \\(R_y = \\sum F_y\\)<\/p>\n<p class=\"numbered-step\">Magnitude: \\(F_R = \\sqrt{R_x^2 + R_y^2}\\)<\/p>\n<p class=\"numbered-step\">Direction: \\(\\tan\\alpha = \\dfrac{|R_y|}{|R_x|}\\) \u2014 state as angle from horizontal<\/p>\n<h3 id=\"equilibrium-condition\">Equilibrium Condition<\/h3>\n<p>For three forces in equilibrium: they must be concurrent and form a closed triangle.<\/p>\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c sin\/cos confused \u2014 always draw the triangle and mark \u03b8 clearly<\/li>\n<li>\u274c Forgetting to include weight \u2014 vertical equilibrium must also hold<\/li>\n<li>\u274c Direction stated as a number only \u2014 must specify “angle from horizontal”<\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"topic-2-motion-graphs\">Topic 2: Motion Graphs<\/h2>\n<p><strong>Question types:<\/strong> Read graph to identify motion; calculate displacement\/acceleration from graph; sketch graph conversions.<\/p>\n<h3 id=\"golden-rules\">Golden Rules<\/h3>\n<table>\n<thead><tr><th>Graph<\/th><th>Gradient =<\/th><th>Area =<\/th><\/tr><\/thead>\n<tr><td>\\(s\\)-\\(t\\)<\/td><td>velocity \\(v\\)<\/td><td>\u2014<\/td><\/tr>\n<tr><td>\\(v\\)-\\(t\\)<\/td><td>acceleration \\(a\\)<\/td><td>displacement \\(s\\)<\/td><\/tr>\n<tr><td>\\(a\\)-\\(t\\)<\/td><td>\u2014<\/td><td>change in velocity \\(\\Delta v\\)<\/td><\/tr>\n<\/table>\n\n<p>\\[s \\xrightarrow{\\text{gradient}} v \\xrightarrow{\\text{gradient}} a \\qquad a \\xrightarrow{\\text{area}} \\Delta v \\xrightarrow{\\text{area}} \\Delta s\\]<\/p>\n<h3 id=\"common-vt-graph-shapes\">Common v-t Graph Shapes<\/h3>\n<table>\n<thead><tr><th>Shape<\/th><th>Meaning<\/th><\/tr><\/thead>\n<tr><td>Horizontal straight line<\/td><td>Uniform velocity (\\(a = 0\\))<\/td><\/tr>\n<tr><td>Straight line sloping up<\/td><td>Uniform acceleration<\/td><\/tr>\n<tr><td>Straight line sloping down<\/td><td>Uniform deceleration<\/td><\/tr>\n<tr><td>Steepening curve<\/td><td>Increasing acceleration<\/td><\/tr>\n<tr><td>Crosses time axis<\/td><td>Velocity reverses direction<\/td><\/tr>\n<\/table>\n\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c Area under v-t graph = displacement (can be negative); not the same as distance<\/li>\n<li>\u274c Curved s-t graph means changing speed, not necessarily projectile motion<\/li>\n<li>\u274c Gradient of v-t = acceleration; area of v-t = displacement (not the other way round)<\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"topic-3-suvat-equations\">Topic 3: SUVAT Equations<\/h2>\n<p><strong>Question types:<\/strong> Given a motion description, find velocity, displacement, time or acceleration.<\/p>\n<h3 id=\"the-four-equations\">The Four Equations<\/h3>\n<table>\n<thead><tr><th>Equation<\/th><th>Missing quantity<\/th><\/tr><\/thead>\n<tr><td>\\(v = u + at\\)<\/td><td>no displacement<\/td><\/tr>\n<tr><td>\\(s = \\dfrac{1}{2}(u+v)t\\)<\/td><td>no acceleration<\/td><\/tr>\n<tr><td>\\(s = ut + \\dfrac{1}{2}at^2\\)<\/td><td>no final velocity<\/td><\/tr>\n<tr><td>\\(v^2 = u^2 + 2as\\)<\/td><td>no time<\/td><\/tr>\n<\/table>\n\n<h3 id=\"method\">Method<\/h3>\n<p class=\"numbered-step\">List all five quantities \\(s, u, v, a, t\\); fill in knowns, mark unknown with ?