Car a hits car b (initially at rest and of equal mass) frombehind while going 35 m/s. immediately after the collision, car bmoves forward at 25 m/s and car a is at rest. what fraction of theinitial kinetic energy is lost in the collision?
my approach:
how exactly do you approach this question? at first, i thoughtusing the the formula σkei = σkef. then, to find the fraction just divide the former from the latter. but is it that cut and dry?
before collision:
via= 35 m/s
vib = 0 m/s
vfa = 0 m/s
vfb =25 m/s
m1 = m2

The fraction of kinetic energy lost in the collision in term of the initial energy is 0.49.

Explanation:

As the final and initial velocities are known it is possible then the kinetic energy is possible to calculate for each instant.

By definition, the kinetic energy is:

k = 0.5*mV^2

Expressing the initial and final kinetic energy for cars A and B:

Since the masses are equals:

For the known velocities, the kinetics energies result:

The lost energy in the collision is the difference between the initial and final kinectic energies:

Finally the relation between the lost and the initial kinetic energy: