forces and laws of motion

1. FORCES AND LAWS OF MOTION
For many centuries, the problem of motion and its causes had puzzled scientists
and philosophers. A ball on the ground, when given a small hit , does not move
forever. Such observations suggestthatrest is the “natural state” of an object. In
our everyday life weobservethat someeffort is required to put a stationary
object into motion or to stop a moving object. We ordinarily experience this as a
muscular effortand say that we must push or hit or pull.
BALANCED AND UNBALANCED FORCES
Consider and wooden block on a horizontaltable. Two strings X and Y are tied to
the oppositefaces of the block. If we apply force by pulling the string X, the block
begins to move to the right. Similarly, if we pull the string Y, the blocks moves to
the left. But, if the block is pulled fromboth the sides with equal forces, the block
will not move. Such forces are called balanced forces and do not change the state
of restof motion of an object.
Now, let us consider a situation in which two opposite forces of
different magnitudes pulls a block. In this case, the block begins to move in the
direction of grater force. Thus, the two forces are not balanced and the
unbalanced forceacts in the direction the block moves. This suggests that
unbalanced forceacting on object brings it in motion.
What happens when some children try to push a box on a rough floor??
If they push the box with a small force, the box does not movebecause of friction
acting in a direction opposite to the push. This friction forces arise between two
surfaces in contact. Itbalance the pushing forceand therefore the box does not
move. The children push the box harder but the box still does not move. This is
because the friction forcestill balances the pushing force. If the children push the
box harder still, the pushing forcebecomes bigger than the friction force. There is
a unbalanced force.

2. FIRSTLAW OF MOTION
An object remains in a state of rest or of uniform motion in a straight line unless
compelled to change that state by an applied force.
In other words, allobjects resista changein their state of motion. In a
qualititative way, the tendency of undisturbed objects to stay at rest or to keep
moving with the same velocity is called inertia. This is why, the firstlaw of motion
is also known as the law of inertia.
Certain experiences that we come across whiletravelling in a motorcar can be
explained on the basis of the law of inertia. We tend to remain at restwith
respect to the seat until the drives applies a breaking forceto stop the motor car.
With application of brakes, the car slows down butour body tends to continue in
the samestate of motion becauseof its inertia. A sudden application of brakes
may thus causeinjury to us by impact or collision with the panels in front. Safety
belts are worn to prevent such accidents. Safety belts exert a forceon our body to
make the forward motion slower.
INERTIA AND MASS
The resistance offered by an object to changeits state of motion. If it is at rest it
tends to remain at rest; If it is moving it tends to keep moving. This property of an
object is called its inertia.
Do all bodies have the same inertia??
We know that it is easier to push an empty box than a box full of books. Instead
of a five-rupees coin if we use a one- rupee coin , wefind that a lesser force is
required to performthe activity. A force that justenough to cause a small cart to
pick up a large velocity will produce a negligible change in the motion of a train.
This is because, in comparison to cart the train has a much lesser tendency to
change its state of motion. Accordingly, wesay that train has moreinertia than
the cart. Clearly, heavier or more massiveobjects offer larger inertia.
Quanitatively, the inertia of an object is measured by its mass.

3. Inertia is the natural tendency of an object to resist a change
in its state of motion or of rest. The mass of an object is a measureof its inertia.
SECOND LAWOF MOTION
The second law of motion states that the rate of change of momentum of an
object is proportionalto the applied unbalanced forcein the direction of force.
The second law of motion is often seen in action in our everyday life. While
catching a fast moving cricket ball, a fielder increases the time during which the
high velocity of the moving ball decreases to zero. Thus, the acceleration of the
ball is decreased and thereforethe impact of catching the fast moving ball. In
doing so, the fielder increases the time during which the high velocity of the
moving ball decreases to zero.
MATHEMATICAL FORMULATION OF SECOND LAWOF MOTION
Supposean objectof mass, m is moving along a straightline with an initial
velocity, u. Itis uniformly accelerated to velocity, v in time, t by application of a
constantforce, F throughoutthe time, t. The initial and finalmomentum of the
object will be, p1=mu and p2= mvrespectively.
The change in momentum ∞p1-p2
∞ mv- mu
∞ m × (v-u)
The rate of change of momentum ∞ m × (v-u)
t
Or, the applied force,
F ∞ m × ( v-u )
t
F ∞ km × ( v- u )
t
= kma
Here a Ι = ( v-u )/ t Ι is the acceleration, which is the rate of change of velocity. The
quantity, k is a constant of proportionality. The SI units of mass and acceleration
are kg and ms2

4. THIRD LAWOF MOTION
According to third law of motion to every action there is an equal and opposite
reaction.
Let consider two spring balance connected together. The fixed end of balance B is
attached with rigid support, like a wall. When a forceis applied through the free
end of spring balances show the same readings on their scales. Itmeans that the
forceexerted by spring balance A on balance B is equal but opposite in direction
to the forceexerted by balance B on balance A. The forcewhich balance A exerts
on balance B is called the action and forceof balance B on balance A is called
reaction.
CONSERVATIONOF MOMENTUM
Supposetwo object of masses mA and mB are travelling in the samedirection
along a straightline at different velocities uA and uB, respectively. And there are
no other external unbalanced forces acting on them. Let uA > UB and the two balls
collide with each other. During collision which last last for a time t, the ball A
exerts a force FAB on ball A.