Mechanics
The UEE Physics mechanics section tests kinematics, Newton's laws, momentum, energy, circular motion, gravitation and statics, usually through multi-step problems and motion graphs.
Core rules
- For constant acceleration: v = v₀ + at, s = v₀t + ½at², v² = v₀² + 2as. These fail if acceleration changes.
- Newton's second law is a vector equation: ΣF = ma. Resolve forces along and perpendicular to the motion; the normal force is whatever the perpendicular equation requires.
- Momentum p = mv is conserved when the net external force is zero. Elastic collisions conserve kinetic energy; inelastic collisions do not.
- Work-energy theorem: W_net = ΔK. With only conservative forces, ½mv₁² + mgh₁ = ½mv₂² + mgh₂.
- Circular motion needs a net inward force mv²/r; it is not an extra force to add.
- Gravitation: F = Gm₁m₂/r², g = GM/r², orbital speed v = √(GM/r).
Worked example
A 2.0 kg block starts from rest and slides 5.0 m down a frictionless 30° incline. Take g = 10 m/s². The vertical drop is h = 5.0 sin30° = 2.5 m. Energy conservation gives mgh = ½mv², so v = √(2gh) = √(2×10×2.5) = √50 ≈ 7.1 m/s. The normal force does no work, which is why the energy route avoids calculating it.
Traps
Using 9.8 m/s² when the paper specifies 10; treating centripetal force as an additional force; dropping signs when friction does negative work; assuming momentum and kinetic energy are both conserved in every collision; saying projectile vertical velocity is zero at the top while forgetting the horizontal component remains.