Resolving Forces & Friction

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A2 Maths – Mechanics – Resolving Forces

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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5A Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Forces 1 • Resolving Angled Forces, Statics • Mech2 Ex5A • 🎲

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• Dr Frost Slides 1-9✦

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 648a: Determine the vertical or horizontal components of a single angled force.
• 648b: Determine the resultant vector from multiple angled forces.
• 648c: Determine the magnitude and direction of the resultant vector from multiple angled forces.
• 648d: Determine the direction of an angled force that would result in equilibrium.
• 648e: Determine the direction of an angled force that would result in equilibrium, with use of a double angle formula.
• 648f: Determine the magnitude of an unknown angled force that leads to a resultant vector.
• 652a: Determine the acceleration of a particle on a horizontal plane, pulled by an inclined force.
• 648: Exam Practice: Determining components of angled forces and manipulating the resultant force vector
• 652: Exam Practice: Forces on an accelerating single particle, on an inclined plane/inclined forces, no F = mu R

Other Videos

Resolving Forces

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Standards Unit Solving Problems Using Newton’s Law✦
• SRWhitehouse
  • Resolving forces✦

A2 Maths – Mechanics – Forces on a Slope

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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5B Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Forces 3 • Dynamics Intro • Mech2 pre-Ex5B • 🎲

Forces 4 • Dynamics, worded • Mech2 pre-Ex5B • 🎲

Forces 5 • Resultant Forces as Vectors • Mech2 pre-Ex5B • 🎲

Forces 6 • Slopes pt. 1 • Mech2 Ex5B • 🎲

Forces 7 • Slopes (worded) pt. 2 • Mech2 Ex5B • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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• Dr Frost Slides 10-13✦

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 652b: Determine the acceleration of a particle on an inclined plane with a force that is parallel to the plane.
• 652: Exam Practice: Forces on an accelerating single particle, on an inclined plane/inclined forces, no F = mu R

Other Videos

The Inclined Plane

Courtesy of Maths Genie (Up to 4:20)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Worksheets

• Labelling Diagrams (WW) Word & PDF
• Mathshelper (Jon Stone)
  • Inclined Planes
• Physics & Maths Tutor
  • Dynamics: F = ma on a slope: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
• MadAsMaths (T. Madas)
  • Connected Particles (M1) Q9 (difficulty 3 of 5)
  • Dynamics: Forces & Friction (M1) Q19, 21 (difficulty 4 of 5)

A2 Maths – Mechanics – Stationary Forces

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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7A Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Forces 2 • Statics Problems • Mech2 Ex5A/7B • 🎲

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• Dr Frost Slides 1-7✦

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Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 649a: Determine the force needed to hold a particle in equilibrium on a smooth inclined plane, when the force is parallel to the plane.
• 649b: Determine the force needed to hold a particle in equilibrium on a smooth inclined plane, when the force is horizontal.
• 649c: Solve a problem involving a particle on a string at an incline to a vertical wall, where an additional force acts perpendicular to the string.
• 649d: Determine the force needed to hold a particle in equilibrium on a smooth inclined plane, when the force is neither horizontal nor parallel to the plane.
• 649e: Determine the normal reaction force when an angled force holds a particle in equilibrium on a smooth inclined plane.
• 649f: Solve a problem involving a particle on a string at an incline to a vertical wall, where an additional force does not act perpendicular to the string.
• 649: Exam Practice: Forces on a single particle in equilibrium, on an inclined plane/inclined forces, no F = mu R

Other Videos

Equilibrium of a particle – Triangle of forces | ExamSolutions

Exam Solutions Force Triangles for Statics/ Resultant Forces

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

A2 Maths – Mechanics – Tension in Stationary Particles

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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7B Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Forces 10 • Connected Particles, Statics without Friction • Mech2 Ex7B • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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• Dr Frost Slides 8-11✦

Extra Questions

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Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 553a: Find the magnitude of unknown forces when a particle is in equilibrium.
• 649g: Determine the tensions when a particle is suspended from a ceiling by two strings.
• 553: Exam Practice: Forces on a single particle in equilibrium, not on an inclined plane, no F = mu R
• 649: Exam Practice: Forces on a single particle in equilibrium, on an inclined plane/inclined forces, no F = mu R

Other Videos

Statics

Courtesy of Maths Genie (Up to 6:19)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Worksheets

• Naiker Maths
  • Modelling with Statics (Without Friction): Exam Qs 2005–11 · Mark scheme
• Physics & Maths Tutor
  • Statics: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
• MadAsMaths (T. Madas)
  • Equilibrium of Particles (M1) Introduction Q8, 9; Further Problems Q20, 21, 25–28, 33, 39 (difficulty 1–5 of 5)

A2 Maths – Mechanics – Frictonal Forces

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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5C1 Slides (Courtesy of Owen134866)

