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Lecturer(s)
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Janková Blanka, Ing. Ph.D.
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Course 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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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. V Plzni : Západočeská univerzita, 2012. ISBN 978-80-261-0138-3.
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Juliš,K.-Tepřík,O.-Slavík,A. Statika. SNLT/. ALFA Praha, 1987.
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