Forces and Newton’s laws (A2 Unit 4: Applied Mathematics B) — WJEC A-Level Mathematics
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Forces and Newton’s laws (A2 Unit 4: Applied Mathematics B) explained
In two dimensions, forces acting on a body often act at angles to the direction of motion.
Read the full explanation
Newton's second law ΣF = ma applies by establishing two mutually perpendicular reference axes. Choosing one axis parallel to acceleration and the other perpendicular simplifies analysis: ΣF_parallel = ma and ΣF_perp = 0. On an inclined plane of angle α, forces resolve parallel to the slope (where weight contributes mg sin α down the slope) and perpendicular to the slope (where weight contributes mg cos α into the slope). Resolving forces correctly is required to evaluate normal reaction R and dynamic friction before computing acceleration.
Your focus
- Select and align optimal orthogonal reference axes for two-dimensional accelerated motion.
- Resolve all applied forces along chosen axes to formulate parallel and perpendicular equations.
- Solve dynamic equations to determine normal reactions, friction, and accelerations on slopes.
Forces and Newton’s laws (A2 Unit 4: Applied Mathematics B) exam tips
Marking Points
- setting up perpendicular reference axes aligned parallel and perpendicular to motion
- resolving all forces correctly along both chosen axes
- formulating ΣF_perp = 0 to determine the normal reaction force R
- formulating ΣF_parallel = ma to solve for acceleration or unknown driving force
Examiner Tips
- 💡Always align axes parallel and perpendicular to the inclined surface to minimise unknown acceleration components.
- 💡Check that normal reaction R accounts for all perpendicular force components, not just mg cos α.
Common Mistakes
- resolving horizontally and vertically on an inclined plane instead of parallel and perpendicular to the plane
- omitting component terms of inclined pulling or pushing forces when finding normal reaction R