Mechanics (AS91171)
Mechanics (AS91171)
NCEA Level 2 Physics mechanics tests motion in one and two dimensions, force, momentum, energy and circular motion. You must select the right model, show vector reasoning and justify conservation laws.
Core rules
- Use SI units and g = 9.81 m s^-2. The constant-acceleration equations v = u + at, s = ut + ½at², v² = u² + 2as and s = ½(u + v)t apply only when acceleration is constant.
- Resolve vectors into perpendicular components. In projectile motion, horizontal velocity is constant and vertical acceleration is g; the two motions share the same time.
- Newton's second law is F_net = ma. Action-reaction pairs are equal and opposite but act on different objects, so they do not cancel in one object's free-body diagram.
- Momentum p = mv. Impulse Δp = FΔt. Momentum is conserved when the net external force is zero.
- Work W = Fd cosθ; power P = W/t; use energy conservation and efficiency = useful energy / total energy. For uniform circular motion, the net force points to the centre: F_c = mv²/r.
Worked example
A 0.50 kg ball is thrown horizontally at 8.0 m s^-1 from a height of 1.25 m. Find the time of flight, horizontal range and impact speed. Vertically: u = 0, s = 1.25 m, a = 9.81 m s^-2, so t = √(2s/a) = √(2 × 1.25 / 9.81) = 0.505 s. Horizontally: range = 8.0 × 0.505 = 4.0 m. Vertical impact velocity v_y = gt = 4.95 m s^-1; speed = √(8.0² + 4.95²) = 9.4 m s^-1.
Traps
Do not mix horizontal and vertical data. Keep a sign convention throughout. Do not call centripetal force an extra force; it is the net force. Check units and whether a quantity is a vector before adding it.