Forces on an inclined plane
G2.3 G2.4
By the end of this lesson you should be able to
- Describe the forces acting on an object on an inclined plane through the use of free-body diagrams. G2.3
- Determine the net force acting on an object on an inclined plane using vector analysis. G2.4
Key ideas
- Tilt your axes: x along the slope, y perpendicular to it. Then only the weight needs resolving.
- Weight splits into \(mg\sin\theta\) down the slope and \(mg\cos\theta\) into the slope.
- The normal force balances the perpendicular part: \(F_N = mg\cos\theta\).
- Frictionless slope: \(F_{net} = mg\sin\theta\) so \(a = g\sin\theta\), independent of mass. Friction acts up the slope against the motion.
Key formulas (QCAA formula book notation)
\[
F_{\parallel} = m g \sin\theta
\]
\[
F_{\perp} = F_N = m g \cos\theta
\]
\[
F_{net} = m g\sin\theta - F_f = m a
\]
Worked example
A 5.0 kg crate slides down a 25° ramp with 8.0 N of friction. Find its acceleration.
- \(F_\parallel = 5.0 \times 9.8 \times \sin 25^\circ = 20.7\) N
- \(F_{net} = 20.7 - 8.0 = 12.7\) N
- \(a = 12.7/5.0 = 2.5\) m s⁻²
Common mistakes
- Using cos for the down-slope component (it's sin when θ is the slope angle).
- Setting F_N = mg on a slope.
- Drawing friction in the direction of motion.
Do
- Read: Textbook (Oxford Physics for Queensland Units 3 & 4) section 3.3
- Do: CYL 3.3 Q2, 4, 5
Try it
Watch
- Breaking the Force of Gravity into its Components on an Incline · Flipping Physics
Further reading
- OpenStax Physics 5.4 Inclined planes (OpenStax, CC BY 4.0)
- Full topic notes: Gravity & Motion