Question

The rolling resistance for steel on steel is quite low; the coefficient of rolling friction is typically 0.002. Suppose a 180,000 kg locomotive is rolling at 10 m/s on level rails. If the engineer disengages the engine, how much time will it take for the locomotive to coast to a stop? How far will the locomotive move during this time?

Answer 1

The locomotive will take approximately 510.2 seconds to coast to a stop and will cover a distance of approximately 26070.4 meters.

Step-by-step explanation:

To find the time it will take for the locomotive to coast to a stop, we can use the equation:

t = v/μg

where t is the time, v is the initial velocity, μ is the coefficient of rolling friction, and g is the acceleration due to gravity.

Plugging in the values, we get:

t = 10 m/s / (0.002 * 9.8 m/s^2)

t ≈ 510.2 seconds

To find the distance the locomotive will move during this time, we can use the equation:

d = vt - (1/2) * μ * g * t^2

Plugging in the values, we get:

d = 10 m/s * 510.2 s - (1/2) * 0.002 * 9.8 m/s^2 * (510.2 s)^2

d ≈ 26070.4 meters