<\/p>\n<p class=\"numbered-step\">Identify 3 knowns + 1 target \u2192 select correct equation<\/p>\n<p class=\"numbered-step\">Substitute \u2014 take care with signs for direction<\/p>\n<h3 id=\"key-phrase-translations\">Key Phrase Translations<\/h3>\n<table>\n<thead><tr><th>Phrase in question<\/th><th>Value<\/th><\/tr><\/thead>\n<tr><td>from rest \/ starts from rest<\/td><td>\\(u = 0\\)<\/td><\/tr>\n<tr><td>comes to rest \/ stops<\/td><td>\\(v = 0\\)<\/td><\/tr>\n<tr><td>deceleration \/ retardation<\/td><td>\\(a\\) is negative<\/td><\/tr>\n<tr><td>free fall \/ dropped<\/td><td>\\(a = 9.81\\ \\text{m s}^{-2}\\), \\(u = 0\\)<\/td><\/tr>\n<tr><td>thrown upward<\/td><td>\\(a = -9.81\\ \\text{m s}^{-2}\\) (taking up as positive)<\/td><\/tr>\n<\/table>\n\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c Deceleration: \\(a\\) must be negative<\/li>\n<li>\u274c If “thrown” not “dropped”, initial velocity is not zero<\/li>\n<li>\u274c Mixed units \u2014 convert first (cm \u2192 m, km\/h \u2192 m\/s)<\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"topic-4-projectile-motion\">Topic 4: Projectile Motion<\/h2>\n<p><strong>Question types:<\/strong> Horizontal or angled launch \u2014 find time of flight, range, velocity at landing.<\/p>\n<h3 id=\"core-principle\">Core Principle<\/h3>\n<p>Horizontal and vertical motions are completely independent; <strong>time is the only link<\/strong>.<\/p>\n<table>\n<thead><tr><th><\/th><th>Horizontal<\/th><th>Vertical<\/th><\/tr><\/thead>\n<tr><td>Acceleration<\/td><td>\\(a_x = 0\\)<\/td><td>\\(a_y = -9.81\\ \\text{m s}^{-2}\\)<\/td><\/tr>\n<tr><td>Velocity<\/td><td>constant: \\(v_x = u\\cos\\theta\\)<\/td><td>changes \u2014 use SUVAT<\/td><\/tr>\n<tr><td>Displacement<\/td><td>\\(s_x = v_x \\times t\\)<\/td><td>use SUVAT<\/td><\/tr>\n<\/table>\n\n<h3 id=\"solution-framework\">Solution Framework<\/h3>\n<pre><code>Vertical (solve first) Horizontal (solve after)\ns_y = ? s_x = ?\nu_y = u sin\u03b8 u_x = u cos\u03b8\na_y = \u22129.81 a_x = 0\n\u2192 find t s_x = u_x \u00d7 t<\/code><\/pre>\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c Horizontal velocity is constant \u2014 do not apply SUVAT to it<\/li>\n<li>\u274c Landing speed requires combining both components: \\(v = \\sqrt{v_x^2 + v_y^2}\\)<\/li>\n<li>\u274c Horizontal component uses \\(\\cos\\theta\\); vertical uses \\(\\sin\\theta\\)<\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"topic-5-momentum-and-impulse\">Topic 5: Momentum and Impulse<\/h2>\n<p><strong>Question types:<\/strong> Collision calculations, bouncing ball, F-t graph, explosion and recoil.<\/p>\n<h3 id=\"key-formulae\">Key Formulae<\/h3>\n<p>\\[p = mv \\qquad \\text{(momentum \u2014 vector)}\\]<\/p>\n<p>\\[\\text{Impulse} = F\\Delta t = \\Delta p = mv – mu\\]<\/p>\n<h3 id=\"conservation-of-momentum\">Conservation of Momentum<\/h3>\n<p>Net external force = 0 (isolated system) \u2192 total momentum is conserved:<\/p>\n<p>\\[m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2\\]<\/p>\n<h3 id=\"elastic-vs-inelastic-collisions\">Elastic vs Inelastic Collisions<\/h3>\n<table>\n<thead><tr><th><\/th><th>Momentum<\/th><th>Kinetic energy<\/th><\/tr><\/thead>\n<tr><td>Elastic<\/td><td>conserved \u2713<\/td><td>conserved \u2713<\/td><\/tr>\n<tr><td>Inelastic<\/td><td>conserved \u2713<\/td><td><strong>not conserved<\/strong> \u2717 (converted to heat\/sound)<\/td><\/tr>\n<tr><td>Perfectly inelastic<\/td><td>conserved \u2713<\/td><td>maximum loss<\/td><\/tr>\n<\/table>\n\n<h3 id=\"ft-graph\">F-t Graph<\/h3>\n<p>\\[\\text{Area under graph} = \\text{impulse} = \\Delta p\\]<\/p>\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c <strong>Sign errors for direction<\/strong> \u2014 most common mark loss<\/li>\n<\/ul>\n<p>Example: ball hits wall at \\(10\\ \\text{m\/s}\\), bounces back at \\(8\\ \\text{m\/s}\\):<\/p>\n<p>\\(\\Delta p = m(-8) – m(+10) = -18m\\), <strong>not<\/strong> \\(-2m\\)<\/p>\n<ul>\n<li>\u274c After a perfectly inelastic collision, both objects share the same final velocity<\/li>\n<li>\u274c Momentum is always conserved in collisions; kinetic energy is only conserved in elastic collisions<\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"topic-6-work-energy-and-power\">Topic 6: Work, Energy and Power<\/h2>\n<p><strong>Question types:<\/strong> Work calculations, energy conservation, power-velocity relationship.<\/p>\n<h3 id=\"key-formulae\">Key Formulae<\/h3>\n<p>\\[W = Fs\\cos\\theta \\qquad E_k = \\frac{1}{2}mv^2 \\qquad \\Delta E_p = mg\\Delta h\\]<\/p>\n<p>\\[P = \\frac{W}{t} = Fv \\qquad \\text{efficiency} = \\frac{\\text{useful output}}{\\text{total input}} \\times 100\\%\\]<\/p>\n<h3 id=\"when-work-done-0\">When Work Done = 0<\/h3>\n<p>Force perpendicular to displacement (\\(\\theta = 90\u00b0\\)) \u2192 \\(W = 0\\)<\/p>\n<p>Example: carrying an object horizontally \u2014 gravity does no work.<\/p>\n<h3 id=\"energy-conservation\">Energy Conservation<\/h3>\n<ul>\n<li>No friction\/air resistance \u2192 mechanical energy conserved: \\(E_k + E_p = \\text{constant}\\)<\/li>\n<li>With friction \u2192 energy lost = friction force \u00d7 distance (converted to thermal energy)<\/li>\n<\/ul>\n<h3 id=\"fs-graph\">F-s Graph<\/h3>\n<p>\\[\\text{Area under graph} = \\text{work done} = W\\]<\/p>\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c Omitting \\(\\cos\\theta\\) when force and displacement are not parallel<\/li>\n<li>\u274c In \\(P = Fv\\), \\(v\\) must be the component of velocity in the direction of force<\/li>\n<li>\u274c Efficiency fraction inverted<\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"topic-7-newtons-laws-and-moments\">Topic 7: Newton’s Laws and Moments<\/h2>\n<p><strong>Question types:<\/strong> Free-body diagrams, equilibrium conditions, moment calculations.<\/p>\n<h3 id=\"conditions-for-equilibrium-both-must-hold-simultaneously\">Conditions for Equilibrium (both must hold simultaneously)<\/h3>\n<p class=\"numbered-step\">Resultant force = 0 in all directions<\/p>\n<p class=\"numbered-step\">Sum of moments = 0 about any point<\/p>\n<h3 id=\"moment-pivot-trick\">Moment Pivot Trick<\/h3>\n<div class=\"seo-note-box\">\n<p>Take moments about the point where an unknown force acts \u2014 its moment = 0, eliminating one unknown from the equation.<\/p>\n<\/div>\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c Omitting the moment of one of the forces<\/li>\n<li>\u274c Not consistently assigning + or \u2212 to clockwise vs anticlockwise<\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"topic-8-solid-materials-and-young-modulus\">Topic 8: Solid Materials and Young Modulus<\/h2>\n<p><strong>Question types:<\/strong> Calculate Young modulus, identify key points on stress-strain graph, classify material type.