Final answer:
The final speed of the three coupled boxcars after collision is 1.67 m/s, calculated using the conservation of momentum. To find the fraction of the initial kinetic energy lost to thermal energy, calculate the initial and final kinetic energies and compute the difference.
Step-by-step explanation:
To solve this problem, we will apply the principle of conservation of momentum. Initially, two coupled boxcars are moving at a velocity of 2.5 m/s before they couple with the third stationary boxcar. Momentum before the collision equals momentum after the collision, assuming no external forces act on the system.
Let's denote the mass of each boxcar as 'm'. Since the two moving boxcars are identical, their combined mass will be '2m', and the velocity is v = 2.5 m/s. The third stationary boxcar has a mass 'm' and a velocity v = 0 m/s.
The total initial momentum (pi) therefore is:
pi = (2m × 2.5 m/s) + (m × 0 m/s) = 5m m/s.
The final momentum (pf) must be the same due to conservation of momentum, and the total mass after coupling is '3m'. If we denote the final velocity of all three coupled boxcars as Vf, we get:
pf = 3m × Vf. From the conservation of momentum:
5m m/s = 3m × Vf
Thus, the final speed Vf is 5m / 3m = 1.67 m/s.
To determine the fraction of the initial kinetic energy that is transformed into thermal energy, we calculate the initial and final kinetic energies. The initial kinetic energy (KEi) is given by KEi = 0.5 × 2m × (2.5 m/s)2, and the final kinetic energy (KEf) is KEf = 0.5 × 3m × (1.67 m/s)2.
After calculating these values, the fraction of initial kinetic energy lost to thermal energy is 1 - (KEf / KEi). This value will show us the energy dissipated during the collision.