Final answer:
To find the speed of three coupled railroad cars after a collision, conservation of linear momentum is used. The total linear momentum before the collision must equal the total linear momentum after the collision. The speed of the coupled cars is calculated to be 1.687 m/s.
Step-by-step explanation:
The scenario involving railroad cars that collide and couple together can be analyzed using the conservation of linear momentum. In this case, a single railroad car, with a mass of 15900.0 kg and speed of 2.48 m/s, collides with two coupled railroad cars, each also with a mass of 15900.0 kg and traveling at a speed of 1.29 m/s.
To find the final speed of all three cars after they couple together, we apply the principle that the total linear momentum before the collision is equal to the total linear momentum after the collision, assuming no external forces act on the system.
Momentum before collision for single car = mass × velocity = 15900.0 kg × 2.48 m/s
= 39432 kg⋅m/s.
Momentum before collision for the two-car combination = (2 × 15900.0 kg) × 1.29 m/s
= 41022 kg⋅m/s.
Total momentum before collision = 39432 kg⋅m/s + 41022 kg⋅m/s
= 80454 kg⋅m/s.
After the collision, all three cars couple together and move as one object with a combined mass of (3 × 15900.0 kg) = 47700.0 kg.
The combined speed of the cars, V_final, can be found using the equation:
Momentum after collision = 47700.0 kg × V_final
= Total momentum before collision
= 80454 kg⋅m/s
Therefore, V_final = 80454 kg⋅m/s / 47700.0 kg = 1.687 m/s
The speed of the three coupled cars after the collision is 1.687 m/s.