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A-level Further Mathematics7367

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3.3 Optional application 1 – mechanics

3.3.1 MA: Dimensional analysis

 Content
MA1Finding dimensions of quantities; checking for dimensional consistency.
 Content
MA2Prediction of formulae; finding powers in potential formulae.

3.3.2 MB: Momentum and collisions

 Content
MB1Conservation of momentum for linear motion and cases where velocities are given as one or two dimensional vectors (problems which require resolving).
 Content
MB2Coefficient of restitution and Newton’s Experimental Law. Use in direct collisions and impacts with a fixed smooth surface. Problems which require resolving.
 Content
MB3Impulse and its relation to momentum. Use of Ft=mv-mu . Problems which require resolving.
 Content
MB4Impulse for variable forces. One dimension only. Use of I=∫Fdt .

3.3.3 MC: Work, energy and power

 Content
MC1Work done by a force acting in the direction of motion or directly opposing the motion. Use of WD=Fd cos⁡θ
 Content
MC2Gravitational potential energy. Use in conservation of energy problems.
 Content
MC3Kinetic energy. Use in conservation of energy problems.
 Content
MC4

Hooke’s Law including using modulus of elasticity.

Use of T=kx or T=λlx

 Content
MC5

Work done by a variable force. Use of WD=∫Fdx .

Use in conservation of energy problems.

 Content
MC6

Elastic potential energy using modulus of elasticity. Use of EPE=kx22 and EPE=λx22l .

Use in conservation of energy problems.

3.3.4 MD: Circular motion

 Content
MD1

Motion of a particle moving in a circle with constant speed (knowledge of radians assumed).

 Content
MD2

Understand the definition of angular speed.

Use both radians and revolutions per unit time.

 Content
MD3Relationships between speed, angular speed, radius and acceleration. Use of v=rω , a=rω2 and a=v2r
 Content
MD4Use position, velocity and acceleration as vectors in the context of circular motion.
 Content
MD5Conical pendulum, with one or two strings.
 Content
MD6Circular motion in a vertical plane. Includes conditions to complete vertical circles. Use of conservation of energy in this context.

3.3.5 ME: Centres of mass and moments

 Content
ME1Centre of mass for a system of particles.
 Content
ME2Centre of mass for a composite body.
 Content
ME3Centre of mass of a lamina by integration.
 Content
ME4Centres of mass of bodies formed by rotating a region about the x -axis.
 Content
ME5Conditions for sliding and toppling. Problems including suspension and on an inclined plane.
 Content
ME6Determine the forces acting on a rigid body in equilibrium. Use of moments and couples.