A railroad car with a mass of 1.98 ✕ 104 kg moving at 2.92 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 1.54 m/s.
(a) What is the speed of the three joined cars after the collision?
2.00 m/s
(b) What is the decrease in kinetic energy during the collision?
I have answer it a and I need help finding b
just add up the KE before and after the collision.
To find the decrease in kinetic energy during the collision, we need to calculate the initial kinetic energy and the final kinetic energy after the collision.
Let's start with the initial kinetic energy. The formula for kinetic energy is:
Kinetic energy = 0.5 * mass * velocity^2
For the two cars already joined together, each with the same mass, we can denote it as m1. The initial kinetic energy for these two cars would be:
KE_initial_1 = 0.5 * m1 * (1.54 m/s)^2
For the third car, we can denote its mass as m2. The initial kinetic energy for the third car would be:
KE_initial_2 = 0.5 * m2 * (2.92 m/s)^2
Now, to find the total initial kinetic energy, we add the kinetic energies of the two cars already joined together and the kinetic energy of the third car:
KE_initial_total = KE_initial_1 + KE_initial_2
Next, we need to find the final kinetic energy after the collision. Since the three cars are joined together and moving with the same velocity, we can denote it as v_final. The final kinetic energy for the three joined cars would be:
KE_final = 0.5 * (m1 + m1 + m2) * v_final^2
Now, to find the decrease in kinetic energy during the collision, we subtract the final kinetic energy from the initial kinetic energy:
Decrease in kinetic energy = KE_initial_total - KE_final
Substituting the values and solving the equation will give us the answer for part (b).