Page 107 - Class-11-Physics-Part-1_Neat

LAWS OF MOTION 93

The property of inertia contained in the First It relates the net external force to the
law is evident in many situations. Suppose we acceleration of the body.
are standing in a stationary bus and the driver Momentum
starts the bus suddenly. We get thrown Momentum of a body is defined to be the product
backward with a jerk. Why ? Our feet are in touch of its mass m and velocity v, and is denoted
with the floor. If there were no friction, we would by p:
remain where we were, while the floor of the bus p = m v (5.1)
would simply slip forward under our feet and the
Momentum is clearly a vector quantity. The
back of the bus would hit us. However,
following common experiences indicate the
fortunately, there is some friction between the
importance of this quantity for considering the
feet and the floor. If the start is not too sudden,
i.e. if the acceleration is moderate, the frictional effect of force on motion.
force would be enough to accelerate our feet • Suppose a light-weight vehicle (say a small
along with the bus. But our body is not strictly car) and a heavy weight vehicle (say a loaded
a rigid body. It is deformable, i.e. it allows some truck) are parked on a horizontal road. We all
relative displacement between different parts. know that a much greater force is needed to
What this means is that while our feet go with push the truck than the car to bring them to
the same speed in same time. Similarly, a
the bus, the rest of the body remains where it is
greater opposing force is needed to stop a
due to inertia. Relative to the bus, therefore, we
heavy body than a light body in the same time,
are thrown backward. As soon as that happens,
if they are moving with the same speed.
however, the muscular forces on the rest of the
body (by the feet) come into play to move the body • If two stones, one light and the other heavy,
along with the bus. A similar thing happens are dropped from the top of a building, a
when the bus suddenly stops. Our feet stop due person on the ground will find it easier to catch
to the friction which does not allow relative the light stone than the heavy stone. The
motion between the feet and the floor of the bus. mass of a body is thus an important
But the rest of the body continues to move parameter that determines the effect of force
forward due to inertia. We are thrown forward. on its motion.
The restoring muscular forces again come into • Speed is another important parameter to
play and bring the body to rest. consider. A bullet fired by a gun can easily
pierce human tissue before it stops, resulting
Example 5.1 An astronaut accidentally in casualty. The same bullet fired with
t
gets separated out of his small spaceship moderate speed will not cause much damage.
accelerating in inter stellar space at a Thus for a given mass, the greater the speed,
constant rate of 100 m s . What is the the greater is the opposing force needed to stop
–2
acceleration of the astronaut the instant after the body in a certain time. Taken together,
he is outside the spaceship ? (Assume that the product of mass and velocity, that is
there are no nearby stars to exert momentum, is evidently a relevant variable
gravitational force on him.) of motion. The greater the change in the
momentum in a given time, the greater is the
Answer Since there are no nearby stars to exert force that needs to be applied.
gravitational force on him and the small • A seasoned cricketer catches a cricket ball
spaceship exerts negligible gravitational coming in with great speed far more easily
attraction on him, the net force acting on the than a novice, who can hurt his hands in the
astronaut, once he is out of the spaceship, is act. One reason is that the cricketer allows a
zero. By the first law of motion the acceleration longer time for his hands to stop the ball. As
of the astronaut is zero. t
you may have noticed, he draws in the hands
5.5 NEWTON’S SECOND LAW OF MOTION backward in the act of catching the ball (Fig.
The first law refers to the simple case when the 5.3). The novice, on the other hand, keeps
net external force on a body is zero. The second his hands fixed and tries to catch the ball
law of motion refers to the general situation when almost instantly. He needs to provide a much
there is a net external force acting on the body. greater force to stop the ball instantly, and

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