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AS Further Mathematics7366

7366

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3.3 Optional application 1 – mechanics

3.3.1 MA: Dimensional analysis

 
Content
MA1
Finding dimensions of quantities; checking for dimensional consistency.
 
Content
MA2
Prediction of formulae; finding powers in potential formulae.

3.3.2 MB: Momentum and collisions

 
Content
MB1
Conservation of momentum for linear motion and cases where velocities are given as one or two dimensional vectors (resolving will not be required).
 
Content
MB2
Coefficient of restitution and Newton’s Experimental Law. Use in direct collisions and impacts with a fixed smooth surface (resolving will not be required).
 
Content
MB3

Impulse and its relation to momentum (in one- or two-dimensions) (resolving will not be required).

Use of

Ft=mv-mu

 
Content
MB4
Impulse for variable forces. One dimension only. Use of
I=∫Fdt
.

3.3.3 MC: Work, energy and power

 
Content
MC1
Work done by a force acting in the direction of motion or directly opposing the motion.
 
Content
MC2
Gravitational potential energy. Use in conservation of energy problems.
 
Content
MC3
Kinetic 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
MD3
Relationships between speed, angular speed, radius and acceleration. Use of
v=rω
,
a=rω2
and
a=v2r