Inclined planes with applied force and connected masses
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
- Choose a positive direction along the slope (usually the direction of motion) and add forces with signs.
- An applied force along the slope needs no resolving.
- Friction always opposes the motion (or the tendency to move).
- For connected masses on a light string over a frictionless pulley, the tension is the same at both ends and both masses share the same acceleration.
Key formulas (QCAA formula book notation)
\[
F_{net} = F_A - m g\sin\theta - F_f = m a \quad \text{(pushed up the slope)}
\]
Worked example
A 900 kg car accelerates up a 10° hill at 0.50 m s⁻² against 600 N of friction. Find the driving force.
- \(m g\sin\theta = 900 \times 9.8 \times \sin 10^\circ = 1532\) N
- \(F_A = ma + mg\sin\theta + F_f = 450 + 1532 + 600 = 2.6 \times 10^3\) N
Common mistakes
- Forgetting the weight component when moving up a slope.
- Giving each connected mass a different acceleration.
Do
- Read: Textbook (Oxford Physics for Queensland Units 3 & 4) section 3.3
- Do: CYL 3.3 Q6, 7; CYL 3.2 Q11
Try it
Watch
- Introductory Kinetic Friction on an Incline Problem · Flipping Physics
- An incline, 2 masses, and a pulley · Flipping Physics
Further reading
- OpenStax Physics 5.4 Inclined planes (OpenStax, CC BY 4.0)
- Full topic notes: Gravity & Motion