Question
Discuss two-dimensional elastic collision.
Solution
Consider two bodies A and B of masses m1 and m2 moving along the same straight line along X-axis with velocities and u2 respectively as shown in the figure.
Let, after collision two bodies move with velocities v1 and v2 making angles θ1 and θ2 with initial direction of motion i.e. with X-axis.
Since collision is an elastic collision, therefore, their momentum and kinetic energy remain conserved.
Momentum is a vector quantity, therefore the momentum along X-axes as well as along Y-axes will conserve individually.
By conservation of momentum along X-axis,
...(1)
By conservation of momentum along Y-axis,
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...(2)
By conservation of kinetic energy,
...(3)
Here, in two-dimension collision, there are four variables v1 v2, θ1 and θ2 to solve, but we have only three equations from this analytical study.
Hence, we cannot find the values of all the variables by analytical method.
To solve the problem, one variable is measured experimentally and the remaining three are calculated from the above three equations.
Let, after collision two bodies move with velocities v1 and v2 making angles θ1 and θ2 with initial direction of motion i.e. with X-axis.
Since collision is an elastic collision, therefore, their momentum and kinetic energy remain conserved.
Momentum is a vector quantity, therefore the momentum along X-axes as well as along Y-axes will conserve individually.
By conservation of momentum along X-axis,
...(1)By conservation of momentum along Y-axis,
...(2)By conservation of kinetic energy,
...(3)Here, in two-dimension collision, there are four variables v1 v2, θ1 and θ2 to solve, but we have only three equations from this analytical study.
Hence, we cannot find the values of all the variables by analytical method.
To solve the problem, one variable is measured experimentally and the remaining three are calculated from the above three equations.
