handbook of modern sensors

9
Force, Strain, and Tactile Sensors
Whereas kinematics studies positions of objects and their motions, dynamics answers
the question “What causes the motion” Classical mechanics deal with moving objects
whose velocities are substantially smaller than the speed of light. Moving particles,
such as atoms and electrons, are the subject of quantum mechanics and the theory of
relativity. A typical problem of classical mechanics is the question: “What is motion
of an object, which initially had a given mass, charge, dipole moment, position, and so
forth and was subjected to external objects having known mass, charge, velocity, and
so forth” That is, to say, classical mechanics deals with interactions of macroobjects.
In a general form, this problem was solved by Sir Isaac Newton (1642–1727), who
claimed he was born in the year when Galileo died. 1 He brilliantly developed ideas
of Galileo and other great mechanics. Newton stated his first law as: Every body
persists in its state of rest or of uniform motion in a straight line unless it is compelled
to change that state by forces impressed on it. Sometimes, this is called the law of
inertia. Another way to state the first law is to say: “If no net force acts on a body, its
acceleration a is zero.”
When force is applied to a free body (not anchored to another body), it gives the
body an acceleration in the direction of force. Thus, we can define force as a vector
value. Newton had found that acceleration is proportional to the acting force F and
inversely proportional to the property of a body called the mass m which is a scalar
value:
a = F m . (9.1)
This equation is known as Newton’s second law; the name was given by the great Swiss
mathematician and physicist Leonhard Euler in 1752, 65 years after the publication
of Newton’s Principia [1]. The first law is contained in the second law as a special
case: When net acting force F = 0, acceleration a = 0.
Newton’s second law allows us to establish the mechanical units. In SI terms,
mass (kg), length (m), and time (s) are the base units (see Table 1.7 of Chapter 1).
Force and acceleration are derivative units. The force unit is the force which will
accelerate 1 kg mass to acceleration 1 m/s 2 . This unit is called a newton.
1 In reality, Newton was born on January 4, 1643.