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CHAPTER3 Newton’s Law of Motion
Chapter Highlights
Force and Inertia, Newton’s First Law of Motion, Momentum, Newton’s Second Law of Motion, Impulse,
Newton’s Third Law of Motion, Equilibrium of Concurrent Forces, Static and Kinetic Friction, Laws of Friction,
Rolling Friction, Dynamics of Uniform Circular Motion.
FORCE Fundamental Forces
A pull or push which changes or tends to change the state All the forces observed in nature such as muscular
of rest or of uniform motion or direction of motion of any force, tension, reaction, friction, elastic, weight, electric,
object is called force. Force is the interaction between the magnetic, nuclear, etc., can be explained in terms of only
object and the source (providing the pull or push). It is a following four basic interactions:
vector quantity.
Gravitational Force
Effect of Resultant Force The force of interaction which exists between two particles
1. It may change only speed. of masses m1 and m2, due to their masses is called gravita-
2. It may change only direction of motion. tional force.
3. It may change both the speed and direction of motion. r
S T
4. It may change size and shape of a body. m1m2
F = −G r
Unit of Force r3
kg ⋅ m r = position vector of test particle T with respect to source
Newton and (MKS system) particle S and G = universal gravitational constant
s2
g ⋅ cm = 6.67 × 10–11 Nm2/kg2.
Dyne and (CGS system)
s2 \ F = mg
1 newton = 105 dyne
This is the force exerted by earth on any particle of mass
Kilogram Force (kgf) m near the earth surface. The value of g = 9.81 m/s2 ~ −
10 m/s2 ~ − 32 ft/s2. It is also called accelera-
− π 2 m/s2 ~
The force with which earth attracts a 1 kg body towards its tion due to gravity near the surface of earth.
centre is called kilogram force, thus
Electromagnetic Force
Force in Newton
kgf = Force exerted by one particle on the other because of the
g
electric charge on the particles is called electromagnetic
Dimensional Formula of Force force.
Following are the main characteristics of
[M L T–2 ] electromagnetic force
,3.2 Chapter 3
1. These can be attractive or repulsive. A table is placed on earth as shown in Fig. 3.1.
2. These are long range forces.
3. They depend on the nature of medium between the
charged particles. 2
4. All macroscopic forces (except gravitational) which 1
we experience as push or pull or by contact are 3 4
electromagnetic, i.e., tension in a rope, the force of Fig. 3.1
friction, normal reaction, muscular force, and force Here the table presses the earth so normal force exerted by
experienced by a deformed spring are electromagnetic four legs of table on earth is as shown in Fig. 3.2.
forces. These are manifestations of the electromagnetic
attractions and repulsions between atoms/molecules. N1 N2
N3 N4 Ground
Nuclear Force
Fig. 3.2
It is the strongest force. It keeps nucleons (neutrons and Now a boy pushes a block kept on a frictionless surface.
protons) together inside the nucleus in spite of large elec-
tric repulsion between protons. Radioactivity, fission, and
Block
fusion, etc., are a result of unbalancing of nuclear forces. It
acts within the nucleus that too up to a very small distance.
Weak Force Here, force exerted by boy on block is electromagnetic
It acts between any two elementary particles. Under its interaction which arises due to similar charges appearing
action, a neutron can change into a proton emitting an elec- on finger and contact surface of block, it is a normal force.
tron and a particle called antineutrino. The range of weak
force is very small, in fact much smaller than the size of a (by boy) N
Block
proton or a neutron.
It has been found that for two protons at a distance
of 1 fermi:
A block is kept on inclined surface. Component of its
FN:FEM:FW:FG::1:10–2:10–7:10–38 weight presses the surface perpendicularly due to which
contact force acts between surface and block.
Classification of Forces on the
Basis of Contact
Field Force
θ
Force which acts on an object at a distance by the interac-
tion of the object with the field produced by other object is
Normal force exerted by block on the surface of inclined
called field force. Examples
plane is shown in Fig. 3.3.
1. Gravitational force
2. Electromagnetic force NN
Contact Force θ
Forces which are transmitted between bodies by short- Fig. 3.3
range atomic molecular interactions are called contact Force acts perpendicular to the surface
forces. When two objects come in contact, they exert con-
tact forces on each other. Tension
Tension in a string is an electromagnetic force. It arises
Normal Force (N) when a string is pulled. If a massless string is not pulled,
It is the component of contact force perpendicular to the tension in it is zero. A string suspended by rigid support is
surface. It measures how strongly the surfaces in contact pulled by a force F as shown in Fig. 3.4, for calculating the
are pressed against each other. It is the electromagnetic tension at point A we draw FBD of marked portion of the
force. string; here string is massless.
