Final answer:
The final velocity of the cars is approximately 23.66 m/s. The collision results in a loss of kinetic energy of approximately 386516 J. The total kinetic energy before the collision is 159125 J, and the total kinetic energy after the collision is 545641.45 J.
Step-by-step explanation:
When two objects collide and stick together, we can use the principles of conservation of momentum and conservation of kinetic energy to solve the problem.
a) Calculation of Final Velocity:
To calculate the final velocity, we need to find the total momentum before the collision and divide it by the total mass of the system.
Initial momentum of car A = 1200 kg * (-8 m/s) = -9600 kg·m/s
Initial momentum of car B = 850 kg * (17 m/s) = 14450 kg·m/s
Total initial momentum = -9600 kg·m/s + 14450 kg·m/s = 48450 kg·m/s
Mass of the system = 1200 kg + 850 kg = 2050 kg
Final velocity = Total initial momentum / Mass of the system = 48450 kg·m/s / 2050 kg ≈ 23.66 m/s
b) Calculation of Kinetic Energy Lost:
To find the kinetic energy lost in the collision, we can calculate the initial and final kinetic energies and subtract the final kinetic energy from the initial kinetic energy.
Initial kinetic energy of car A = 0.5 * 1200 kg * (8 m/s)^2 = 38400 J
Initial kinetic energy of car B = 0.5 * 850 kg * (17 m/s)^2 = 120725 J
Total initial kinetic energy = 38400 J + 120725 J = 159125 J
Final kinetic energy = 0.5 * 2050 kg * (23.66 m/s)^2 = 545641.45 J
Kinetic energy lost = Total initial kinetic energy - Final kinetic energy = 159125 J - 545641.45 J ≈ -386516 J
Since the kinetic energy lost is negative, it means that energy has been converted to other forms such as deformation of the cars.
Total Kinetic Energy:
Total kinetic energy before the collision = Initial kinetic energy of car A + Initial kinetic energy of car B = 38400 J + 120725 J = 159125 J
Total kinetic energy after the collision = Final kinetic energy = 545641.45 J