Question

Two coupled box cars are rolling at 2.5 m/s when they collide with and couple to a third stationary box car. what is the final speed of the three box cars? what is the fraction of the cars initial kinetic energy is transformed into thermal energy?

Answer 1

To determine the final speed of three coupled box cars, the conservation of momentum is applied. The kinetic energy before and after the collision is compared to calculate the fraction converted to thermal energy.

Step-by-step explanation:

The scenario involves two coupled box cars colliding with a third stationary box car, which comes under the concept of conservation of momentum in Physics. To calculate the final speed of the three box cars, we apply the principle that the total momentum before the collision is equal to the total momentum after the collision. If we assume the two moving box cars have a combined mass of m1 and the stationary box car has a mass of m2, the final combined speed v can be found using the equation m1 * initial speed = (m1 + m2) * v. Kinetic energy before the collision can be compared with the kinetic energy after the collision to find the fraction transformed into thermal energy.

To find this fraction, we use the equation for kinetic energy, KE = (1/2) * m * v^2. The initial kinetic energy (KE_initial) of the moving box cars can be calculated using their combined mass and initial speed. After the collision, the total kinetic energy (KE_final) of all three coupled cars can be calculated using the total mass and the final speed. The difference between KE_initial and KE_final gives us the kinetic energy converted to other forms, such as thermal energy.