♦ Learn about : concept of force , Forces & their classification , contact force , non-contact force , spring force ♦
Concept of force :
A force is a push or a pull acting on a body. It is a vector quantity : i.e. it has both magnitude & direction.
In 3 dimensions, using vector notation, we can write , where Fx, Fy and Fz represent the x, y, z components of the force . , and represent the (dimensionless) unit vectors along x, y and z respectively.
Forces are measured in SI units in Newton.
1 Newton (N) is that force which when applied to a body of mass 1 kg, causes an acceleration of 1 m/s2.
A system consists of bodies, whose motion is to be analysed. In this chapter we will be analysing the motion of rigid bodies.
Forces and their classification
The first classification is self explanatory.
All forces acting on a body can be classified as:
(a) contact, and
(b) non-contact forces.
(a) Contact force: Forces experienced by objects due to contact with each other are contact forces The component of the contact force normal to the surface of contact (or line of contact) is usually known as the normal reaction, and a tangential component of the force, may act along the surface of contact.
(b) Non-contact force: Bodies can exert forces on each other without actual physical contact. This is known as action at a distance. Such forces are known as non-contact forces .e.g. gravitation, coulomb repulsion between like charges, etc.
For the moment, we will deal with actual forces. Suffice it to say that there exist pseudo-forces acting in a non-inertial frame of reference.
Forces may be conservative or non-conservative depending on whether work done against them by an external agent is recoverable or otherwise. This will be discussed in a later chapter. Some typical forces we will be dealing with are tension, spring force, normal reaction, etc. Some free body diagrams for these forces are shown below :
(i) Tension in a string : For a block A pulled by a string,
(ii) Spring forces :
(a) F = kx
Where x = extension in the spring
= present length – normal length
(b) F’ = kx’
where x’ = compression in the spring
= normal length − present length
You can use either of the above diagrams: (A) or (B)
(iii) Normal Reaction
A block A rests on another block B. The normal reaction N acts between A and B as shown in the diagram.