Mechanics: Motion, Forces, Moments and Energy
Mechanics: motion, forces and energy
Begin with the language of motion. Distance and speed are scalars; displacement and velocity are vectors, so direction matters. Acceleration is the rate of change of velocity. For uniform acceleration, use v = u + at, s = ut + ½at² and v² = u² + 2as. On a distance–time graph the gradient is speed; on a velocity–time graph the gradient is acceleration and the area beneath the line is displacement.
Dynamics centres on Newton's laws. A resultant force changes motion; zero resultant force means constant velocity or rest. Use F = ma and weight W = mg, keeping mass in kilograms and weight in newtons. Friction opposes relative motion and transfers energy to thermal stores. Moments describe turning effects: moment = force × perpendicular distance from the pivot. A body is in equilibrium when resultant force and resultant moment are both zero; use the principle of moments. Work is force × distance moved along the force, W = Fs. Energy is conserved: kinetic energy ½mv² and gravitational potential energy mgh interchange, with some energy dissipated. Power is work done per second, P = W/t, and efficiency = useful output ÷ total input × 100%.
Common traps: mixing mass and weight; using a sloping distance instead of the perpendicular distance in moments; forgetting to convert cm to m or g to kg; assuming area under a velocity–time graph is always distance when direction reverses; and quoting efficiency above 100%.
Worked example: A 900 kg car at 20 m/s brakes to rest over 50 m. Using v² = u² + 2as gives 0 = 400 + 100a, so a = −4 m/s². The braking force is F = ma = 900 × 4 = 3600 N, opposing motion.