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3. Further Mechanics

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  1. 3.1 Motion of a projectile

    1. 3.1.1Projectile motion

      • model the motion of a projectile as a particle moving with constant acceleration and understand any limitations of the model Vector methods are not required

    2. 3.1.2Projectile motion

      • use horizontal and vertical equations of motion to solve problems on the motion of projectiles, including finding the magnitude and direction of the velocity at a given time or position, the range on a horizontal plane and the greatest height reached

    3. 3.1.3Projectile motion

      • derive and use the Cartesian equation of the trajectory of a projectile, including problems in which the initial speed and/or angle of projection may be unknown. Knowledge of the 'bounding parabola' for accessible points is not included.

  2. 3.2 Equilibrium of a rigid body

    1. 3.2.1Moments

      • calculate the moment of a force about a point For questions involving coplanar forces only; understanding of the vector nature of moments is not required.

    2. 3.2.2Centre of mass

      • use the result that the effect of gravity on a rigid body is equivalent to a single force acting at the centre of mass of the body, and identify the position of the centre of mass of a uniform body using considerations of symmetry

    3. 3.2.3Centre of mass

      • use given information about the position of the centre of mass of a triangular lamina and other simple shapes Proofs of results given in the MF19 List of formulae are not required.

    4. 3.2.4Centre of mass

      • determine the position of the centre of mass of a composite body by considering an equivalent system of particles Simple cases only, e.g. a uniform L -shaped lamina, or a uniform cone joined at its base to a uniform hemisphere of the same radius.

    5. 3.2.5Rigid body equilibrium

      • use the principle that if a rigid body is in equilibrium under the action of coplanar forces then the vector sum of the forces is zero and the sum of the moments of the forces about any point is zero, and the converse of this

    6. 3.2.6Toppling and sliding

      • solve problems involving the equilibrium of a single rigid body under the action of coplanar forces, including those involving toppling or sliding.

  3. 3.3 Circular motion

    1. 3.3.1Angular speed

      • understand the concept of angular speed for a particle moving in a circle, and use the relation vr ~=

    2. 3.3.2Circular acceleration

      • understand that the acceleration of a particle moving in a circle with constant speed is directed towards the centre of the circle, and use the formulae r 2~ and r v2. Proof of the acceleration formulae is not required.

    3. 3.3.3Circular acceleration

      • solve problems which can be modelled by the motion of a particle moving in a horizontal circle with constant speed

    4. 3.3.4Vertical circular motion

      • solve problems which can be modelled by the motion of a particle in a vertical circle without loss of energy. Including finding a normal contact force or the tension in a string, locating points at which these are zero, and conditions for complete circular motion.

  4. 3.4 Hooke's law

    1. 3.4.1Hooke's law

      • use Hooke's law as a model relating the force in an elastic string or spring to the extension or compression, and understand the term modulus of elasticity

    2. 3.4.2Elastic energy

      • use the formula for the elastic potential energy stored in a string or spring Proof of the formula is not required.

    3. 3.4.3Problems involving forces due to elastic

      • solve problems involving forces due to elastic strings or springs, including those where considerations of work and energy are needed. e.g. a particle moving horizontally or vertically or on an inclined plane while attached to one or more strings or springs, or a particle attached to an elastic string acting as a 'conical pendulum'.

  5. 3.5 Linear motion under a variable force

    1. 3.5.1

      • solve problems which can be modelled as the linear motion of a particle under the action of a variable force, by setting up and solving an appropriate differential equation. Including use of v x v d d for acceleration, where appropriate. Calculus required is restricted to content from Pure Mathematics 3 in Cambridge International A Level Mathematics (9709). Only differential equations in which the variables are separable are included.

  6. 3.6 Momentum

    1. 3.6.1Coefficient of restitution

      • recall Newton's experimental law and the definition of the coefficient of restitution, the property e01GG, and the meaning of the terms 'perfectly elastic' (e = 1) and 'inelastic' (e = 0)

    2. 3.6.2Momentum and impacts

      • use conservation of linear momentum and/or Newton's experimental law to solve problems that may be modelled as the direct or oblique impact of two smooth spheres, or the direct or oblique impact of a smooth sphere with a fixed surface.