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Product Statics samenvattingEmma Binnendijk
Inhoudsopgave
Tentamenstof.......................................................................................................................................... 2
Mechanica ............................................................................................................................................... 3
Chapter 1 General Principles ............................................................................................................... 3
Chapter 2 Force Vectors ...................................................................................................................... 4
Chapter 3 Equilibrium of a Particle ..................................................................................................... 6
Chapter 4 Force System Resultants ..................................................................................................... 6
Chapter 5 Equilibrium of a Rigid Body............................................................................................... 12
Chapter 6 Structural Analysis ............................................................................................................ 16
Chapter 8 Friction (only 8.1 to 8.3) ................................................................................................... 19
Chapter 9 Center of Gravity and Centroid (only 9.1 and 9.2 ) .......................................................... 21
Functietheorie....................................................................................................................................... 23
Calculus ................................................................................................................................................. 26
Chapter 12 Vectors an the Geometry of Space (only 12.1 to 12.4) .................................................. 26
Chapter 5 Integrals (only 5.3 to 5.5).................................................................................................. 29
Chapter 7 Techniques of Integration (only 7.1) ................................................................................ 31
Chapter 14 Techniques of Integration (only 14.1 and 14.3 ) ............................................................ 31
Chapter 15 Multiple Integrals (only 15.2 and 15.4) .......................................................................... 32
Electronics ............................................................................................................................................. 33
HC 1 ................................................................................................................................................... 33
HC 2 ................................................................................................................................................... 34
HC 3 ................................................................................................................................................... 35
HC 4 ................................................................................................................................................... 35
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Tentamenstof
Calculus Mechanica Electronics Overig
12.1 t/m 12.4 Tot 6.6 HC’s BS Functietheorie
5.3 t/m 5.5 8.1 t/m 8.3
7.1 9.1 en 9.2
14.1 en 14.3
15.2 en 15.4
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Mechanica
Chapter 1 General Principles
Length, time, mass and force are basic quantities in mechanics. A force is considered as a
push or pull exerted by one body or another.
Three important idealizations:
- A particle has a mass, but the size can be neglected.
- A rigid body large number of particles, the body’s shapes does not change when load is
applied)
- A concentrated force (represents the effect of a loading which is assumed to act at a
point on a body).
Newton’s laws of motion:
- First Law: A particle at rest or moving in a straight line with constant velocity tends to
remain in this state provided the particle is not subjected to an unbalanced force.
- Second Law: F=ma, a particle acted upon by an unbalanced force F experiences an
acceleration a that has the same direction as the force and a magnitude that is directly
proportional to the force.
- Third Law: mutual forces of action and reaction between two particles are equal,
opposite, and collinear (Action = -reaction).
Newton’s Law of Gravitational Attraction, a law governing the gravitational attraction
𝑚𝑚 𝑚𝑚
between any two particles. 𝐹𝐹 = 𝐺𝐺 𝑟𝑟1 2 2
In the case of a particle located at or near the surface of the earth, however, the only
gravitational force having any sizable magnitude is that between the earth and the particle.
𝑚𝑚 𝑀𝑀𝑀𝑀
This force, the weight, will be the only gravitational force. 𝑊𝑊 = 𝐺𝐺 𝑟𝑟2 with g = GMe/r2, W=mg.
International System of Units:
Quantity Unit Symbol
Length Meter m
Mass Kilogram Kg
Time Seconds s
Electric current Ampere A
Thermodynamic temperature Kelvin K
Amount of substance Mole mol
Prefixes
Exponential Form Prefix SI Symbol
1 000 000 000 109 Giga G
1 000 000 106 Mega M
1 000 103 Kilo k
0.001 10-3 Milli m
0.000 001 10-6 Micro µ
0.000 000 001 10-9 Nano n
Numerical calculations:
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- The terms of any equation used to describe a physical process must be dimensionally
homogeneous.
- The number of significant figures contained in any number determines the accuracy of
the number.
- Any numerical figure ending in a number greater than five is rounded up and a umber
less than five is not rounded up. If a number ends in 5 and the digit preceding the 5 is
odd, then it is rounded up. If the digit preceding the 5 is even, then the 5 is not rounded
up.
Chapter 2 Force Vectors
A scalar is a quantity that can be specified by its magnitude.
A vector is a quantity that requires both a magnitude and a direction. Graphically a vector is
shown by an arrow, the length represents the magnitude, the angle between the vector and
a fixed axis the direction of its line of action, and the head indicates the sense of direction.
Vectors can be multiplied in both a positive and a negative scalar.
Adding or subtracting two or more vectors can be done using either the parallelogram law or
the triangle rule. To resolve a force into two components the parallelogram law can also be
used.
The cosine and sine laws can be used to obtain the magnitude and direction of the force.
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