Forces & Connected Particles

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AS Maths – Mechanics – Force Diagrams

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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10A Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Forces 1 • Intro and Resultant Forces • Mech1 Ex10A • 🚀

Forces 2 • Simple Equilibrium • Mech1 Ex10A • 🚀

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 1-4✦

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

• 553a: Find the magnitude of unknown forces when a particle is in equilibrium.
• 553: Exam Practice: Forces on a single particle in equilibrium, not on an inclined plane, no F = mu R

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

AS Maths – Mechanics – Forces as Vectors

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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10B Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Forces 3 • As Vectors • Mech1 Ex10B • 🚀

Forces 4 • Additional vectors example • Mech1 Ex10B • 🚀

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 5-7✦

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

• 554a: Determine the resultant vector of forces expressed in i and j notation.
• 554b: Determine unknown components in force vectors that gives a resultant vector or achieves equilibrium.
• 554c: Determine the magnitude of a force vector.
• 554d: Determine the direction of a force vector as an angle.
• 554e: Solve problems where the resultant vector is parallel to a given direction.
• 554: Exam Practice: Forces as vectors

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Worksheets

• Jethwamaths Starter Activities (p11-12)
• Mathshelper (Jon Stone)
  • Resultant Vectors
• Naiker Maths
  • Forces as Vectors: Exam Qs 2005–11 · Mark scheme
• MadAsMaths (T. Madas)
  • Vectors in Mechanics (M1) Various Q3 (difficulty 4 of 5)

AS Maths – Mechanics – F=ma

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Blank notes download

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10C Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Forces 5 • F=ma • Mech1 Ex10C • 🚀

Forces 6 • F=ma, harder questions • Mech1 Ex10C • 🚀

Forces 7 • Deceleration example • Mech1 Ex10C • 🚀

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Blank notes download

(Courtesy of King’s Chester Maths Department)

Download slides

Dr Frost Slides 8-11✦

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

• 555a: Calculate the acceleration of a particle.
• 555b: Determine the magnitude of missing forces when a particle is accelerating.
• 555c: Calculate the acceleration of a particle in context, including normal reaction, tension and gravitational forces.
• 555d: Determine the magnitude of missing forces in context, including normal reaction, tension and gravitational forces.
• 555e: Determine an unknown force by using constant acceleration formulae.
• 555f: Determine a time, distance or velocity, where the acceleration must first be calculated using forces.
• 555: Exam Practice: Forces on an accelerating single particle, not on an inclined plane, no F = mu R

Further Practice

• Practise Questions

Other Videos

Newton's Second Law

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• The Chalk Face Gravity Investigation
• BossMaths
  • Newton’s Laws & Lifts Question Generators (Interactive)

AS Maths – Mechanics – F=ma in 2D

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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10D Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Forces 8 • F=ma with Vectors • Mech1 Ex10D • 🚀

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 12-14✦

Exam Practice

• Exam Practice
• Exam Practice– combination of vectors section to date.

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

• 555g: Determine the acceleration vector of a body given force vectors acting on it.
• 555h: Determine missing components of forces given the acceleration vector of the body.
• 555: Exam Practice: Forces on an accelerating single particle, not on an inclined plane, no F = mu R

Further Practice

• Practise Questions

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Worksheets

• Jethwamaths Starter Activities (p15-16)
• Mathsaurus PPQ Booklet from Multiple Exam Boards
• MadAsMaths (T. Madas)
  • Vectors in Mechanics (M1) With Acceleration Q1–3, 7–11, 20; Various Q2, 4 (difficulty 2–4 of 5)

AS Maths – Mechanics – Connected Particles

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept. (Up to 5:10 if just looking at connected particles)

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10E Slides (Courtesy of Owen134866) – (Whole Section)

Bicen Maths Live Lesson

Forces 9 • Horizontal Connected Particles, Tension vs Thrust • Mech1 Ex10E • 🚀

Forces 10 • Extra Thrust example • Mech1 Ex10E • 🚀

Forces 11 • Vertical Connected Particles • Mech1 Ex10E • 🚀

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths (Stacked Particles below)

Forces 12 • Lifts • Mech1 Ex10E • 🚀

Forces 13 • Boxes on top of Boxes in Lifts • Mech1 Ex10E • 🚀

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 14-16 (or to 19 if Including Stacked Particles)✦

Extra Questions

• Dr Frost Questions: Including Stacked Particles · Connected Only

Key Skills

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

• 556a: Determine the tension in the string connecting two particles on smooth horizontal ground.
• 556b: Determine the tension in the string connecting two particles on rough horizontal ground.
• 557a: Determine the time or distance taken for one particle to come to rest, after being disconnected from another particle on horizontal ground.
• 556: Exam Practice: Forces on accelerating connected particles, not on an inclined plane, no F = mu R
• 557: Exam Practice: Considering forces on accelerating particles (no inclines nor F = mu R) to make calculations about subsequent motion

Other Videos

Connected Particles AS Level

Courtesy of Maths Genie (Up to 8:12)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Worksheets

