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Lecturer(s)
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Jonášová Alena, Ing. Ph.D.
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Course content
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1. Mechanics as a fundamental branch of physics. Historical overview of mechanics development, topics and fields of mechanics. 2. Scalar and vector physical quantities and their units. Review of fundamental mathematics. 3. Vector and its geometric representation in plane (2D) and space (3D). Determining the components of a vector in 2D and 3D. 4. Position vector. Coordinate systems and their transformations. 5. Fundamentals of vector calculus for solving mechanics problems (basic vector operations, unit direction vector, dot product, vector product). 6. Basic concepts of statics. Force and its determination in 2D and 3D. Axioms of statics 7. Force composition and decomposition in 2D and 3D - use of analytical and graphical methods. Funicular polygon method. 8. Moment of a force about a point and about an axis. Principle of moments (Varignon's theorem). 9. Force couple and its moment. Basic theorems of statics. 10. Theory of force systems - resultant force, equivalent force systems and mechanical equilibrium: - system of collinear forces in 2D and 3D, - system of concurrent forces in 2D and 3D. 11. Theory of force systems - resultant force, equivalent force systems and mechanical equilibrium: - system of parallel forces in 2D and 3D, - system of non-concurrent (general) forces in 2D and 3D. 12. Determination of the centre of gravity (mass) of a body. 13. Application of the 1st and 2nd Pappus-Guldinus theorems.
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Learning activities and teaching methods
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- Preparation for an examination (30-60)
- 30 hours per semester
- Contact hours
- 30 hours per semester
- Undergraduate study programme term essay (20-40)
- 20 hours per semester
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| prerequisite |
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| Knowledge |
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| have basic knowledge of vector and matrix calculus |
| have a basic knowledge of algebra |
| orient yourself in the basics of differential and integral calculus |
| Skills |
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| define a vector in plane and space |
| solve systems of linear algebraic equations |
| calculate derivatives and integrals of basic types of functions |
| Competences |
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| N/A |
| N/A |
| learning outcomes |
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| Knowledge |
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| explain the basic concepts of statics |
| explain the difference between substitution, equivalence and equilibrium in force systems |
| formulate equilibrium conditions for a general force system |
| explain the general procedure for determining the position of the center of mass (center of gravity) |
| Skills |
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| determine the replacement of any system of forces in 1 to 3 dimensions |
| calculate the moment of force to a point or to an axis |
| determine the resultant of any system of forces |
| determine the position of the center of mass (center of gravity) for simple material objects |
| Competences |
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| N/A |
| N/A |
| teaching methods |
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| Knowledge |
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| Lecture |
| Practicum |
| Self-study of literature |
| One-to-One tutorial |
| Skills |
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| Lecture supplemented with a discussion |
| Practicum |
| One-to-One tutorial |
| Competences |
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| Lecture supplemented with a discussion |
| Practicum |
| Self-study of literature |
| One-to-One tutorial |
| assessment methods |
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| Knowledge |
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| Combined exam |
| Seminar work |
| Skills |
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| Combined exam |
| Seminar work |
| Competences |
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| Combined exam |
| Seminar work |
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Recommended literature
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Hibbeler, Russell C. Engineering mechanics. Statics / R.C. Hibbeler. 11th ed. Upper Saddle River: Prentice Hall, 2006. ISBN 0-13-221500-4.
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Hlaváč, Zdeněk; Vimmr, Jan. Sbírka příkladů ze statiky a kinematiky. 2. vyd. Plzeň: Západočeská univerzita, 2012. ISBN 978-80-261-0138-3.
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Juliš,K.-Tepřík,O.-Slavík,A. Statika. SNLT/. Praha: ALFA, 1987.
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