(Created 2011-09-01.)

MECHANICS, BASIC COURSE | VSMA15 |

**Aim**

The aim of the course is to give basic knowledge in mechanics with application to real-world problems. Modelling is trained in the course. The problem-solving ability is developed by using the laws of Newton and mathematical tools for defining and analysing computational models describing the physical world.

*Knowledge and understanding*

For a passing grade the student must

- Be able to explain basic concepts as force, moment, velocity, acceleration, work, energy, power, impulse and momentum.
- Be able to use the basic concepts in a physical context.

*Skills and abilities*

For a passing grade the student must

- Be able to use relations (i.e. laws of acceleration, energy and impulse) describing bodies in equilibrium and motion, based on the basic concepts.
- In an idealised physical world, separate an object from its surroundings (making a free-body diagram), identify relevant basic concepts and relations an use them for solving the problem.

*Judgement and approach*

For a passing grade the student must

- Be able to assess the reasonableness in obtained computational results.
- Be able to report the solution of a problem in a clear way (basic conditions, assumptions, calculations, results and conclusions).

**Contents**

A characteristic feature of mechanics is that it tries to capture the patterns of behaviour and and phenomena of nature in terms of mathematical models. The subject thereby has a strong connection to calculus and linear algebra courses. Two basic models for bodies are treated in detail - particle and rigid body. It is important to, in a real situation, have the ability to separate a problem from its surroundings (drawing a free-body diagram) and choose a suitable model for analysis of the problem. Mathematical concepts and methods from linear algebra and calculus are consolidated and deepened when they can be given a clear physical interpretation in the models of mechanics.

The Mechanics course can roughly be divided into statics and dynamics, depending on whether the bodies which are studied are at rest or in motion. Dynamics can be further divided into particle dynamics and rigid body dynamics, depending on whether the extension of the body in question needs to be taken into account.

Statics: two and three-dimensional force systems. Equilibrium. Centre of mass and centroid, friction.

Dynamics: kinematics of particles, kinetics of particles (Newtons second law, work and energy, impulse and momentum). Plane kinematics of rigid bodies. Plane kinetics of rigid bodies.

Project work: The students are introduced into an engineering way of thinking, trained in critcal examination and identifying the question at issue in a more complex situation by an assignment where they choose a problem related to the course and present a report.

**Literature**

Grahn, R. och Jansson, P-Å.: Mekanik statik och dynamik.Studentlitteratur 2002.