Mechanika
What you must know
Mechanika on the maturita is mostly kinematics, Newton's laws, momentum, work-energy and a little statics. Be fluent with the kinematic equations for constant acceleration (v = v₀ + at, s = v₀t + ½at², v² = v₀² + 2as), free fall, and the difference between distance and displacement. For dynamics, know that net force produces acceleration (F = ma), that friction is F = μN, and that on an incline the driving component is mg·sin α while the normal force is mg·cos α. Momentum p = mv is conserved in collisions; kinetic energy is conserved only in perfectly elastic ones.
Traps
- Mixing up mass and weight; weight is mg in newtons.
- Forgetting that normal force is not always mg (incline, lift, curved track).
- Using s = vt when the body accelerates; the average velocity is (v₀ + v)/2 only for constant acceleration.
- Sign conventions: choosing a direction as positive and then flipping signs halfway.
- Circular motion: centripetal force is a net inward force, not an extra force you add to gravity or tension.
Worked example
A block slides from rest down a frictionless 30° incline of length 5 m. Find the speed at the bottom. Acceleration along the slope a = g·sin 30° = 9.8 × 0.5 = 4.9 m/s². Using v² = 2as: v = √(2 × 4.9 × 5) = √49 ≈ 7 m/s. Note the mass cancels - a common shortcut in questions.
Rule of thumb: draw the free-body diagram first, resolve forces along and perpendicular to the motion, then apply F = ma in each direction.