A railroad car with a mass of 1.81 104 kg moving at 3.04 m/s joins with two railroad cars already joined together, each with the same mass as the single car and initially moving in the same direction at 1.32 m/s.

What is the decrease in kinetic energy during the collision?

I was going to answer this one, but drwls answered it in the first post in related questions.

To calculate the decrease in kinetic energy during the collision, we need to find the initial and final kinetic energies of the system.

The initial kinetic energy of the system is the sum of the kinetic energies of the three railroad cars before the collision.

The kinetic energy of an object can be calculated using the formula:

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

Therefore, the initial kinetic energy of the three cars is:

KE_initial = (1/2) * mass_car1 * velocity_car1^2 + (1/2) * mass_car2 * velocity_car2^2 + (1/2) * mass_car3 * velocity_car3^2

Given:
mass_car1 = mass_car2 = mass_car3 = 1.81 * 10^4 kg
velocity_car1 = 3.04 m/s
velocity_car2 = velocity_car3 = 1.32 m/s

Substituting the values into the formula, we get:

KE_initial = (1/2) * 1.81 * 10^4 kg * (3.04 m/s)^2 + (1/2) * 1.81 * 10^4 kg * (1.32 m/s)^2 + (1/2) * 1.81 * 10^4 kg * (1.32 m/s)^2

Simplifying the equation gives us:

KE_initial = (1/2) * 1.81 * 10^4 kg * 9.2416 m^2/s^2 + (1/2) * 1.81 * 10^4 kg * 1.7424 m^2/s^2 + (1/2) * 1.81 * 10^4 kg * 1.7424 m^2/s^2

KE_initial = 1.8029984 * 10^8 J

Now, let's find the final kinetic energy of the system. Since the cars are joining together, their velocities will become the same after the collision. Let's say the final velocity of the combined cars is vf.

The mass of the combined cars is 1 car + 1 car + 1 car = 3 cars = 3 * 1.81 * 10^4 kg.

Using the formula for kinetic energy, the final kinetic energy is given by:

KE_final = (1/2) * mass_combined * vf^2
KE_final = (1/2) * 3 * 1.81 * 10^4 kg * vf^2

Now, to find the decrease in kinetic energy, we calculate the difference between the initial and final kinetic energies:

Decrease in kinetic energy = KE_initial - KE_final

Substitute the values and solve the equation to find the decrease in kinetic energy.