Question

A $1kg$ ball moving at $12m/sec$. collides head on with $2kg$. ball moving in the opposite direction at $14m/s$. If the coefficient of restitution is $2/3$, then how much energy is lost in collision?

• A. $240J$
• B. $120J$
• C. $360J$
• D. $400J$

Answer 1

The correct option is A $240J$

Let initial velocities of $1kg$ ball and $2kg$ ball be $u_1,u_2$ respectively and final velocities be $v_1,v_2$ respectively .

By conservation of linear momentum ,

$1\times u_1+2\times u_2=1\times v_1+2\times v_2$

$u_1=12m/s,u_2=-14m/s$

$v_1+2v_2=-16$

Coefficient of restitution e=$\frac{2}{3}$

$e=\frac{v_2-v_1}{u_2-u_1}=\frac{2}{3}$

$3v_1-3v_2=52$

Solving these equations,

$v_1=\frac{56}{9},v_2=-\frac{100}{9}$

Loss of kinetic energy

$\delta K=\frac{1}{2}[u_1^2+2u_2^2-v_1^2-2v_2^2]=125J$

Option B is closest.