Question

At the train station, you notice a large horizontal spring at the end of the track where the train comes in. This is a safety device to stop the train so that it will not plow through the station if the engineer misjudges the stopping distance. While waiting, you wonder what would be the fastest train that the spring could stop at its full compression which is L=3 ft . To keep the passengers safe when the train stops, you assume a maximum stopping acceleration of g/2. You also guess that a train weighs half a million lbs. For purpose of getting an estimate, you decide to assume that all frictional force are negligible.I've already posted this and someone gave me the wrong answer and i cannot for the life of me figure it out. The answer is not 7.66 m/s and should not be in meters, as the question gives everything else in feet.

Answer 1

v₀ = 9,798 ft / s

Step-by-step explanation:

We can solve this problem with kinematics in one dimension, when the train stops the speed is zero, the acceleration is negative so that the train stops. Let's use the equation

v² = v₀² - 2 a d

v = 0

v₀ = √2 a d

In the problem it indicates that the acceleration is g / 2, we substitute

v₀ = √2 (g / 2) d

Let's calculate

v₀ = √ 2 32/2 3 = √32 3

v₀ = 9,798 ft / s