25 Mechanics 2
|Centres of Mass||and|
|Work and Energy||Work done, constant force:
Work done, variable force in direction of motion in a straight line:
Gravitational Potential Energy
Elastic potential energy
|The application of mathematical modelling to situations that relate to the topics covered in this module.|
|Finding the moment of a force about a given point.||Knowledge that when a rigid body is in equilibrium, the resultant force and the resultant moment are both zero.|
|Determining the forces acting on a rigid body when in equilibrium.||This will include situations where all the forces are parallel, as on a horizontal beam or where the forces act in two dimensions, as on a ladder leaning against a wall.|
|Centres of Mass.||Integration methods are not required.|
|Finding centres of mass by symmetry (eg for circle, rectangle).|
|Finding the centre of mass of a system of particles.||Centre of mass of a system of particles is given by where and|
|Finding the centre of mass of a composite body.|
|Finding the position of a body when suspended from a given point and in equilibrium.|
|Relationship between position, velocity and acceleration in one, two or three dimensions, involving variable acceleration.||Application of calculus techniques will be required to solve problems.|
Finding position, velocity and
acceleration vectors, by the
differentiation or integration
of , with respect to .
Vectors may be expressed in the form as column
|Application of Newtons laws to situations, with variable acceleration.||Problems will be posed in one, two or three dimensions and may require the use of integration or differentiation.|
where simple differential equations are formed as a result of the application of Newtons second law.
Use of for acceleration, to form simple differential equations, for example,
Use of .
The use of is not required.
Problems will require the use of the method of separation of variables.
|Motion of a particle in a circle with constant speed.||Problems will involve either horizontal circles or situations, such as a satellite describing a circular orbit, where the gravitational force is towards the centre of the circle.|
Knowledge and use of the relationships
Angular speed in radians
converted from other units
such as revolutions per minute or time for one revolution.
|Use of the term angular speed.|
|Position, velocity and acceleration vectors in relation to circular motion in terms of and .||Candidates may be required to show that motion is circular by showing that the body is at a constant distance from a given point.|
|Work done by a constant force.||
Forces may or may not act in the direction of motion.
|Gravitational potential energy.||
Universal law of gravitation will not be required.Gravitational Potential Energy
|Kinetic energy.||Kinetic Energy|
|The work-energy principle.||Use of Work Done = Change in Kinetic Energy.|
|Conservation of mechanical energy.||Solution of problems using conservation of energy. One-dimensional problems only for variable forces.|
|Work done by a variable force.||Use of will only be used for elastic strings and springs.|
|Elastic potential energy for strings and springs.||Candidates will be expected to quote the formula for elastic potential energy unless explicitly asked to derive it.|
|Power, as the rate at which a force does work, and the relationship .|
|Circular motion in a vertical plane.||Includes conditions to complete vertical circles.|