§ 5 Force. Kinds of forces

In mechanics, we consider two types of effects on the body of the other bodies.
1) this body under the influence of other bodies changes its velocity, i.e., an acceleration.
2) this body under the influence of other bodies are deformed, i.e., a change in shape and size
To describe these effects use of the concept of force:

Force - a vector quantity is a measure of the mechanical action on the body under consideration by other bodies.

The forces that impose bodies acceleration or distorting them can split into two groups:
a) The distribution of force by volume of the body, such as gravity.
For such a force characteristic that each unit of the body experiences a force independent of the presence or absence of adjacent body parts.

b) concentrated force, that is, attached to a specific location of the body - at a point along a line or surface of the body. In this case, the action of an external force is transferred from one part to the other because of the existence of mutual relationships between them (this leads to deformation).


I elastic force.

Under the forces applied to the body, it is deformed. If the termination of the powers the body takes its original size and shape, the deformation is called elastic, and if you do not restore the shape and size, the strain - inelastic. Elastic deformations are observed when the applied force is less than the limit of force at which a inelastic deformation (the so-called elastic limit)

Consider a spring one end of which is fixed and the other attached to a tensile (or compressive) force Fext.

From experience, it follows that at small strains extension springs X is directly proportional to the tensile strength.


 by the law of Newton III

 - Hooke's law

Hooke's law: the elastic force Felast directly proportional to the strain (displacement) X. The coefficient of proportionality in Hooke's law is called the spring constant (stiffness)- k.

The rod acts like a spring. If by the end of the rod to attach equal F1 = F2 = F is uniformly distributed over the surface of the rod S forces directed along the axis, the initial length of the bar will change to. To characterize the deformation of the rod is introduced relative change in its length ε-relative deformation.


Physical quantity that is numerically equal to the elastic force dFelast per unit area dS section of the body is called stress.


If force dFelast along the normal to the area dS, called normal stress and is denoted by σ. If dFelast tangential to the area dS - tangent and is denoted τ.

Hooke's law (for the rod): voltage elastically deformed body is directly proportional to the strain

Young's modulus E is the elastic modulus, which is numerically equal to the voltage that occurs when the strain is equal to one. The value of α = 1 / E is called the coefficient of elasticity.


Shift is called the deformation of the body, in which all of its flat layers parallel to a shear plane,  not curved and has not changed in size, move in parallel.

For a small shift

 - absolute shift;

γ - shift angle or the relative shift in radians.



G-shear modulus, is equal to shearing stress at the relative shift tg γ = 1, therefore, γ = 45° (although almost all substances are destroyed at much lower corners).

III. Gravity and weight

Under the force of gravity to the Earth all bodies fall with the same acceleration relative to the Earth's surface g = 9.8 m/s2 - acceleration due to gravity. Hence, on any body of mass m subject to a force called gravity.

(rotation of the Earth does not take into account).


The force of gravity causes a fall of loose bodies on Earth. It is equal to the force with which a fixed relative to the Earth's body presses on the horizontal support (or acts on the vertical suspension) due to gravity to the Earth. The point of application of the force of gravity, i.e. point of application of the resultant of gravity of all the particles of the body, called the center of gravity of the body. Center of gravity coincides with the center of mass and the body of regular geometric shape is defined as the symmetric point in the bodies of irregular geometry as a point of equilibrium (the torque about the center of gravity in the equilibrium should be 0).


Power, with which the body acts on the suspension or support, called the weight of the body.






If the body is immovable relative to the earth (v = 0), then . If the body and support moves with some acceleration relative to the Earth, the .

2nd Newton's Law:

The 3rd Newton's Law:


Projection on the Y axis

  1. system is at rest

Weight is the force of gravity.

2 System is accelerated up

Weight greater than gravity.

III system is accelerated down

Weight less than the force of gravity

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