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LearnAQA7408First teaching 2015Paper 1 · Paper 1Mechanics and materials

Paper 1 · Module

Mechanics and materials

11 subtopics≈ 400 min in total

Start the module: Equations of motion and graphs Open graphing calculator

Equations of motion and graphs
For constant acceleration in a straight line, five quantities ( $s$ , $u$ , $v$ , $a$ , $t$ ) are linked by four equations. Choose the one that contains the three you know and the one you want. Pick a positive direction and stick to it: for vertical motion, $a=-9.81$ m s⁻² if up is positive. Graphs give the same information: gradients and areas.
≈ 40 min
Work, power and efficiency
Work is done when a force moves its point of application: $W=Fs\cos\theta$ , the force times the displacement in its direction. It's the area under a force–displacement graph, and $W=p\Delta V$ for a gas expanding at constant pressure. Power is the rate of doing work: $P=\dfrac Wt$ , and for a force moving at steady speed, $P=Fv$ . Efficiency compares useful output with total input.
≈ 35 min
Newton's laws and momentum
An object keeps its velocity unless a resultant force acts (first law). The resultant force equals the rate of change of momentum, $F=\dfrac{\Delta p}{\Delta t}$ , which is $F=ma$ for constant mass (second law). Forces come in equal and opposite pairs on different objects (third law). Drag grows with speed, so falling objects reach a terminal velocity.
≈ 40 min
Stress, strain and the Young modulus
A spring or wire obeys Hooke's law, $F=kx$ , up to its limit of proportionality. To compare materials rather than particular objects, use stress ( $\sigma=\tfrac FA$ ) and strain ( $\varepsilon=\tfrac xL$ ). Their ratio in the linear region is the Young modulus, $E=\dfrac\sigma\varepsilon$ , a property of the material alone.
≈ 35 min
Moments, couples and equilibrium
The moment of a force is force times the perpendicular distance from the pivot to its line of action. A couple is a pair of equal, opposite, parallel forces: it turns without moving the object along, with torque $=$ one force $\times$ the separation. An object is in equilibrium when the resultant force and the resultant moment are both zero; then its forces form a closed vector polygon.
≈ 40 min
Conservation of momentum and collisions
In any interaction with no external resultant force, total momentum is conserved, in every direction. In an elastic collision kinetic energy is also conserved, and the relative speed of approach equals the relative speed of separation. In an inelastic collision some kinetic energy becomes heat, sound or deformation. In two dimensions, conserve momentum separately in perpendicular directions.
≈ 40 min
Projectile motion
A projectile moves horizontally at constant velocity while accelerating vertically at $g$ . The two motions are independent and share only the time of flight. Resolve the launch velocity into components, solve the vertical motion for the time, then use it for the horizontal distance. Air resistance shortens the range and makes the path lopsided.
≈ 40 min
Density, pressure and upthrust
Pressure in a fluid increases with depth: $\Delta p=\rho g\Delta h$ . Because the pressure on the bottom of a submerged object is greater than on its top, there's a net upward force, the upthrust, equal to the weight of fluid displaced: $F=\rho gV$ . An object floats when the upthrust equals its weight.
≈ 35 min
Kinetic and potential energy
Kinetic energy $E_k=\tfrac12mv^2$ comes from the work done to accelerate a mass from rest. The change in gravitational potential energy near the Earth is $\Delta E_p=mg\Delta h$ , from the work done lifting it. Energy problems become bookkeeping: initial energy $=$ final energy $+$ energy dissipated against friction.
≈ 35 min
Elastic and plastic behaviour
Below its elastic limit, a material returns to its original shape when the load is removed; beyond it, it's permanently (plastically) deformed. The work done stretching a material is the area under its force–extension graph, and within the limit of proportionality the stored elastic potential energy is $E_P=\tfrac12Fx=\tfrac12kx^2$ . Ductile materials deform plastically a lot before breaking; brittle ones snap.
≈ 30 min
Scalars and vectors
Scalars have magnitude only; vectors have magnitude and direction. Vectors add tip-to-tail; for two at right angles use Pythagoras and trigonometry, and for other angles use a scale drawing or the cosine rule. Any vector can be resolved into two perpendicular components: $F\cos\theta$ along the reference direction and $F\sin\theta$ perpendicular to it.
≈ 30 min