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MECHANICS FOR PP4
Mechanics for Paper 4 an introduction
General expectations for this paper.
1. Nature of Questions
- Paper 4 Mechanics questions are mainly numerical
- They test mechanical principles without requiring very difficult algebra or trigonometry
- Questions may involve realistic contexts, but you should treat each body as a particle (all forces act at a single point)
- Vector notation is not used — you'll always work with magnitudes, directions, and resolved components
Key Insight: Expect applied maths problems where you'll model real-world situations using simplified particle mechanics.
2. Trigonometric Results You Must Know
These essential identities are often used in mechanics:
| Identity | Expression |
|---|---|
| Complementary sine | sin(90° - θ) ≡ cosθ |
| Complementary cosine | cos(90° - θ) ≡ sinθ |
| Tangent identity | tanθ ≡ sinθ/cosθ |
| Pythagorean identity | sin²θ + cos²θ ≡ 1 |
Application: These are commonly needed when resolving forces or dealing with slopes and inclines.
3. Assumed Mathematical Knowledge
From Pure Mathematics 1, you are expected to already know how to:
- Rearrange and solve algebraic equations
- Work with fractions, indices, and surds
- Expand and simplify expressions
- Factorise and solve quadratic equations
- Solve simultaneous equations (linear and quadratic)
- Manipulate formulae to make one variable the subject
- Work with inequalities
- Basic differentiation and integration (used for motion: velocity, acceleration, displacement)
- Graph sketching and interpreting
Example: When dealing with motion under constant acceleration, you might need to rearrange equations like:
v = u + at
to solve for different variables depending on the question.
4. Key Idea in Mechanics
- Always model the object as a particle unless told otherwise
- Forces such as weight, tension, normal reaction, and friction are applied as single forces
- The motion or equilibrium of the particle is then analysed using Newton's laws or equations of motion
Particle Assumption: In mechanics, treating an object as a particle means assuming all forces act at a single point, simplifying calculations while maintaining accuracy for many practical situations.
Quick-Check Summary
| Concept | Key Points |
|---|---|
| Question Types | Numerical problems, particle modeling, no vector notation |
| Essential Trig | sin(90°-θ)=cosθ, cos(90°-θ)=sinθ, tanθ=sinθ/cosθ, sin²θ+cos²θ=1 |
| Math Skills | Algebra, equations, differentiation, integration |
| Core Approach | Model as particles, resolve forces, apply Newton's laws |
5. Problem-Solving Strategy
- Identify the object(s) of interest and model as particles
- Draw a clear diagram showing all forces acting on each particle
- Resolve forces into appropriate components
- Apply relevant principles (Newton's laws, conservation of energy, etc.)
- Solve the resulting equations
- Check your answer for reasonableness
Remember: Mechanics problems in Paper 4 are designed to be solvable with the mathematical tools from Pure Mathematics 1. Focus on understanding the physical principles and applying them systematically.
Abel Masitsa
Assumptions Used in Mechanics
- Particle model: Bodies treated as point masses (size/shape ignored).
- Rigid body: Distances between points in a body remain constant (no deformation).
- Smooth surface: No friction between contacting surfaces unless stated.
- Light string/rod: String or rod mass is negligible compared with connected masses.
- Inextensible string: String does not stretch → connected objects share displacement/acceleration.
- Uniform gravity: g is constant and acts vertically downward (use given value where specified).
- Negligible air resistance: Ignore drag unless the problem mentions it.
- Instantaneous collision: Impacts take zero time; external forces during collision are ignored.
- Smooth pulley: Pulley has no friction and does not change string length across it.
- Small-angle approximations: For small θ (radians): sinθ ≈ θ, cosθ ≈ 1, tanθ ≈ θ (only when stated).
Tip: Always check which assumptions are allowed or must be dropped in the question (e.g., include friction or air resistance if specified).