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What Is Collision ?, Classification Of Collisions, Important Topics For JEE 2024
What Is Collision : Collision, in physics, the sudden, forceful coming together in direct contact of two bodies, such as, for example, two billiard balls, a golf club and a ball, a hammer and a nail head, two railroad cars when being coupled together, or a falling object and a floor
Shrivastav 22 Jan, 2024
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What Is Collision :
Collision is an isolated event in which a strong force acts
between two or more bodies for a short time, which results
in change in their velocities. In a collision, a relatively large
force acts on each colliding particle for a relatively short
time. The basic idea of a ‘collision’ is that the motion of the
colliding particles (or of at least one of them) changes rather
abruptly and that we can make a relatively clean separation of
times that are ‘before the collision’ and those that are ‘after
the collision’.
(i)
It is not necessary that a physical contact takes place in
a collision, e.g., when an alpha particle (He) ‘collides’ with the nucleus of gold (‘Au’), the force acting between
them being repulsive—the particles may not touch, even
then it may be called a ‘collision’.
(ii)
When a space probe approaches a large planet, swings
around it, and then continues its course with increased
speed (a slingshot encounter), that too is a collision. The
probe and planet do not actually “touch”, but a collision
does not require contact, and a collision force does not
have to be a force of contact; it can just as easily be a
gravitational force, as in this case.
The collision is, in fact, a redistribution of total momentum
of the particles. Thus, law of conservation of linear momentum
is indispensable in dealing with the phenomenon of collision
between particles.
The collision is, in fact, a redistribution of total momentum
of the particles. Thus, law of conservation of linear momentum
is indispensable in dealing with the phenomenon of collision
between particles.
Important Line of Impact :
The line passing through the common normal to the surfaces
in contact during the impact is called line of impact. The force
during collision acts along this line on both the bodies.
Direction of line of impact can be determined by.
(i)
geometry of colliding objects such as spheres, discs, ‘wedge, etc.
(ii)
direction of change of momentum.
If one particle is stationary before collision, then the line
of impact will be along its motion after collision.
Classification of Collisions :
(a)On the Basis of Line of Impact
Head-on collision
:
The velocities of the particles are along the same line before and after the collision.
Oblique collision:
The velocities of the particles are along different lines before and after the collision.
(b)On the Basis of Energy
Elastic collision
: In an elastic collision, the particles
regain their shape and size completely after collision.
That is, no fraction of mechanical energy remains
stored as deformation potential energy in the bodies.
Thus, kinetic energy of a system after collision is
equal to kinetic energy of a system before collision.
Thus, in addition to the linear momentum, kinetic
energy also remains conserved before and after
collision
Inelastic collision
: In an inelastic collision, the
particles do not regain their shape and size completely
after collision. Some fraction of mechanical energy
is retained by the colliding particles in the form
of deformation potential energy. Thus, the kinetic
energy of the particles no longer remains conserved.
However, in the absence of external forces, law of
conservation of linear momentum still holds good.
Coefficient of Restitution (e) :
The coefficient of restitution is defined as the ratio of the
impulses of recovery and deformation of either body.
The most general expression for coefficient of restitution is
Two smooth balls
A
and
B
approach each other such that their centres are moving along the line
CD
in the absence of external impulsive force. Let the velocities of
A
and
B
just before collision be
u
1
and
u
2
. Respectively, and the velocities of a and B just after collision be
v
1
and
v
2
, respectively.
Since, momentum is conserved for the system.
∴
F
ext
= 0
Note
:
e is independent of shape and mass of the object but
depends on the material.
The coefficient of restitution is constant for two particular
objects.
(a)
Fore = 1
= Impulse of reformation = Impulse of deformation
⇒
Velocity of separation = Velocity of approach
⇒
Kinetic energy is conserved.
= Elastic collision
(b)
Fore = 0
= Impulse of reformation = 0
= Velocity of separation = 0
= Kinetic energy is not conserved
= Perfectly inelastic collision
(c)
For 0 < e < 1
= Impulse of reformation < Impulse of deformation
= Velocity of separation < Velocity of approach
= Kinetic energy is not conserved
= Inelastic collision
Head on Elastic Collision :
Let the two balls of masses
m
1
and
m
2
collide each other elastically with velocities
v
1
and
v
2
in the
directions shown in Fig. Their velocities become
v
1
′ and
v
2
′ after the collision along the
same line. Applying conservation of linear momentum,
we get
In an elastic collision kinetic energy before and after collision is also conserved. Hence,
Solving Eqs. (iii) and (iv) for
and
we get
and
Head on Inelastic Collision :
Head on Inelastic Collision :
As we have discussed earlier also, in an inelastic collision, the particles do not regain their shape and
size completely after collision. Some fraction of mechanical energy is retained by the colliding
particles in the form of deformation potential energy. Thus, the kinetic energy of the particles no
longer remains conserved. However, in the absence of external forces, law of conservation of linear
momentum still holds good.
Suppose the veloci
ties of two particles of mass
m
1
and
m
2
before collision be
v
1
and
v
2
in the directions shown in
figure. Let
and
be their velocities after collision. The law of conservation of linear momentum gives.
m
1
v
1
+
m
2
v
2
=
m
1
v
1
+
m
2
v
2
=
Collision Examples
1.
If a ball strikes with a velocity
u
1
at the wall which itself is approaching it with a velocity
u
2
, then find the velocity of the ball after collision with the wall.
Sol.
As the wall is heavy so after collision it will continue to move with the same velocity
u
2
. Relative velocity of separation is equal to relative velocity of approach. Hence,
In case of perfectly elastic collision,
e
= 1.
– ive sign indicates backward direction.
2.
A ball of mass m hits the floor with velocity do making an angle of incidence α with the normal.
The coefficient of restitution is e. Find the speed of the reflected ball and the angle of reflection of the ball.
Sol.
The component of velocity
v
0
along common tangent direction
v
0
sin α will remain unchanged. Let
v
be the component along common norma, direction after collision. Applying relative speed of separation = e × (relative speed of approach along common normal direction, we get)
v
=
ev
0
cos
α
Thus, after collision, components of velocity
v
’ are
v
0
sin α and
ev
0
cos α
∴
and
Note
:
For elastic collision,
e
= 1
∴
v
’
v
0
and
β
=
α
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