subject: Oblique Collision [print this page] Collision between two bodies is defined as mutual interaction of the bodies for a very short interval of time because of which the energy and linear momentum of the colliding bodies change. In the language of physics collision is said to be occur if two bodies physically collide with each other and it may be possible that the path of one body will be affecting by the interaction of the other body. There are two types of collision one is head on collision that means the colliding bodies moving in the one dimension before and after collision and the other is oblique collision in which the two colliding bodies are moving in two dimension before and after the collision.
Types of Oblique Collision:
There are two type of oblique collision.
(i) Elastic oblique collision.
(ii) Inelastic oblique collision.
The collision in which both the kinetic energy and the linear momentum of the colliding bodies remains conserved are called the elastic oblique collision. The collisions in which linear momentum of the colliding bodies conserved but the kinetic energy is not conserved are called the inelastic oblique collision. Here we discuss the elastic oblique collision of two bodies.
Characteristics of the Elastic and Inelastic Oblique Collision:
Characteristics of the elastic oblique collision:
(i) The linear momentum is conserved.
(ii) The kinetic energy is conserved.
(iii) The mechanical energy is conserved.
(iv) The mechanical energy is not converted in any other form of the energy such as sound, heat, etc.
(v) Forces, which are involving in the collision, are conservative in nature.
Characteristics of the inelastic oblique collision:
(vi) The linear momentum is conserved.
(vii) The kinetic energy is not conserved.
(viii) The mechanical energy is conserved.
(ix) The part or whole of the mechanical energy is into any other form of the energy such as sound, heat, etc.
(x) Some or all forces, which are involving in the collision, are non-conservative in nature.
Consider two perfect elastic bodies A and B of mass M and m respectively, moving in the same straight line with velocities u1 and u2 in the X-axis direction. Here u1 > u2 so they collide with each other. After collision, the two bodies A and B move with velocities v1 and v2 along the directions q and f with the X-axis.
Because the collision is elastic, so kinetic energy must be conserved.
M u1^2 + m u2^2 = M v1^2 + m v2^2 .(1)
We know that the momentum is a vector quantity so resolve the momentum in X axis and Y axis components.
Apply the law of conservation of momentum in X-axis direction, we get
M u1 + m u2 = M v1 Cos + m v2 Cos (2)
Now apply the law of conservation of momentum in Y-axis direction, we get
0 = M v1 Sin + m v2 (-Sin)
0 = M v1 Sin - m v2 Sin .(3)
After solving the three equations, we get the values of v1 and v2.
