Question

Which statement is true for an elastic collision in two dimensions?

Answer 1

an elastic collision occurred in two dimensions?

Answer 2

Statement plz!!!!!!

Answer 3

Anyway in any eleastic collision total kinetic energy before collision will b eaqual to the total kinetic energy after collision

Answer 4

In general for elastic collisions, the subsequent statements are checked:
1) total kinetic energy is conserved;
2) total momentum is conserved.

So, let's consider, for example the subsequent collision between two particles with the same mass, say M, and one particle is moving with velocity V, and the other one is at rest:

Answer 5

after collision, we have velocity of particle 1, is u_1, and velocity of particle 2 is u_2. Whereas \theta is the angle between suc velocities.

Answer 6

Now, using 1) we can write:
\[u_1^2 + u_2^2 = {v^2}\]
whereas using 2), we can write:
\[{{\mathbf{u}}_{\mathbf{1}}} + {{\mathbf{u}}_{\mathbf{2}}} = {\mathbf{v}}\]
please note that, the last equation, is a vector equation

Answer 7

making the square of both sides of the last equation, we get:
\[u_1^2 + u_2^2 + 2{{\mathbf{u}}_{\mathbf{1}}} \cdot {{\mathbf{u}}_{\mathbf{2}}} = {v^2}\]
and substituting the conservation of kinetic energy, we get:
\[{{\mathbf{u}}_{\mathbf{1}}} \cdot {{\mathbf{u}}_{\mathbf{2}}} = {\mathbf{0}}\]
in other words, the angle between the velocities u_1 and u_2 is always 90 degrees