## MATH1410 Modelling Force and Motion

### 10 creditsClass Size: 250

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2005/06

### Pre-requisites

MATH1400, or equivalent.

This module is approved as an Elective

### Objectives

To introduce the basic concepts of single particle mechanics and to develop the relevant vector algebra. On completion of this module, students should be able to: (a) carry out basic manipulations involving vector addition and multiplication; (b) formulate the equations of motion for particles in one and two dimensions; (c) solve these equations of motion in simple cases; (d) obtain the energy equation for one and two dimensional particle motion under the action of a conservative force.

### Syllabus

The study of what causes objects to move, and how they move (or stand still !) is the subject of this module. The natural language to describe such motions in three dimensions is that of vectors, and the module starts with a discussion of the algebra of vector quantities. The laws describing the motion of objects are developed: the same laws apply whether the motion is that of a motor car, a parachute jumper, or a spacecraft. Mathematical models for each of these examples are considered, together with several others, use being made of the differential equations studied in module MATH 1400. Topics covered include: 1. Vector algebra: parallelogram law, components, unit vectors and direction cosines, scalar and vector products, triple products. 2. Introduction to mechanics: Newton's laws, forces, gravitation and weight. 3. One dimensional motion: including constant gravity, air resistance etc. Oscillation of a spring/mass system: SHM, damped and forced oscillations, beats and resonance. 4. Two dimensional motion: including projectile and resisted projectile, circular motion. Energy methods: KE and work done, conservative forces and PE.

### Teaching methods

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Lectures (22 hours) and tutorials (11 hours).

### Methods of assessment

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

2 hour written examination at end of semester (85%), coursework (15%).