LINEAR
MOMENTUM
To understand this term, let us review some common
observations :
(i) In the game of table tennis, if the ball hits a player, he
is not hurt . But when a cricket ball moving at the same speed as the table
tennis ball hits a spectator, he is hurt. This is because cricket ball is much
heavier than the table tennis ball.
(ii) A truck moving at speeds as low as 5 metre per second may
kill a person coming its way. This is again because of heavy mass of the truck.
(iii) A bullet of small mass fired from a gun may kill a
person. This is because of large velocity of the bullet.
We observe that impact of motion produced by objects depends
on their mass and velocity. Therefore, there must be some quantity of
importance that combines mass of a body and velocity of the body. Newton
identified this quantity and named it as linear momentum of the body. We define
:
Linear momentum of a body as the product of mass of the body
and velocity of the body.
If
m = mass of a body,
V = velocity of the body,
And,
p = linear momentum of the body, then
linear momentum = mass x velocity
p = mv
i.e., linear momentum of a body at rest is zero or a body at
rest possesses no linear momentum. Linear momentum is a vector quantity, possessing
both, the magnitude as well as direction. The direction momentum is the same as
the direction of velocity.
As SI
unit of mass is kilogram and SI unit of velocity is metre/second ; therefore,
SI unit of linear momentum is kilogram metre per second, which is written as kg
m/s or kg ms-1,
We find
that when mass of a body is made twice, keeping its velocity unchanged, the
linear momentum of the body becomes twice. Similarly, when velocity of a body
of given mass is made twice, its linear momentum becomes twice again. If both,
mass and velocity were made tiwice. the linear momentum would become four
times.
From
Newton's first law of motion, we have learnt that a force is required to change
the velocity of a body. When velocity of the body changes, its linear momentum
also changes. Therefore, an external force is required to change the linear
momentum of the body.
NEWTON'S SECOND LAW OF MOTION
To understand Newton's second law of motion,
let us imagine a situation in which a car with a dead battery is to be started.
We know that a speed of 1 m/s given to the car may be sufficient to start its
engine. Now, if one or two persons give a sudden push to the car, it hardly
starts. But when the car is pushed continuously for some time over a straight
road, it might start. This is because speed of the car increases gradually from
zero to 1 m/s, over this time.
From this
situation, we learn that change in linear momentum of the car is brought about
by suitable magnitude of force, and the suitable time during which the force is
exerted. Newton concluded from his studies that force necessary to change
linear momentum of a body would depend upon the time rate of change of linear
momentum of the body. This led to second law of motion.
According to Newton's second law of motion, the rate of change
of linear momentum of a body is directly proportional to the external force
applied on the body, and this change takes place always in the direction of the
applied force.
Now, the
rate of change of linear momentum of a body can be obtained by dividing change
in linear momentum of the body by the time taken’ for this change. Thus,
according to Newton's second law of motion,
change in
linear momentum/time takenµForce
applied
It means
that when a bigger force is applied on a body, its linear momentum changes at a
faster rate (taking less time) and vice-versa. Further, the momentum will
change always in the direction of the applied force.
SOME APPLICATIONS OF NEWTON'S SECOND LAW OF MOTION
Some of
our day-to-day observations can be explained in terms of Newton's second law of
motion. As
F = ma =m(v – u)/t
therefore,
force F can be reduced by incre: ing time taken t for the change in linear
momentum of the body. For example :
1. Catching a cricket ball
To catch
a fast cricket ball, a player pulls his hands backwards to prevent injury to
his hands. By doing so, the player increases the time during which high
velocity of the cricket ball reduces to zero. Thus, the acceleration of the
ball a = (v - u)/t is decreased, and therefore, the impact of catching the fast
ball (i.e., F = ma) is reduced, i.e., the player has to apply a smaller force
against the ball in order to stop it. The ball, in turn, exerts a smaller force
on his hands and the hands are not injured.
If the
ball were stopped suddenly, the high velocity of the ball would be reduced to
zero in a very short interval of time, t. Therefore, rate of change of linear
momentum of the ball would be large, and therefore, a large force would have to
be applied for holding the catch. The hands of the player would be hurt.
2. High jump
In the athletic event 'High Jump’, the athletes are made to
fall either on a cushioned bed or on a sa bed. This is done to avoid injury to
the athlete. Falling on a cushioned bed or on a sand bed will increase thu time
during which high velocity of the athlete would be reduced to zero. This would
decrease the rate of change of momentum of the athlete and hence the force on
the athlete. The injury to the athlete is thus
avoided.
3. Use of seat belts in cars
All the cars, these days are provided with seat belts for the
passengers, which are rightly called safety belts. The purpose of seat belts is
to prevent injuries to the passengers in case of an accident or in case of
sudden application of brakes. In both the cases, the large momentum of the car
reduces to zero in a very shor interval of time resulting in the development of
a large force causing injuries. The stretchable safety belts worn by the
passengers of the car exert a force on their body and make the forward motion
slower. The time taken by the passengers to fall forward increases. Therefore,
rate of change of momentum of passengers is reduced. Hence, the stopping force
acting on the passengers is reduced. They may not get injuries at all or they
may get away with minor injuries.
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