<\/p>\n<h3 id=\"key-formulae\">Key Formulae<\/h3>\n<p>\\[\\sigma = \\frac{F}{A} \\quad \\text{(stress, Pa)} \\qquad \\varepsilon = \\frac{\\Delta L}{L} \\quad \\text{(strain \u2014 dimensionless)}\\]<\/p>\n<p>\\[E = \\frac{\\sigma}{\\varepsilon} = \\frac{FL}{A\\Delta L} \\quad \\text{(Young modulus, Pa)}\\]<\/p>\n<p>\\[F = k\\Delta x \\qquad E_{el} = \\frac{1}{2}F\\Delta x = \\frac{1}{2}k(\\Delta x)^2\\]<\/p>\n<div class=\"seo-note-box\">\n<p>Area under F-x graph = elastic potential energy stored<\/p>\n<\/div>\n<h3 id=\"key-points-on-the-stressstrain-graph\">Key Points on the Stress-Strain Graph<\/h3>\n<table>\n<thead><tr><th>Point<\/th><th>Name<\/th><th>Meaning<\/th><\/tr><\/thead>\n<tr><td>End of straight line<\/td><td>Limit of Proportionality<\/td><td>Above this, Hooke’s law no longer holds<\/td><\/tr>\n<tr><td>First point after curve<\/td><td>Elastic Limit<\/td><td>Above this, permanent deformation occurs<\/td><\/tr>\n<tr><td>Sudden large extension<\/td><td>Yield Point<\/td><td>Sudden large plastic deformation<\/td><\/tr>\n<tr><td>Highest point<\/td><td>UTS<\/td><td>Maximum stress the material can withstand<\/td><\/tr>\n<tr><td>End of graph<\/td><td>Breaking Point<\/td><td>Fracture<\/td><\/tr>\n<\/table>\n\n<div class=\"seo-note-box\">\n<p>Read Young modulus from the <strong>gradient of the straight-line section<\/strong>: \\(E = \\Delta\\sigma \/ \\Delta\\varepsilon\\)<\/p>\n<\/div>\n<h3 id=\"three-material-types\">Three Material Types<\/h3>\n<table>\n<thead><tr><th>Type<\/th><th>Graph feature<\/th><th>Examples<\/th><\/tr><\/thead>\n<tr><td>Ductile<\/td><td>Large plastic region before fracture<\/td><td>Copper, mild steel<\/td><\/tr>\n<tr><td>Brittle<\/td><td>Fractures at or near elastic limit<\/td><td>Glass, cast iron<\/td><\/tr>\n<tr><td>Polymeric<\/td><td>Non-linear; loading and unloading paths differ<\/td><td>Rubber<\/td><\/tr>\n<\/table>\n\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c Strain has no unit \u2014 it is a dimensionless ratio<\/li>\n<li>\u274c Use extension \\(\\Delta L\\), not total length \\(L\\)<\/li>\n<li>\u274c Area = \\(\\pi r^2\\) \u2014 remember to halve the diameter to get radius<\/li>\n<li>\u274c Elastic limit and limit of proportionality are different points (close but distinct)<\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"practice-questions\">Practice Questions<\/h2>\n<p><strong>Q1.<\/strong> 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.<\/p>\n<details><summary>Answer<\/summary><div class=\"answer-block\"><p>\\(A = \\pi(0.5\\times10^{-3})^2 = 7.85\\times10^{-7}\\ \\text{m}^2\\)<\/p>\n<p>\\(\\sigma = 80 \/ 7.85\\times10^{-7} = 1.02\\times10^8\\ \\text{Pa}\\)<\/p>\n<p>\\(\\varepsilon = 0.50\\times10^{-3} \/ 2.0 = 2.5\\times10^{-4}\\)<\/p>\n<p>\\(E = \\sigma\/\\varepsilon = \\mathbf{4.1\\times10^{11}\\ \\text{Pa}}\\)<\/p><\/div><\/details>\n<hr>\n<p><strong>Q2.<\/strong> A \\(5.0\\ \\text{N}\\) force acts at \\(37\u00b0\\) to the horizontal. Find the horizontal and vertical components. (\\(\\sin37\u00b0=0.60\\), \\(\\cos37\u00b0=0.80\\))<\/p>\n<details><summary>Answer<\/summary><div class=\"answer-block\"><p>\\(F_x = 5.0\\cos37\u00b0 = \\mathbf{4.0\\ \\text{N}}\\)<\/p>\n<p>\\(F_y = 5.0\\sin37\u00b0 = \\mathbf{3.0\\ \\text{N}}\\)<\/p><\/div><\/details>\n<hr>\n<p><strong>Q3.