Question

Two blocks of masses M and 2M are initially traveling at the same speed v but in the opposite directions. They collide and stick together. How much mechanical energy is lost to other forms of energy during the collision

Answer 1

Answer:

Explanation:

Given

Two masses M and 2 M with velocity v in opposite direction

After collision they stick together

Initial momentum

$P_i=Mv-2Mv$

final momentum

$P_f=3Mv'$

Conserving momentum

$P_i=P_f$

$-Mv=3Mv'$

$v'=\frac{v}{3}$

i.e. system moves towards the direction of 2M mass

Initial kinetic Energy $K_1=\frac{1}{2}Mv^2+\frac{1}{2}2Mv^2$

$K_1=\frac{3}{2}Mv^2$

Final Kinetic Energy $K_2=\frac{1}{2}\cdot (3M)\cdot (\frac{v}{3})^2=\frac{3}{18}Mv^2$

loss of Energy$=K_1-K_2$

$=\frac{3}{2}Mv^2-\frac{3}{18}Mv^2$

$=\frac{4}{3}Mv^2$