Resolution of Forces

OCR

GCSE

Resolution of forces is the analytical process of separating a single force vector into two orthogonal components, typically horizontal and vertical, to simplify the analysis of physical systems. This technique utilizes trigonometric functions, specifically sine and cosine, to determine the magnitude of components acting parallel and perpendicular to a plane or axis. Mastery of resolution is essential for solving problems involving inclined planes, projectiles, and systems in equilibrium where the resultant force is zero. It provides the mathematical foundation for analyzing complex vector interactions by reducing them to independent one-dimensional problems.

Objectives

Exam Tips

Pitfalls

Key Terms

Mark Points

What You Need to Demonstrate

Key skills and knowledge for this topic

Award 1 mark for drawing vectors to scale with correct orientation and arrowheads indicating direction
Award 1 mark for arranging vectors tip-to-tail to determine a resultant force
Credit the correct application of Pythagoras' theorem to calculate the magnitude of the resultant force
Award 1 mark for resolving a force into horizontal and vertical components using correct trigonometric ratios (Higher Tier only)
Allow error carried forward (ECF) for the magnitude if the scale drawing is accurate but the conversion back to Newtons is incorrect

Example Examiner Feedback

Real feedback patterns examiners use when marking

"You have correctly calculated the magnitude, but remember that force is a vector—you must also state the direction."
"Your scale drawing is accurate, but too small. Use a larger scale to improve the precision of your measurement."
"Check your trigonometry: you used sin(theta) for the adjacent component where cos(theta) was required."
"Excellent use of the tip-to-tail method. To secure full marks, ensure you explicitly label the resultant force."

Marking Points

Key points examiners look for in your answers

Award 1 mark for drawing vectors to scale with correct orientation and arrowheads indicating direction
Award 1 mark for arranging vectors tip-to-tail to determine a resultant force
Credit the correct application of Pythagoras' theorem to calculate the magnitude of the resultant force
Award 1 mark for resolving a force into horizontal and vertical components using correct trigonometric ratios (Higher Tier only)
Allow error carried forward (ECF) for the magnitude if the scale drawing is accurate but the conversion back to Newtons is incorrect

Examiner Tips

Expert advice for maximising your marks

💡Always state your chosen scale clearly (e.g., '1 cm = 5 N') and ensure the diagram fills at least half the provided space to maximize precision
💡Check your calculator mode; ensure it is set to Degrees, not Radians, before performing trigonometric calculations
💡When resolving on an inclined plane, define your axes parallel and perpendicular to the slope to simplify the calculation

Common Mistakes

Pitfalls to avoid in your exam answers

Drawing component vectors tip-to-tip instead of forming a valid vector triangle or rectangle
Confusing sine and cosine when resolving forces, particularly when the angle is given relative to the vertical
Omitting the direction (angle or bearing) when asked to calculate a resultant vector, providing magnitude only
Using a scale that is too small, leading to significant precision errors in the final answer

Study Guide Available

Comprehensive revision notes & examples

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Key Terminology

Essential terms to know

Vector decomposition into orthogonal components

Trigonometric determination of component magnitudes

Equilibrium conditions on inclined planes

Calculation of resultant forces from components

Likely Command Words

How questions on this topic are typically asked

Calculate

Determine

Draw

Explain

Show

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