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23 April, 02:19

The floor of a railroad flatcar is loaded with loose crates having a coefficient of static friction of 0.320 with the floor. If the train is initially moving at a speed of 49.0 km/h, in how short a distance can the train be stopped at constant acceleration without causing the crates to slide over the floor?

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  1. 23 April, 05:23
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    Answer: 29.50 m

    Explanation: In order to calculate the higher accelation to stop a train without moving the crates inside the wagon which is traveling at constat speed we have to use the second Newton law so that:

    f=μ*N the friction force is equal to coefficient of static friction multiply the normal force (m*g).

    f=m. a=μ*N = m*a = μ*m*g = m*a

    then

    a=μ*g=0.32*9.8m/s^2 = 3.14 m/s^2

    With this value we can determine the short distance to stop the train

    as follows:

    x = vo*t - (a/2) * t^2

    Vf=0 = vo-a*t then t=vo/a

    Finally; x=vo*vo/a-a/2 * (vo/a) ^2=vo^2/2a = (49*1000/3600) ^2 / (2*3.14) = 29.50 m
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