24 Mechanics 1

Candidates will be expected to be familiar with the knowledge, skills and understanding implicit in the modules Core 1 and Core 2. Candidates may use relevant formulae included in the formulae booklet without proof.

Candidates should learn the following formulae, which are not included in the formulae booklet, but which may be required to answer questions.

Constant Acceleration Formulae
 $v^2 = u^2 + 2as$
Weight $W = mg$
Momentum $\text{Momentum} = mv$
Newton's Second Law $F = ma \space \space$  or   Force = rate of change of momentum
Friction, dynamic $F = \mu R$
Friction, static $F \leqslant \mu R$
 Use of assumptions in simplifying reality. Candidates are expected to use mathematical models to solve problems. Mathematical analysis of models. Modelling will include the appreciation that: it is appropriate at times to treat relatively large moving bodies as point masses; the friction law  $F \leqslant \mu R \space$ is experimental. Interpretation and validity of models. Candidates should be able to comment on the modelling assumptions made when using terms such as particle, light, inextensible string, smooth surface and motion under gravity. Refinement and extension of models.
Displacement, speed, velocity, acceleration. Understanding the difference between displacement and distance.
Sketching and interpreting kinematics graphs. Use of gradients and area under graphs to solve problems.
Use of constant acceleration equations
 $v^2 = u^2 + 2as$
Vertical motion under gravity.
Average speed and average velocity.
Application of vectors in two dimensions to represent position, velocity or acceleration. Resolving quantities into two perpendicular components.
Use of unit vectors $\space \bf{\mbox{i}} \space$ and $\space \bf{\mbox{j}}$. Candidates may work with column vectors.
Magnitude and direction of quantities represented by a vector.
Finding position, velocity, speed and acceleration of a particle moving in two dimensions with constant acceleration. The solution of problems such as when a particle is at a specified position or velocity, or finding position, velocity or acceleration at a specified time. Use of constant acceleration equations in vector form, for example,

$\bf{\mbox{v}} = \bf{\mbox{u}} + \bf{\mbox{a}}\mathit{t}\space$.

Problems involving resultant velocities. To include solutions using either vectors or vector triangles.
 Drawing force diagrams, identifying forces present and clearly labelling diagrams. When drawing diagrams, candidates should distinguish clearly between forces and other quantities such as velocity. Force of gravity (Newton's Universal Law not required). The acceleration due to gravity,$\space g$, will be taken as $\space 9.8 \space\mbox{ms}^{-2}$. Friction, limiting friction, coefficient of friction and the relationship of $\space F \leqslant \mu R$. Candidates should be able to derive and work with inequalities from the relationship $\space F \leqslant \mu R$. Normal reaction forces. Tensions in strings and rods, thrusts in rods. Modelling forces as vectors. Candidates will be required to resolve forces only in two dimensions. Finding the resultant of a number of forces acting at a point Candidates will be expected to express the resultant using components of a vector and to find the magnitude and direction of the resultant. Finding the resultant force acting on a particle. Knowledge that the resultant force is zero if a body is in equilibrium Find unknown forces on bodies that are at rest.
 Concept of momentum Momentum as a vector in one or two dimensions. (Resolving velocities is not required.) Momentum $= mv \space$ The principle of conservation of momentum applied to two particles. Knowledge of Newton’s law of restitution is not required.
 Newton’s three laws of motion. Problems may be set in one or two dimensions Simple applications of the above to the linear motion of a particle of constant mass. Including a particle moving up or down an inclined plane. Use of $\space F = \mu R \space$ as a model for dynamic friction.
 Connected particle problems. To include the motion of two particles connected by a light inextensible string passing over a smooth fixed peg or a smooth light pulley, when the forces on each particle are constant. Also includes other connected particle problems, such as a car and trailer.
 Motion of a particle under gravity in two dimensions. Candidates will be expected to state and use equations of the form $x = V \space \space \cos \alpha t \space$ and $\space \space y = V \sin \alpha t - \frac{1}{2} gt^2$. Candidates should be aware of any assumptions they are making. Calculate range, time of flight and maximum height. Formulae for the range, time of flight and maximum height should not be quoted in examinations. Inclined plane and problems involving resistance will not be set. The use of the identity$\space \sin 2 \theta = 2 \sin \theta \cos \theta \space$ will not be required. Candidates may be expected to find initial speeds or angles of projection. Modification of equations to take account of the height of release.