Know that forces may produce changes in the size and shape of an object

Cambridge IGCSE Physics 0625 – Effects of Forces

Learning Objective

Explain how forces can change the size, shape or state of motion of an object and use the quantitative tools required by the syllabus to analyse these effects.

1. Vectors and Resultant Forces

• Scalar quantities: magnitude only (e.g. mass, temperature).
• Vector quantities: magnitude + direction (e.g. force, displacement, velocity, acceleration).
• Common vectors in the syllabus:
  • Force $\vec F$ (N)
  • Displacement $\vec s$ (m)
  • Velocity $\vec v$ (m s⁻¹)
  • Acceleration $\vec a$ (m s⁻²)
• Resultant force – a single force that has the same effect as all the individual forces acting on a body.
• Finding the resultant:
  • Collinear forces: $R = F_1 \pm F_2$ (sign shows direction).
  • Perpendicular forces: $R = \sqrt{F_1^{2}+F_2^{2}}$, direction $\tan\theta = \dfrac{F_2}{F_1}$.
  • More than two forces: resolve each into components, sum the components, then recombine.

2. Deformation Produced by Forces

3. Stress, Strain and Young’s Modulus

• Stress $\displaystyle \sigma = \frac{F}{A}$ (Units: pascals, Pa) $F$ = applied force (N), $A$ = cross‑sectional area (m²).
• Strain $\displaystyle \varepsilon = \frac{\Delta L}{L_0}$ (dimensionless) $\Delta L$ = change in length, $L_0$ = original length.
• Hooke’s law (elastic region) $\displaystyle \sigma = E\,\varepsilon$ $E$ = Young’s modulus (Pa), a measure of stiffness.

3.1 Load‑Extension (Stress‑Strain) Graph

A typical graph contains the following points (all are exam‑relevant):

• Proportional limit – end of the straight‑line portion where $\sigma$ is directly proportional to $\varepsilon$.
• Elastic limit – maximum stress for which deformation is completely reversible.
• Yield point – stress at which permanent (plastic) deformation begins.
• Ultimate strength (optional) – maximum stress the material can sustain.
• Fracture point – where the material breaks.

In the linear region, the slope of the graph is $E$.

4. Elastic vs. Plastic Behaviour

1. Elastic deformation: occurs when the applied stress is **below the elastic limit**; the material returns to its original shape when the force is removed.
2. Plastic deformation: occurs when the stress exceeds the elastic limit; the change in shape is permanent.
3. Materials differ:
   • Metals – clear yield point.
   • Polymers – gradual transition from elastic to plastic.
   • Rubber – large elastic region, little plastic deformation.

5. Turning Effect of Forces – Moment & Equilibrium

• Moment (torque) about a pivot: $\displaystyle M = F \times d$ $F$ = force (N), $d$ = perpendicular distance from the line of action to the pivot (m). Units: N m.
• Conditions for static equilibrium:
  • Translational: $\displaystyle \sum \vec F = 0$
  • Rotational: $\displaystyle \sum M = 0$
• Example – Uniform beam of length $L$ on a central fulcrum. If a weight $W_1$ is $a$ m to the left and $W_2$ is $b$ m to the right, equilibrium requires $W_1 a = W_2 b$.

6. Centre of Gravity (CG) and Stability

• The point through which the total weight of a body can be considered to act.
• For uniform, symmetric objects the CG coincides with the geometric centre (e.g., centre of a uniform rod, sphere, rectangle).
• Stability criterion: an object is stable if its CG lies vertically below the base of support; it is unstable if the CG is above the base.
• Useful for analysing balance, tipping of ladders, and design of vehicles.

7. Friction

• Dry (solid) friction: $F_f = \mu R$
  • $\mu_s$ – coefficient of static friction (prevents motion).
  • $\mu_k$ – coefficient of kinetic friction (acts during motion).
  • $R$ – normal reaction (N).
• Fluid (viscous) drag:
  • Low speeds: $F_d = k v$ (linear with speed).
  • Higher speeds: $F_d \approx \tfrac12 C \rho A v^{2}$ (quadratic).
  • Variables: $C$ = drag coefficient, $\rho$ = fluid density, $A$ = projected area.
• Air resistance – a special case of fluid drag, important for fast‑moving objects such as falling bodies, cyclists, and projectiles.
• Everyday examples: sliding a book (dry friction), swimming (fluid drag), riding a bike against wind (air resistance).

8. Momentum & Impulse

• Linear momentum $\displaystyle p = mv$ (kg m s⁻¹).
• Impulse (change in momentum) $\displaystyle \Delta p = F\,\Delta t$.
• Conservation of momentum (isolated system): $\displaystyle \sum p_{\text{initial}} = \sum p_{\text{final}}$.
• Example problem – Two carts, $m_1 = 2\,$kg moving at $4\,$m s⁻¹ to the right and $m_2 = 3\,$kg moving at $2\,$m s⁻¹ to the left, stick together after an inelastic collision. $\displaystyle (2)(4) + (3)(-2) = (2+3)v_f \;\Rightarrow\; v_f = 0.4\,$m s⁻¹ to the right.

9. Practical Illustrations of Deformation

• Elastic example – Compressing a sponge: it regains its original shape when the load is removed.
• Plastic example – Shaping soft clay: the new shape remains after the force ceases.
• Mixed behaviour – Twisting a metal rod: low torque gives elastic twist; exceeding the yield torque produces permanent deformation.

10. Key Points for Examination

• Identify the type of force (compression, tension, shear, torsion, bending) and describe the deformation it produces.
• Distinguish clearly between elastic and plastic deformation; state the role of the proportional limit, elastic limit and yield point.
• Use $\sigma = F/A$, $\varepsilon = \Delta L/L_0$ and $E = \sigma/\varepsilon$ to calculate stress, strain and deformation where required.
• Apply moment and equilibrium equations ($\sum F = 0$, $\sum M = 0$) to turning‑effect problems.
• Remember that forces can change shape/size **or** motion – treat both aspects in answers.
• Be comfortable with vector addition (collinear, perpendicular, component method) and the basic friction formulas.
• For momentum questions, write the conservation equation first, then substitute numbers.

11. Suggested Diagrams (to be drawn in the exam booklet)

1. Bar diagram showing the five deformation types with force arrows and labels.
2. Load‑extension (stress‑strain) graph indicating proportional limit, elastic limit, yield point, plastic region and ultimate strength.
3. Free‑body diagram of a beam in equilibrium showing forces, distances and calculated moments.
4. Location of the centre of gravity for a rectangular block and for a triangular plate.
5. Vector‑addition diagram for two perpendicular forces (resultant magnitude and direction).