Question

A railroad car collides with and sticks to an identical railroad car that is initially at rest. After the collision, the total kinetic energy of the two cars is:__________
A) the same as before.
B) half as much as before.
C) one third as much as before.
D) one fourth as much as before.
E) twice as much as before.Background image

Answer 1

Answer:

Answer B:  "half as much as before"

Explanation:

Consider the conservation of momentum to start with in order to find the velocity of the conglomerate of the two cars after collision:

$p_i=m\,v_i+m\,(0)=m\,v_i\\p_f=(m+m)\,v_f=2\,m\,v_f\\p_i=p_f\\m\,v_i=2\,m\,v_f\\v_f=\frac{v_i}{2}$

With this important result, we can nor compare the initial kinetic energy to the final one:

$K_i=\frac{1}{2} m\,v_i^2+\frac{1}{2} m\,0^2=\frac{1}{2} m\,v_i^2\\K_f=\frac{1}{2} (m+m)\,v_f^2=\frac{1}{2} \,2\,m\,v_f^2=m\,(\frac{v_i}{2}) ^2=\frac{1}{4} \,m\,v_i^2$

Therefore, the final kinetic energy is one half of the initial kinetic energy.