• Jethwamaths Starter Activities (p21-22)
• Mathsaurus PPQ Booklet (Includes a Lift Q) from Multiple Exam Boards
• MathedUp
  • Connected particles: Questions · Challenge · Answers
• Mathsaurus (Kevin Olding)
  • Connected particles and pulleys (exam questions)
• Naiker Maths
  • Connected Objects: Horizontal Plane: Exam Qs 2005–11 · Mark scheme
• MadAsMaths (T. Madas)
  • Connected Particles (M1) Q2, 6, 7, 12, 14, 22, 24 (difficulty 2–4 of 5)
  • Dynamics: Forces & Friction (M1) Q5, 14, 18, 23 (difficulty 2–5 of 5)

AS Maths – Mechanics – Connected Particles

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept. (Up to 5:10 if just looking at connected particles)

Download Blank Notes

Download Slides

10E Slides (Courtesy of Owen134866) – (Whole Section)

Bicen Maths Live Lesson

Forces 12 • Lifts • Mech1 Ex10E • 🚀

Forces 13 • Boxes on top of Boxes in Lifts • Mech1 Ex10E • 🚀

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 17-19✦

Extra Questions

• Dr Frost Questions: Including Connected Particles · Stacked Particles Only

Key Skills

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

• 556c: Determine the acceleration or tension in the string attached to a lift.
• 556d: Connect the motion of a lift with a body inside to determine a reaction force, tension or reaction force.
• 556j: Determine the mass of a lift and a body inside it.
• 556: Exam Practice: Forces on accelerating connected particles, not on an inclined plane, no F = mu R

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Worksheets

• Jethwamaths Starter Activities (p13-14 & 23-24)

AS Maths – Mechanics – Forces and Pulleys

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

10F Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Forces 14 • Pulleys • Mech1 Ex10F • 🚀

Forces 15 • Extra Pulley example • Mech1 Ex10F • 🚀

Forces 16 • Subsequent Motion with Pulleys • Mech1 Ex10F • 🚀

Forces 17 • Subsequent Motion with Pulleys, extra example • Mech1 Ex10F • 🚀

Forces 18 • Pulley on Table including Subsequent Motion • Mech1 Ex10F • 🚀

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 20-23✦

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

• 556e: Determine the acceleration of two particles or the tension in a connecting string passing over a smooth pulley.
• 556f: Determine the mass of one of two particles connected by a string passing over a smooth pulley.
• 556g: Determine the tension in the string passing over a smooth pulley connecting particles whose mass are variables.
• 556h: Determine the acceleration of two particles or the tension in a connecting string passing over a smooth pulley on the corner of a table.
• 556i: Determine the tensions and acceleration when three particles are joined by strings.
• 557b: Determine the time taken for one particle to hit the pulley, where the other particle is hanging over a table.
• 557c: For particles hanging vertically over a pulley, determine the time taken for one particle to hit the ground after the string breaks.
• 557d: Determine the maximum height reached by a particle connected to another by a string passing over a pulley.
• 557e: For particles hanging vertically over a pulley, determine the time or distance from when the string becomes slack to becoming taut.
• 556: Exam Practice: Forces on accelerating connected particles, not on an inclined plane, no F = mu R
• 557: Exam Practice: Considering forces on accelerating particles (no inclines nor F = mu R) to make calculations about subsequent motion

Further Practice

• Practise Questions

Other Videos

Connected Particles AS Level

Courtesy of Maths Genie (From 8:12)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• The Chalk Face Falling Problem
• BossMaths
  • Pulleys Question Generator (Applet) (Interactive)

Worksheets

• Jethwamaths Starter Activities (p17-20)
• Mathsaurus PPQ Booklet from Multiple Exam Boards
• Mathshelper (Jon Stone)
  • Pulleys
• Naiker Maths
  • Connected Objects: Pulleys: Exam Qs 2005–11 · Mark scheme · Exam-style Qs · Solutions
• MadAsMaths (T. Madas)
  • Connected Particles (M1) Q1, 3, 10, 16, 17, 19–21, 27, 28 (difficulty 2–5 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.)
• PMT
  • Edexcel Dynamics – F = ma horizontally
  • AQA Newton’s Laws
  • OCR Newton’s First and Third Laws, Newton’s Second Law and Weight
  • OCR MEI Forces, Newton’s Laws of Motion (Yr. 1)
  • Cheat Sheet

Other Whole Topic Resources

•  Lucyjc1612 Summary Poster (Forces & Motion)

Worksheets

• MathedUp
  • Forces: Questions · Challenge · Answers
• Maths Genie
  • Forces and Motion: Questions · Solutions · Lesson · Topic page
• Mathsaurus (Kevin Olding)
  • Forces and acceleration (exam questions)
• Physics & Maths Tutor
  • Forces and Newton’s Laws of Motion: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS)
• Dr Austin Maths
  • Resultant Equilibrium Fill in the Blanks (Word | PDF✦ | Answers✦)
  • Diagrams and Acceleration Practice Grid (Word | PDF✦ | Answers✦)
  • Vector Acceleration Fill in the Blanks (Word | PDF✦ | Answers✦)

Activities

• MEI
  • MEI teaching notes, misconceptions & prompts: Forces and newtons laws of motion✦
  • Newton’s Laws Experiments✦
  • Feeling forces✦
• The Physics Classroom
  • Free-body diagrams self-checking interactive✦
• Andy Lutwyche
  • Erica’s Errors Motion