Question

What is the maximum acceleration that the train can achieve on an incline of 1 in 250, considering the locomotive's maximum pull of 160 kN, the locomotive's mass of 80,000 kg, the train's mass of 400,000 kg, and resistance to motion of 24 kN?

A) 0.15 m/s²
B) 0.30 m/s²
C) 0.45 m/s²
D) 0.60 m/s²

Answer 1

The maximum acceleration of the train on the incline is approximately 0.272 m/s².

Step-by-step explanation:

To calculate the maximum acceleration of the train on an incline, we need to consider the forces acting on the train. The maximum pull of the locomotive is 160 kN, and the resistance to motion is 24 kN. The train's mass is 400,000 kg, and the locomotive's mass is 80,000 kg.

Using Newton's second law of motion, we can calculate the net force acting on the train. The net force is the difference between the maximum pull and the resistance to motion:

Net Force = Maximum Pull - Resistance to Motion

Substituting the given values, we get:

Net Force = 160,000 N - 24,000 N = 136,000 N

Now, using the formula for acceleration, where acceleration is the net force divided by the total mass of the train:

Acceleration = Net Force / Total Mass

Substituting the values, we calculate:

Acceleration = 136,000 N / (80,000 kg + 400,000 kg) = 0.272 m/s²

Therefore, the maximum acceleration that the train can achieve on the incline is approximately 0.272 m/s².