<\/strong> 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.<\/p>\n<details><summary>Answer<\/summary><div class=\"answer-block\"><p>Acceleration = gradient \\(= (0-12)\/4 = \\mathbf{-3.0\\ \\text{m s}^{-2}}\\) (deceleration)<\/p>\n<p>Displacement = area of triangle \\(= \\frac{1}{2}\\times4\\times12 = \\mathbf{24\\ \\text{m}}\\)<\/p><\/div><\/details>\n<hr>\n<p><strong>Q4.<\/strong> A car brakes from \\(30\\ \\text{m\/s}\\) to rest with deceleration \\(5.0\\ \\text{m\/s}^2\\). Find the braking distance.<\/p>\n<details><summary>Answer<\/summary><div class=\"answer-block\"><p>\\(v=0\\), \\(u=30\\), \\(a=-5.0\\). Use \\(v^2 = u^2 + 2as\\):<\/p>\n<p>\\(0 = 900 + 2(-5.0)s \\Rightarrow s = \\mathbf{90\\ \\text{m}}\\)<\/p><\/div><\/details>\n<hr>\n<p><strong>Q5.<\/strong> 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}\\))<\/p>\n<details><summary>Answer<\/summary><div class=\"answer-block\"><p>Vertical: \\(20 = \\frac{1}{2}(10)t^2 \\Rightarrow t = 2.0\\ \\text{s}\\)<\/p>\n<p>Horizontal: \\(s_x = 6 \\times 2.0 = \\mathbf{12\\ \\text{m}}\\)<\/p><\/div><\/details>\n<hr>\n<p><strong>Q6.<\/strong> 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.<\/p>\n<details><summary>Answer<\/summary><div class=\"answer-block\"><p>Taking initial direction as positive:<\/p>\n<p>\\(\\Delta p = 0.2 \\times (-3-5) = -1.6\\ \\text{N s}\\)<\/p>\n<p>Magnitude \\(= \\mathbf{1.6\\ \\text{N s}}\\)<\/p><\/div><\/details>\n<hr>\n<p><em>Want more? Visit <a href=\"https:\/\/flowxiom.com\">flowxiom.com<\/a><\/em><\/p>\n<footer class=\"site-footer\">\n <p>Free resource by <a href=\"https:\/\/flowxiom.com\">Flowxiom<\/a> \u2014 Edexcel A-level Physics<br>\n High-frequency topics only, covering ~80% of exam marks.<\/p>\n<\/footer>\n<\/body>\n<\/html>\n\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This page is a “must-know” guide for Unit 1 Physics. It breaks down difficult concepts like projectile motion and energy conservation into simple steps. Key features include:<\/p>\n<p>Formula Breakdowns: Clear explanations of SUVAT, Momentum, and Young Modulus.<\/p>\n<p>Exam Tips: Specific advice on how to avoid losing marks on common errors.<\/p>\n<p>Graph Analysis: Simple rules for interpreting motion and stress-strain graphs.<\/p>\n<p>Practice: Worked examples to help you apply the theory to real exam questions.<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-34","post","type-post","status-publish","format-standard","hentry","category-exam-sprint-pack-physics-exam-sprint-pack"],"_links":{"self":[{"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/posts\/34","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/comments?post=34"}],"version-history":[{"count":3,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/posts\/34\/revisions"}],"predecessor-version":[{"id":41,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/posts\/34\/revisions\/41"}],"wp:attachment":[{"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/media?parent=34"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/categories?post=34"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/tags?post=34"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}