7.5MechanicsStretch

Dynamics and Inclined Planes

When a particle accelerates on a slope, Newton’s second law replaces equilibrium along the plane. Resolve perpendicular for the reaction (and friction), then apply F = ma down the slope.

26 min Video by Zeeshan Zamurred Applications of Forces

Edexcel A Level Maths: 7.5 Dynamics and Inclined PlanesWatch the full walkthrough before the notes below.

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What you'll be able to do

Apply F = ma on an inclined plane
Include friction in the dynamics
Find acceleration on a slope
Combine with suvat for motion

Newton’s second law on a slope

Perpendicular to the slope there is no acceleration, so $R = m g cos θ$ . Along the slope, the net force gives $ma$ : e.g. sliding down a rough slope, $m g sin θ - μ R = ma$ .

m g sin θ - μ m g cos θ = ma

Newton’s second law down a rough slope.

m g sin θ = 9.8

μ m g cos θ = 0.2 (2) (9.8) cos 30° \approx 3.39

a = (9.8 - 3.39) /2 \approx 3.2

m/s².

Answer

a \approx 3.2

m/s²

Tip — Friction acts UP the slope when the particle slides down — opposing the motion.

Formula recap

R = m g cos θ

Normal reaction.

m g sin θ - μ R = ma

Sliding down a rough slope.

Common mistakes to avoid

Putting friction down the slope when the block slides down.

Friction opposes motion, so it acts up the slope.

Forgetting the slope is rough (omitting μR).

Include friction unless told the slope is smooth.

Key takeaways

Perpendicular: R = mg cos θ (no acceleration).
Along slope: net force = ma.
Friction opposes the direction of motion.

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