Course objectives:
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The aim of this course is to make students acquainted with basic terms of mechanics and to introduce them into the problems of statics. On the basis of acquired knowledge of the theory of force systems, the students will be able to solve simple real problems.
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Requirements on student
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Credit requirements:
Student elaborates the terminal work.
Credit obtained in previous years of study is not accepted.
Exam requirements:
Student proves knowledge in the test and the oral exam.
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Content
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1. Historical overview of mechanics development, topics and fields of mechanics. Scalar and vector quantities. Vector and its representation in plane and 3D space.
2. Fundamentals of vector calculus for applications in mechanics (basic vector operations, unit vector, dot product, vector product).
3. Fundamentals of differential and integral calculus for applications in mechanics.
4. Basic concepts of statics - force and its determination, axioms of statics, forces composition and decomposition in plane and in 3D space.
5. Moment of a force to a point and about an axis. Varignon's theorem. Force couple. Principle theorems of statics.
6. Force fields. Mechanical work and power of a force and a moment. Efficiency of mechanical systems.
7. Theory of force systems - forces replacement, equivalence and equilibrium. Collinear forces. Force system passing a single point - planar and 3D problem.
8. System of parallel forces in plane. General planar system of forces.
9. General system of forces in 3D space.
10. System of parallel forces in 3D space and determination of its centre.
11. Determination of the centre of mass (gravity) of 1D objects, application of the first Pappus theorem.
12. Determination of the centre of mass (gravity) of 2D objects, application of the second Pappus theorem.
13. Determination of the centre of mass (gravity) of 3D objects.
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Activities
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Fields of study
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Guarantors and lecturers
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Literature
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Preparation for an examination (30-60)
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30
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Undergraduate study programme term essay (20-40)
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20
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Contact hours
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30
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Total
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80
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
disponovat základními znalostmi vektorového a maticového počtu |
mít základní znalosti z algebry |
orientovat se v základech diferenciálního a integrálního počtu |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
definovat vektor v rovině a prostoru |
řešit soustavy lineárních algebraických rovnic |
vypočítat derivace a integrály základních typů funkcí |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
vysvětlit základní pojmy statiky |
vysvětlit rozdíl mezi náhradou, ekvivalencí a rovnováhou u silových soustav |
formulovat podmínky rovnováhy pro obecnou silovou soustavu |
vysvětlit obecný postup stanovení polohy střediska hmotnosti (těžiště) |
Skills - skills resulting from the course: |
určit náhradu libovolné soustavy sil v 1D - 3D |
vypočítat moment síly k bodu či k ose |
stanovit výslednici libovolné soustavy sil |
určit polohu střediska hmotnosti (těžiště) u jednoduchých hmotných objektů |
Competences - competences resulting from the course: |
N/A |
N/A |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Combined exam |
Seminar work |
Skills - skills achieved by taking this course are verified by the following means: |
Combined exam |
Seminar work |
Competences - competence achieved by taking this course are verified by the following means: |
Combined exam |
Seminar work |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture |
Practicum |
Self-study of literature |
One-to-One tutorial |
Skills - the following training methods are used to achieve the required skills: |
Lecture supplemented with a discussion |
Practicum |
One-to-One tutorial |
Competences - the following training methods are used to achieve the required competences: |
Lecture supplemented with a discussion |
Practicum |
Self-study of literature |
One-to-One tutorial |
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