Textbook Exercise References

5C Q1, 2, 6, 7

Bicen Maths Live Lesson

Forces 8 • Friction • Mech2 Ex5C • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Forces 9 • Friction (simple worded) • Mech2 Ex7C • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths (up to 4:54)

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• Dr Frost Slides 14-16✦

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 651a: Solve problems involving an accelerating particle on a rough horizontal plane pulled by a horizontal force.
• 653a: Solve problems involving an accelerating particle on a rough horizontal plane and an inclined force.
• 651: Exam Practice: Forces on an accelerating single particle, not on an inclined plane, using F = mu R
• 653: Exam Practice: Forces on an accelerating single particle, on an inclined plane/inclined forces, using F = mu R

Other Videos

Friction

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

A2 Maths – Mechanics – Equilibrium Particles with Friction

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept. Up to 6:57

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7C1 Slides (Courtesy of Owen134866)

Textbook Exercise References

7C Q1-5

Bicen Maths Live Lesson

Forces 11 • Statics including Friction • Mech2 Ex7C • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths (up to 10:24)

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• Dr Frost Slide 12✦

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Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 647a: Solve problems where a horizontal force pulls a particle in limiting equilibrium.
• 650a: Label a force diagram involving an inclined plane/inclined forces and friction. (not yet active)
• 650b: Solve problems involving a particle in equilibrium on a rough horizontal plane pulled by an inclined force.
• 647: Exam Practice: Forces on a single particle in equilibrium, not on an inclined plane, using F = mu R
• 650: Exam Practice: Forces on a single particle in equilibrium, on an inclined plane/inclined forces, using F = mu R

Other Videos

• link to ExamSolutions playlist

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Worksheets

• Naiker Maths
  • Friction & Static Particles: Exam Qs 2005–11 · Mark scheme
• MadAsMaths (T. Madas)
  • Equilibrium of Particles (M1) Further Problems Q1, 2, 5, 8, 9, 11, 15, 22, 38 (difficulty 2–5 of 5)

A2 Maths – Mechanics – Forces and Friction on a Slope

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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5C2 Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Forces 9 • Friction (simple worded) • Mech2 Ex7C • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths (from 4:54)

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• Dr Frost Slides 17-19✦

Exam Practice

• Exam Practice

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 653b: Solve problems involving a particle accelerating down a rough inclined plane with no additional forces.
• 653: Exam Practice: Forces on an accelerating single particle, on an inclined plane/inclined forces, using F = mu R

Further Practice

• Practise Questions

Other Videos

The Inclined Plane

Courtesy of Maths Genie (From 4:20)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Worksheets

• MathedUp
  • Forces on an incline: Questions · Challenge · Answers
• MadAsMaths (T. Madas)
  • Dynamics: Forces & Friction (M1) Q3, 10, 16, 20, 25 (difficulty 2–5 of 5)

A2 Maths – Mechanics – Equilibrium Particles with Friction

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept. From 6:57

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7C2 Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Forces 11 • Statics including Friction • Mech2 Ex7C • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths (from 10:24)

Forces 12 • Range of Values for Equilibrium • Mech2 Ex7C • 🎲

Forces 13 • Will the particle move? • Mech2 Ex7 ExamQ • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 13-14✦

Exam Practice

• Exam Practice

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 650c: Solve problems involving a particle on a rough inclined plane where a tension or other force prevents it from slipping down the plane.
• 650d: Determine the range of a force acting on a particle on a rough inclined plane where the particle could slip up or down the plane. (not yet active)
• 650e: Prove that mu = tan θ is the angle of inclination at which a block will slide on a rough inclined plane.
• 650f: Prove an inequality involving a particle on a rough surface on an inclined plane/with inclined forces. (not yet active)
• 650: Exam Practice: Forces on a single particle in equilibrium, on an inclined plane/inclined forces, using F = mu R

Further Practice

• Practise Questions

Other Videos

Statics

Courtesy of Maths Genie (From 6:18)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• The Chalk Face Slippery Slope
• The Chalkface
  • Slippery Slope: PDF

Worksheets

• MadAsMaths (T. Madas)
  • Equilibrium of Particles (M1) Further Problems Q3, 6, 10, 12, 13, 17–19, 23, 24, 29, 32, 34 (difficulty 2–4 of 5)

A2 Maths – Mechanics – f=ma on an inclined plane

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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7E Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Forces 14 • Dynamics with Friction • Mech2 Ex7E • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 18-20✦

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 652c: Determine the acceleration of a particle on an inclined plane with a force that is not parallel to the plane.
• 653c: Solve problems involving an accelerating particle on a rough inclined plane and an additional force.
• 652: Exam Practice: Forces on an accelerating single particle, on an inclined plane/inclined forces, no F = mu R
• 653: Exam Practice: Forces on an accelerating single particle, on an inclined plane/inclined forces, using F = mu R

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Worksheets

• Naiker Maths
  • Dynamics & Inclined Planes: Exam Qs 2005–11 · Mark scheme
• MadAsMaths (T. Madas)
  • Dynamics: Forces & Friction (M1) Q4, 6, 13, 15, 17 (difficulty 2–3 of 5)

