Quantities, Units & Modelling (Edexcel A-Level Mathematics): Revision Notes

1.1.5 Modelling Assumptions

In A-Level Mechanics, simplifying real-world problems through modelling assumptions is essential. These assumptions make problems more manageable by reducing complexity, allowing you to apply mathematical techniques more easily. However, it's important to be aware of these assumptions as they can influence the accuracy of your results.

1. Particle

• Assumption: The object is treated as a point mass, meaning its size and shape are ignored.
• Implications:
  • Rotational effects and air resistance are ignored.
  • The mass of the object is assumed to act at a single point.

2. Rigid Body

• Assumption: The object does not deform under the action of forces; its shape and size remain constant.
• Implications:
  • Forces causing deformation are ignored.
  • The object can rotate, but all parts of it remain in their original positions relative to each other.

3. Smooth Surface

• Assumption: The surface provides no friction.
• Implications:
  • Frictional forces are ignored in calculations.
  • Only normal contact forces are considered.

4. Rough Surface

• Assumption: The surface provides friction.
• Implications:
  • Frictional forces must be considered and calculated using the coefficient of friction.
  • The object may not slide easily over the surface.

5. Light Object

• Assumption: The object has negligible mass compared to other objects in the problem.
• Implications:
  • The object's weight is ignored.
  • Tension is assumed to be the same throughout if the object is part of a string or pulley system.

6. Inextensible String

• Assumption: The string does not stretch under tension.
• Implications:
  • The acceleration is the same for all objects connected by the string.
  • The string remains taut during motion.

7. Smooth Pulley

• Assumption: The pulley has no friction and rotates without resistance.
• Implications:
  • Tension in the string is the same on both sides of the pulley.
  • The pulley does not affect the motion of the string.

8. Uniform Body

• Assumption: The object has uniform density, so its mass is evenly distributed.
• Implications:
  • The centre of mass is at the geometric centre of the object.

9. Air Resistance

• Assumption: Often ignored unless specifically stated.
• Implications:
  • Objects are assumed to move without any drag force from air.
  • Simplifies calculations for objects in free fall or projectile motion.

10. Gravity

• Assumption: Gravity acts downwards uniformly with a constant acceleration.
• Implications:
  • The value of gravitational acceleration ( $g$) is taken as $9.8 \, \text{m/s}^2$ .
  • The effects of gravity are considered the same everywhere in the problem.

Summary