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100 PHYSICS

Answer Figures 5.8(b) and 5.8(c) are known as other types of supports), there are mutual
free-body diagrams. Figure 5.8(b) is the free-body contact forces (for each pair of bodies) satisfying
diagram of W and Fig. 5.8(c) is the free-body the third law. The component of contact force
diagram of point P. normal to the surfaces in contact is called
Consider the equilibrium of the weight W. normal reaction. The component parallel to the
Clearly,T = 6 × 10 = 60 N. surfaces in contact is called friction. Contact
2
forces arise also when solids are in contact with
Consider the equilibrium of the point P under
the action of three forces - the tensions T and fluids. For example, for a solid immersed in a
1 fluid, there is an upward bouyant force equal to
T , and the horizontal force 50 N. The horizontal
2
and vertical components of the resultant force the weight of the fluid displaced. The viscous
must vanish separately : force, air resistance, etc are also examples of
contact forces (Fig. 5.9).
T cos θ = T = 60 N
1 2 Two other common forces are tension in a
T sin θ = 50 N string and the force due to spring. When a spring
1
which gives that is compressed or extended by an external force,
a restoring force is generated. This force is
usually proportional to the compression or
Note the answer does not depend on the length elongation (for small displacements). The spring
of the rope (assumed massless) nor on the point force F is written as F = – k x where x is the
at which the horizontal force is applied. t displacement and k is the force constant. The
negative sign denotes that the force is opposite
5.9 COMMON FORCES IN MECHANICS
to the displacement from the unstretched state.
In mechanics, we encounter several kinds of For an inextensible string, the force constant is
forces. The gravitational force is, of course, very high. The restoring force in a string is called
pervasive. Every object on the earth experiences tension. It is customary to use a constant tension
the force of gravity due to the earth. Gravity also T throughout the string. This assumption is true
governs the motion of celestial bodies. The for a string of negligible mass.
gravitational force can act at a distance without In Chapter 1, we learnt that there are four
the need of any intervening medium. fundamental forces in nature. Of these, the weak
All the other forces common in mechanics are and strong forces appear in domains that do not
contact forces.* As the name suggests, a contact concern us here. Only the gravitational and
force on an object arises due to contact with some electrical forces are relevant in the context of
other object: solid or fluid. When bodies are in mechanics. The different contact forces of
contact (e.g. a book resting on a table, a system mechanics mentioned above fundamentally arise
of rigid bodies connected by rods, hinges and from electrical forces. This may seem surprising

Fig. 5.9 Some examples of contact forces in mechanics.

* We are not considering, for simplicity, charged and magnetic bodies. For these, besides gravity, there are
electrical and magnetic non-contact forces.

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