Why must the two components chosen when resolving be perpendicular to each other?

Perpendicular components are independent, so neither has any effect along the direction of the other and the two can be treated as separate one-dimensional problems.

A force of 250 N acts at 30° above the horizontal. Calculate its horizontal component.

The horizontal component is 250 cos 30° = 217 N acting horizontally, and 217 ÷ 250 = 0.866, which is cos 30° as required.

A force of 250 N acts at 30° above the horizontal. Calculate its vertical component.

The vertical component is 250 sin 30° = 125 N acting vertically upwards, and 125 ÷ 250 = 0.500, which is sin 30° as required.

Explain why the two perpendicular components of a vector add arithmetically to more than the vector itself.

Perpendicular components recombine by Pythagoras rather than by addition, so for a 250 N force at 30° the components 217 N and 125 N give √(217² + 125²) = 250 N, not 342 N.

CCEA A-Level Physics 1210

Physical Quantities, Scalars and Vectors

Topic overview Physical quantities and SI base units Prefixes and standard form Scalars and vectors Resolving vectors and finding resultants Coplanar forces in equilibrium

Moments and Equilibrium

Topic overview Moment of a force Centre of gravity The principle of moments Determining unknown masses using moments

Linear Motion and Dynamics

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Newton's Laws of Motion

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Linear Momentum and Impulse

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Work, Energy and Power

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Current, Charge and Potential Difference

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Resistance and Resistivity

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Internal Resistance and Potential Dividers

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Quantum Physics

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Simple Harmonic Motion

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The Nucleus and Radioactive Decay

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Fundamental Particles

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Physical Quantities, Scalars and Vectors

Resolving vectors and finding resultants

3 things to know
Unit AS 1

Overview

Recall questions on what resolving means and why the components must be perpendicular, the F cos θ and F sin θ expressions, the resultant of two perpendicular vectors and its direction from tan⁻¹, components on an inclined slope, and finding a resultant by scale drawing rather than calculation.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

Describe how the resultant of two coplanar vectors is found by scale drawing.

Key term

What is meant by resolving a vector?

Key term

A force F acts at an angle θ to the horizontal. Give expressions for its horizontal and vertical components.

Questions from this subtopic

Each one with the model answer underneath.

1
What is meant by resolving a vector?
Model answer
Resolving a vector means replacing it with two perpendicular components which together have exactly the same effect as the original vector.
2
A force F acts at an angle θ to the horizontal. Give expressions for its horizontal and vertical components.
Model answer
The horizontal component is F cos θ and the vertical component is F sin θ, where θ is measured from the horizontal.
3
Why must the two components chosen when resolving be perpendicular to each other?
Model answer
Perpendicular components are independent, so neither has any effect along the direction of the other and the two can be treated as separate one-dimensional problems.
4
A force of 250 N acts at 30° above the horizontal. Calculate its horizontal component.
Model answer
The horizontal component is 250 cos 30° = 217 N acting horizontally, and 217 ÷ 250 = 0.866, which is cos 30° as required.
5
A force of 250 N acts at 30° above the horizontal. Calculate its vertical component.
Model answer
The vertical component is 250 sin 30° = 125 N acting vertically upwards, and 125 ÷ 250 = 0.500, which is sin 30° as required.
6
Explain why the two perpendicular components of a vector add arithmetically to more than the vector itself.
Model answer
Perpendicular components recombine by Pythagoras rather than by addition, so for a 250 N force at 30° the components 217 N and 125 N give √(217² + 125²) = 250 N, not 342 N.

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