5.2MechanicsStretch
Inclined Planes
On a slope it is far easier to resolve forces parallel and perpendicular to the plane rather than horizontally and vertically. Weight then splits neatly into a component down the slope and one into it.
What you'll be able to do
- Resolve parallel and perpendicular to a slope
- Split weight into mg sin θ and mg cos θ
- Apply Newton’s second law along the plane
- Find the normal reaction
1
Resolving on a slope
For a slope at angle , the weight resolves into down the slope and into the slope. The normal reaction balances the perpendicular component.
Weight components on a slope.
1Down-slope force N.
2 m/s².
Answer m/s² down the slope.
Tip — Down the slope uses sin θ; into the slope uses cos θ.
Formula recap
Component down the slope.
Component into the slope (= normal reaction if no other ⊥ forces).
Common mistakes to avoid
Resolving horizontally and vertically on a slope.
Resolve parallel and perpendicular to the plane.
Swapping sin and cos for the weight components.
Down the slope: sin θ; into the slope: cos θ.
Key takeaways
- Resolve parallel and perpendicular to the slope.
- Weight: mg sin θ down the slope, mg cos θ into it.
- Normal reaction balances the perpendicular component.
Test yourself
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