A 3kg mass moving initially to the right along the x axis with a speed of 8m/s makes a perfectly inelastic collision with a 5kg mass initially at rest at the origin.what fraction of the initial kinetic energy of the system is lost in the collision.what formula must i use.

The masses stick together so have the sum of masses and the same velocity after collision:

3*8 = 8 * v
v = 3 m/s after

Ke before = (1/2)(3)(64)

Ke after = (1/2)(8)(9)

answer = ( Ke before - Ke after)/Ke before

To determine the fraction of the initial kinetic energy lost in a perfectly inelastic collision, you need to use the conservation of momentum and the conservation of kinetic energy principles.

First, let's calculate the initial kinetic energy of the system before the collision. The kinetic energy (KE) of an object is given by the formula:

KE = (1/2) * mass * velocity^2

For the 3kg mass moving at 8m/s, the initial kinetic energy will be:

KE1 = (1/2) * 3kg * (8m/s)^2 = 96J

For the 5kg mass initially at rest, the initial kinetic energy will be:

KE2 = (1/2) * 5kg * (0m/s)^2 = 0J

The initial total kinetic energy of the system is:

KE_initial = KE1 + KE2 = 96J + 0J = 96J

After the perfectly inelastic collision, the two masses stick together and move with a combined velocity. Let's denote the combined mass as M and the final velocity as V.

Using the conservation of momentum principle, we have:

(initial momentum) = (final momentum)
(mass1 * velocity1) + (mass2 * velocity2) = (combined mass * final velocity)

Substituting the given values:

(3kg * 8m/s) + (5kg * 0m/s) = (8kg * V)

24kg*m/s = 8kg * V
V = 24kg*m/s / 8kg = 3m/s

Now, we can calculate the final kinetic energy of the system after the collision using the formula:

KE_final = (1/2) * combined mass * final velocity^2

KE_final = (1/2) * 8kg * (3m/s)^2 = 36J

The fraction of kinetic energy lost during the collision is given by:

Fraction of KE lost = (KE_initial - KE_final) / KE_initial

Fraction of KE lost = (96J - 36J) / 96J = 60J / 96J = 0.625

Therefore, the fraction of the initial kinetic energy lost in the collision is 0.625, or 62.5%.