A2 Maths – Mechanics – Particles on an inclined pulley system

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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7F Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Forces 15 • Connected Particles with Friction, Resultant Forces on Pulleys • Mech2 Ex7F • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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• Dr Frost Slides 21-24✦

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 655a: Determine the acceleration of two connected particles on a rough horizontal plane.
• 655b: Determine the coefficient of friction between a rough horizontal plane and two connected particles.
• 655c: Determine the tension in a string connecting a particle on a rough horizontal table and a vertically hanging particle.
• 655d: Determine the coefficient between a table and a particle when the particle is connected to another hanging over the edge, where the acceleration is given.
• 656a: Determine the tension or thrust in an inline towbar (where forces of resistance are given). (not yet active)
• 656b: Determine the acceleration of two connected vehicles on an inclined road (where forces of resistance are given). (not yet active)
• 656c: Determine the acceleration of a system that connects one particle on a smooth inclined plane and one hanging freely. (not yet active)
• 656d: Determine the tension in a string that connects one particle on a smooth inclined plane and one hanging freely. (not yet active)
• 657a: Solve a problem involving a particle on a rough inclined plane connected to one hanging freely. (not yet active)
• 657b: Solve a problem involving a a particle on a rough inclined plane connected to one on a rough horizontal plane. (not yet active)
• 657c: Determine the magnitude of the force acting on a pulley that connects particles involving an inclined plane. (not yet active)
• 657d: Solve a problem involving a block on a block with a rough inclined slope. (not yet active)
• 658b: Make calculations about the motion of a hanging particle before hitting the ground, when connected to a particle on a rough inclined plane. (not yet active)
• 658c: Make calculations about the motion of a particle on a rough inclined plane after it is disconnected from a particle vertically. (not yet active)
• 658e: Make calculations about the motion of a particle on a rough horizontal plane after it is disconnected from a particle hanging over an inclined plane. (not yet active)
• 655: Exam Practice: Forces on accelerating connected particles, not on an inclined plane, using F = mu R
• 656: Exam Practice: Forces on accelerating connected particles, on an inclined plane/inclined forces, no F = mu R
• 657: Exam Practice: Forces on accelerating connected particles, on an inclined plane/inclined forces, using F = mu R
• 658: Exam Practice: Considering forces on accelerating particles (with an incline and possibly F = mu R) to make calculations about subsequent motion

Other Videos

Connected Particles

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• The Chalk Face Breaking Strain
• The Chalkface
  • Breaking Strain: PDF

Worksheets

• Naiker Maths
  • Connected Particles: Exam Qs 2005–11 · Mark scheme
• Physics & Maths Tutor
  • Dynamics: Connected Particles: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
• MadAsMaths (T. Madas)
  • Connected Particles (M1) Q4, 5, 13, 18, 26, 29, 30 (difficulty 3–5 of 5)
  • Equilibrium of Particles (M1) Further Problems Q16, 30 (difficulty 3–4 of 5)

External Whole Topic Past Paper Style Questions

• WW Dr Frost Style QQQs (Version 1) Word Doc, PDF (Q’s Only) or PDF (Q’s & Sol.)
• WW Dr Frost Style QQQs (Version 2) Word Doc, PDF (Q’s Only) or PDF (Q’s & Sol.)
• Jethwa Maths Starter Activities
• PMT
  • AQA Resolving Forces
  • Edexcel
    • Dynamics – Connected Particles
    • Dynamics – F = ma on a Slope
    • Statics – Equilibrium Problems
    • Statics
  • OCR
    • Friction
    • Newton’s Second Law and Weight
  • OCR MEI
    • Frictional Force and Normal Contact Force
    • Newton’s Laws of Motion (Yr. 2)
    • Vector Treatment of Forces
  • Cheat Sheet: Chapter 5 · Chapter 7

Other Whole Topic Resources

•  Lucyjc1612 Summary Poster (Forces & Friction and Applications of Forces)

Worksheets

• Maths Genie
  • Forces and Friction: Questions · Solutions · Lesson · Topic page
  • Applications of Forces: Questions · Solutions · Lesson · Topic page
• Mathsaurus (Kevin Olding)
  • Forces and motion (exam questions)
• Physics & Maths Tutor
  • Forces and Newton’s Laws of Motion: Questions 2021–24 · Mark scheme · Model answers
• Dr Oliver Mathematics
  • Statics and Dynamics questions✦ (answers✦)

Activities

• MEI
  • MEI teaching notes, misconceptions & prompts: Force and motion✦
  • MEI teaching notes, misconceptions & prompts: Friction✦
  • Law of friction✦
• Exam Solutions
  • What is friction, limiting equilibrium and the coefficient of friction?✦
• Andy Lutwyche
  • Erica’s Errors
  • Erica’s Errors on Applications