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3NEWTON’S LAWS OF MOTION
Introduction
In the previous chapter we studied about the motion. Now we will study about the cause behind the
motion. Dynamics is the study of that cause and its effect. In this chapter we will study the consequences
of the cause of motion. The equation of motion is affected by choice of reference frame. So we will
also study the equations of motion in different types of reference frame.
3.1 Fundamental Forces
Force is defined as push or pull experienced by the body or the system. There are four fundamental
kinds of force :
(i) Gravitational Force
(ii) Electromagnetic Force
(iii) Nuclear Force
(iv) Weak Force
3.2 Derived Forces
All forces in nature can in principle be derived from one of the fundamental forces.
All contact forces arise from electromagnetic interaction between the charged particles in the bodies
making contact. For example, the collision of billiard balls, a boxer's punch, the pressure on a body
submerged in water and the frictional force on a car's tires, all arise from electromagnetic forces
acting between the interacting bodies. Even the forces holding matter together - atom to atom - are
electromagnetic in origin.
1. The TENSION force
Forces are often applied by means of cables or ropes that are used to pull on objects. For instance,
figures show force T being applied to the right end of a rope that is attached to a box. Each particle in
the rope, in turn, applies a force to its neighbour. As a result of this process, the force is applied to the
box at the other end.
T
T
(a) (b)
–T T
(c)
In situations such as that in figures, we say that "the force T is applied to the box because of the
tension in the rope", meaning that the tension in the rope and the force applied to the box have the
same magnitude.
Amity Institute for Competitive Examinations Phones: 24336143, 24336144, 25573111/2/3/4, 95120-2431839/42
- 3.1-
,AICE (IIT-JEE) Newton’s Laws of Motion
Regarding the tension in string, the following three points are important to remember :
(a) If a string is inextensible, the magnitude of acceleration of any number of masses connected
through string is always same.
(b) If a string is massless, the tension in it is same everywhere. However, if a string has a mass,
tension at different points may be different.
(c) If there is friction between string and pulley, tension is different on two sides of the pulley, but if
there is no friction between pulley and string, tension will be same on both sides of the pulley.
2. Spring Force
When a spring is stretched, some of the adjacent molecules within the spring are pulled slightly farther
apart from each other, and an attractive electromagnetic force attempts to pull them back to their
original positions. Compression of a spring also produces a force in the spring. In this case, adjacent
molecules are pushed together, and it is repulsive electromagnetic force that is at work, attempting to
push the molecules back to their original positions.
Both the magnitude and the direction of the spring force are indicated by writing the force law in the
form.
Fx = – kx, where k is spring constant, x is stretch or compression.
(a) (b)
(c)
Amity Institute for Competitive Examinations Phones: 24336143, 24336144, 25573111/2/3/4, 95120-2431839/42
- 3.2-
,Newton’s Laws of Motion AICE (IIT-JEE)
(a) Springs are assumed to be massless. This is why the restoring elastic force in a spring is assumed
to be the same everywhere.
(b) For small stretch of compression, springs obey Hook's law, i.e., for a spring
Force stretch (or compression) i.e., | F | ky
i.e., restoring force is linear. This force in a spring is not constant and depends on stretch (or
compression) y. Greater the stretch (or compression) greater will be the force and vice-versa.
Force constant k
F 1/
F F y
Hyperbola
k=tan
y (Stretch or compression) length of spring
(A) (B)
(c) Force constant of composite springs : If a number of springs are connected to a body and we
want to reduce it to a single spring, following three cases of common interest are possible :
(A) (B)
(C)
(i) Spring in parallel : This situation is shown in fig. (A). If the force F pulls the mass m by y, the
stretch in each spring will be y, i.e.,
y1 = y2 = y ........... (1)
Now as for a spring F = ky and as k's are not equal F1 F2 but for equilibrium
F F1 F2 i.e., ky = k1y1 + k2y2 [as F = ky]
which in the light of eq. (1) reduces to
k = k1 + k2 .......... (A)
This is like capacitors in parallel or resistances in series.
(ii) Spring in series : This situation is shown in fig. (B), as springs are massless, so force in these
must by same, i.e., F1 F2 F ......... (2)
Now as F = ky and as k's are not equal, stretches will not be equal,
i.e., y1 y2 but y = y1 + y2
F F1 F2 F
or k k k as for F ky, y k
1 2
1 1 1
which in the light of eq. (1), reduces to ......... (B)
k k1 k 2
Amity Institute for Competitive Examinations Phones: 24336143, 24336144, 25573111/2/3/4, 95120-2431839/42
- 3.3-
, AICE (IIT-JEE) Newton’s Laws of Motion
(iii) Springs in series with a mass between them : As shown in fig. (C), if force F stretches a
spring by y, the other will be compressed by same amount so
y1 y2 y ......... (3)
Now as F = ky and k's are not equal, F1 F2 but
F F1 F2 i.e., ky k1 y1 k2 y2 [as F = ky]
which in the light of eq. (3) reduces to k k1 k2 ............ (C)
3. The normal force :
A book resting on a table feels the force of gravity pulling toward the Earth. But the book is not
accelerating so there must be an opposing force acting on the book. This force is caused by the table
and is known as the Normal force. The normal force arises from the repulsive forces between the
atoms at the surface of the books and the atoms at the surface of the table. The normal force is
perpendicular to the surface that causes it.
You can "see" the normal force in
FN
some situations. If you place a thin
piece of wood or plastic so that it is
supported by both ends (by book
perhaps) and place a small heavy
object in the center, the piece of wood
will bend.
Of course it wants to straighten out so it exerts an upward force on the object. This upward force is the
normal force, FN. You can feel the force yourself if you push down in the center of the piece of wood.
The harder you push the more the wood bends and the harder it pushes back.
The other way of thinking about the normal force is to imagine that the atoms inside of solid objects are
connected together by tight springs. You might think of the spring mattress on your bed. (Of course the
atoms are actually held together by molecular bonds but this is a rather good model for may solid
materials.) When you place an object on top of a table, (or on the ground for that matter), the table
deforms very slightly. This slight bend is usually not visible to the naked eye but can be seen with
sophisticated equipment.
It is important to remember that the normal force is always perpendicular to the surface.
If the surface is not horizontal than the normal force will FN
not point upwards but it is perpendicular to the surface.
The sketch below shows the normal force exerted on a
block by an incline.
For a book resting on a table not only does the table exert
a normal force on the book but the book also exerts a
normal force on the table.
Block can exert normal reaction perpendicular to its surface
as shown in the figures.
Wedge can exert normal reaction perpendicular to its surface.
Sphere can exert normal reaction perpendicular to surfaces. So the
normal reaction acting on the sphere always passes through the center of the sphere.
Amity Institute for Competitive Examinations Phones: 24336143, 24336144, 25573111/2/3/4, 95120-2431839/42
- 3.4-
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