Systems of units used in engineering mechanics

In engineering mechanics length, mass, time and force are the basic units used therefore; the following are the units systems are adopted in the engineering mechanics

1. International System of Units (SI):

In SI system of units the basic units are length, time, and mass which are arbitrarily defined as the meter (m), second (s), and kilogram (kg). Force is the derived unit.

1N = 1 kg. 1 m/s2

2. CGS systems of units

In CGS system of units, the basic units are length, time, and mass which are arbitrarily defined as the centimetre (cm), second (s), and gram (g). Force is the derived

Units 1 Dyne = 1 g. 1 cm/s2

3. British systems of units

In CGS system of units, the basic units are length, time, and mass which are arbitrarily defined as the centimetre (cm), second (s), and gram (g). Force is the derived Units

1 lb = 1lbg. 1ft/s2

4. U.S. Customary Units

The basic units are length, time, and force which are arbitrarily defined as the foot (ft), second (s), and pound (lb). Mass is the derived unit,

Trigonometry

The measurement of the triangle sides and angles is called trigonometry. Let us consider right-angled triangle ABC as shown in figure

Than the following ratio can be considered for both the triangles

Sin θ = per/hyp = a/b Sin θ = per/hyp = c/b

Cos θ = base/hyp = c/b Cos θ = base/hyp =a/b

Tan θ = per/base = a/c Tan θ = per/base = c/a

The any side of the right angled triangle may be calculated by

b2 = a2 + b2

Similarly consider the following Triangle

The any side of the triangle can be calculated by using the cosine law, let suppose

we have to calculate the side “AC” that is “b” then

b² = a² + c² – (2bc)cos γ

Similarly, to calculate sides “AB” that is “c” and “AC” that is “a” then by using the

cosine law as below

c² = a² + b² – 2abcos α

And                                            a² = c² + b² – 2cbcos β

The sides of the triangle ABC can be calculated by using the sin law

Principle of transmissibility of forces

The state of rest of motion of a rigid body is unaltered if a force acting in the body is replaced by another force of the same magnitude and direction but acting anywhere on the body along the line of action of the replaced force.

For example the force F acting on a rigid body at point A. According to the principle of transmissibility of forces, this force has the same effect on the body as a force F applied at point B.

The following two points should be considered while using this principle.

1. In engineering mechanics we deal with only rigid bodies. If deformation of the body is to be considered in a problem. The law of transmissibility of forces will not hold good.

2. By transmission of the force only the state of the body is unaltered, but not the internal stresses which may develop in the body Therefore this law can be applied only to problems in which rigid bodies are involved.