Mechanics
What Mechanics tests
Cambridge IAL Mechanics models the motion of particles and rigid bodies using forces, Newton’s laws, energy and momentum. Paper 4-style questions test equilibrium of a particle or rigid body, motion in a straight line with constant acceleration, projectiles, friction, connected particles, work, power and collisions. The physics is simple; the marks come from correct modelling, clear resolution of forces and consistent signs.
Core rules
- SUVAT equations such as v = u + at and s = ut + ½at² apply only while acceleration is constant.
- Resolve forces along convenient perpendicular axes; for a particle in equilibrium the resultant force is zero, and for a rigid body the sum of moments about any point is zero.
- Newton’s second law: F = ma along the direction of motion. On a rough surface, friction opposes impending motion and limiting friction is F = μN.
- Work done by a force is Fd cos θ; KE = ½mv²; change in PE = mgh; power P = Fv.
- Momentum is conserved in collisions in the absence of external impulsive forces; impulse = change in momentum = mv − mu. For projectiles, horizontal velocity is constant while vertical acceleration is g.
Worked example
A 2 kg block on a rough horizontal plane is pulled by a string with tension 10 N at 30° above the horizontal. The coefficient of friction is 0.3. Find the acceleration, using g = 10 m s⁻². Vertical equilibrium: N + 10 sin 30° = 2g = 20, so N = 15 N. Limiting friction: F = μN = 0.3 × 15 = 4.5 N. Horizontal driving force: 10 cos 30° = 8.66 N. Resultant: 8.66 − 4.5 = 4.16 N, so a = F/m = 4.16/2 = 2.08 m s⁻².
Marks that go missing
- Using SUVAT when acceleration changes, or mixing sign conventions between upward and downward motion.
- Assuming N = mg when a vertical component of tension or an inclined plane is present.
- Reversing the direction of friction, or using μN when the body is not at limiting equilibrium.
- Taking the full tension rather than its horizontal component when calculating work or acceleration.
- Using a perpendicular distance from the wrong point in a moments equation.