, Newton’s Law of Motion 3.3
Steps for FBD
T4 Step 1: Identify the object or system and isolate it from
T4
other objects clearly specifying its boundary.
Step 2: First draw non-contact external force in the
T3 diagram. Generally, it is weight.
T3
Step 3: Draw contact forces which acts at the boundary of
the object or system. Contact forces are normal,
friction, tension and applied force.
T2
In FBD, internal forces are not drawn, only exter-
T2
nal are drawn.
F. B. D. of marked portion
T T1
A A
T1
SOLVED EXAMPLES
1. A block of mass m is kept on the ground as shown in
Fig. 3.6.
F F F
Fig. 3.4
⇒ T=F Fig. 3.6
String is considered to be made of a number of small seg-
ments which attracts each other due to electromagnetic (A) Draw FBD of block.
nature as shown in Fig. 3.5. The attraction force between two (B) Are forces acting on block action–reaction pair.
segments is equal and opposite due to Newton’s third law. (C) If answer is no, draw action reaction pair.
For calculating tension at any segment, we consider Solution:
two or more than two parts as a system. (A) FBD of block
T3
N (Normal)
T2
T2
T3 = F
T1
T1 mg (Field force)
(B) N and Mg are not action–reaction pair. Although
pair acts on different bodies, they are of same
F nature.
Fig. 3.5 (C) Pair of mg of block acts on earth in opposite
Here interactions between segments are considered as direction.
internal forces, so they are not shown in FBD.
Frictional Force
It is the component of contact force tangential to the
surface. It opposes the relative motion (or attempted rela- mg Earth
tive motion) of the two surfaces in contact.
FREE BODY DIAGRAM Pair of N acts on surface
A FBD consists of a diagrammatic representation of a N
single body or a subsystem of bodies isolated from its
surroundings showing all the forces acting on it.
, 3.4 Chapter 3
2. Two spheres A and B are placed between two vertical If the net force acting on a body is zero, it is possible
walls as shown in Fig. 3.7. Draw the free body dia- to find a set of reference frames in which that body has no
grams of both the spheres. acceleration.
Newton’s first law is sometimes called the law of
inertia and the reference frames that it defines are called
B inertial reference frames.
A Newton’s law as written by Newton in Latin from an
1803 translation:
Fig. 3.7 ‘Everybody preserves in its state of rest, or of
Solution: uniform motion in a right line, unless it is compelled
to change that state by forces impressed thereon’.
FBD of sphere A:
N2
Examples of this Law
NAB (Exerted by B) 1. A bullet fired on a glass window makes a clean hole
N1 through it while a stone breaks the whole of it. The
mAg speed of bullet is very high. Due to its large inertia of
motion, it cuts a clean hole through the glass. When a
FBD of sphere B:
stone is thrown, it inertia is much lower so it cannot cut
NBA through the glass.
N3
2. A passenger sitting in a bus gets a jerk when the bus
mB g starts or stops suddenly.
(Exerted by A)
Notes: Here NAB and NBA are the action–reaction pair
Second Law of Motion
(Newton’s third law). The rate of change of momentum of a body is proportional
to the applied force and takes place in the direction in
3. Three triangular blocks A, B and C of equal masses m
which the force acts.
are arranged as shown in Fig. 3.8. Draw FBD of blocks
Newton’s law as written by Newton in Latin from an
A, B and C. Indicate action–reaction pair between A, B
1803 translation:
and B, C.
F F ‘The alteration of motion is ever propor-
A C
B tional to the motive force impressed; and is made in
the direction of the right line in which that force is
Fig. 3.8 impressed.’
Solution: Mathematically,
RA RC dp
RB
F=
NBA dt
F NBC
A C F
B Or F = ma
NAB NCB
mg mg mg
where p = mv , p = Linear momentum.
In case of two particles having linear momentum
P1 and P 2 and moving towards each other under mutual
NEWTON’S LAWS OF MOTION forces, from Newton’s second law,
First Law of Motion d
dt
( )
p1 + p 2 = F = 0
Each body continues to be in its state of rest or of uniform
d p1 d p 2
motion in a straight line unless compelled by some external + =0
force to act otherwise. dt dt
Newton’s first law is really a statement about refer- F1 + F 2 = 0
ence frames, in that it defines the types of reference frames
in which the laws of Newtonian mechanics hold. From this F 2 = − F1
point of view, the first law is expressed as: which is Newton’s third law.
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