Engineering
MP120: Engineering Mechanics (5 ECTS)
Taught in Semester(s) I. Examined in Semester(s) I.
Workload: 48 hours (36 Lecture hours, 12 Tutorial hours).
Module Learning Outcomes.
On successful completion of this module the learner should be able to:
- perform simple geometrical calculations using vectors, calculate the Cartesian components of vectors, calculate the dot and cross products of vectors and interpret them geometrically;
- solve simple one-dimensional problems in kinematics for both uniform and non-uniform acceleration, plot velocity-time diagrams and interpret them;
- solve relative velocity problems using vector methods;
- calculate the motion of some simple systems by identifying the external forces acting and using Newton's laws, apply the laws of friction in the solution of problems;
- analyse some systems involving sudden impacts using the concepts of linear momentum and impulse, solve direct and oblique collision problems using conservation of momentum and Newton's experimental law;
- solve problems using the principle of work, solve problems using conservation of momentum and energy;
- calculate the centre of mass of some standard bodies;
- solve some simple static problems for rigid bodies.
Indicative Content
- Vectors in two and three dimensions: definition of vectors and scalars, simple vector algebra, Cartesian components of vectors, the dot product and its properties, some geometry with vectors;
- Kinematics: one-dimensional motion, displacement, velocity, acceleration, formulae for uniform acceleration and examples of their use, vertical motion under gravity, motion in two and three dimensions;
- Relative velocity: the relative velocity formula and examples of its use in solving problems;
- Newton's laws of motion: the three laws and an elucidation of their meaning via examples, examples of forces, pulley systems, motion on surfaces and the laws of friction;
- Conservation of momentum: impulse, momentum, sudden impacts, conservation of momentum, direct impacts, oblique impacts, examples;
- Work, power and energy: the line integral and the definition of work, power, kinetic energy, the principle of work, solution of problems using the principle of work, conservative forces and potential energy, conservation of mechanical energy, the solution of problems using conservation laws;
- Circular motion and angular momentum: the equations of motion in polar coordinates, circular motion, angular speed and velocity, examples;
- Systems of particles and rigid bodies: the centre of mass of a system of particles and its motion, the calculation of the centre of mass of some standard bodies, the cross product and angular momentum, moment of force, rigid bodies, derivation of the equation for motion about the centre of mass, solution of some simple static problems for rigid bodies.
Module Resources
Introducing Mechanics, B. Jefferson & T. Beadsworth, Oxford
Further Mechanics, B. Jefferson & T. Beadsworth, Oxford
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