science

What is science?

Everyone around us has some idea about
nature and their relation to it. Science is fact based ideas come together. You observe nature try to understant your observations and predict new things but those must be checked by experiments and critical thinking This way we build up an understanding for nature which we address as science. There is no place of unchecked ideas in science. we do research that is we search same things again and again to be sure it is correct. If experiment shows an idea wrong we may completely discard it.

Now a physics question

Lets solve a standard collision problem. a particle of mass m collide and deflect with some angle from a no then particle of same mass. Let's find a relation between velocity of the first particle after the collision with the velocity of 1st particle before the collision and the deflection angle.

Note that if there was no deflection and the scattering was head-on than particle 1 stops and particle 2 would go with that speed. Now, for the above case, we have conservation of momentum (handy component) and

$\begin{array}{}m{v}_1=m{v}_2·\; <!--\; middle\; dot\; -->\cos \mathrm{\alpha \; <!--\; greek\; small\; letter\; alpha\; -->}+m{v}_3\cos \mathrm{\beta \; <!--\; greek\; small\; letter\; beta\; -->}\\ 0=m{v}_2\sin \mathrm{\alpha \; <!--\; greek\; small\; letter\; alpha\; -->}+m{v}_3\sin \mathrm{\beta \; <!--\; greek\; small\; letter\; beta\; -->}\\ \frac{1}{2}m{v}_1^2=\frac{1}{2}m{v}_2^2+\frac{1}{2}m{v}_3^2\end{array}$

Conservation of energy. we can get rid of mass since its same in every term and rewrite

where we use the trigonometric relation to simplify

$\begin{array}{}{\left(v_1-v_2\cos \mathrm{\alpha \; <!--\; greek\; small\; letter\; alpha\; -->}\right)}^2=v_3^2{\cos }^2\mathrm{\beta \; <!--\; greek\; small\; letter\; beta\; -->}\\ v_2^2{\sin }^2\mathrm{\alpha \; <!--\; greek\; small\; letter\; alpha\; -->}=v_3^2·\; <!--\; middle\; dot\; -->{\sin }^2\mathrm{\beta \; <!--\; greek\; small\; letter\; beta\; -->}\\ v_1^2-v_2^2=v_3^2\end{array}$

${\cos }^2\mathrm{\alpha \; <!--\; greek\; small\; letter\; alpha\; -->}+{\sin }^2\mathrm{\alpha \; <!--\; greek\; small\; letter\; alpha\; -->}=1$

Summing up first 2 eqn's and use 3rd eq in it we have

$\begin{array}{}{v}_1^2-2v_1{v}_2\cos \mathrm{\alpha \; <!--\; greek\; small\; letter\; alpha\; -->}+v_2^2=y^2=v_1^2-v_2^2\\ v_2=v_1\cos \mathrm{\alpha \; <!--\; greek\; small\; letter\; alpha\; -->}\end{array}$

Therefore velocity of the 1st object after hitting to the second object can be found initial velocity and the deflection angle. A simple consequence of this relation is the angle between 1st and 2nd object after collision is always 90 degree. so if deflection angle 30 degrees than 2nd object go down with 60' degrees.