A runaway locomotive (mass = m 1 ) is switched onto a railroad siding (a separat

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A runaway locomotive (mass = m1) is switched onto a railroad siding (a separate section of track), so that it will crash safely at a

A runaway locomotive (mass = m1) is switched onto a railroad siding (a separate section of track), so that it will crash safely at a "dead-end." That's where another "junk" rail car (mass = m2) sits at rest on a level track against a relaxed ideal spring (stiffness = k), as shown in Fig. A. The locomotive's engine has been shut off, but its brakes have failed completely, and it's still going at speed vi as it rolls onto the siding from the main line. Its travel along the siding is shown here in two different views. As shown in Fig. B (a side view) here, it climbs a slope (with an altitude gain of h), then crosses the level width of a plateau to where the junk car and spring are located. Fig. C shows an overhead view of this. It also shows the wind blowing horizontally (across that plateau only) at an angle q degree north of east. The average force of that wind on the locomotive (exerted in the direction of that wind) is Fair. The total distance traveled along the siding from the main line to the junk car is d. The plateau width is w. The average rolling resistance of the rails (and still air) opposing the locomotive's motion all along the siding is Fr. Find the maximum compression of the spring after impact.

Explanation / Answer

the kinetic energy of spring is equal to kinetic energy of mass therefore (1/2)kd^2 = (1/2)mv^2 or v^2 = (k/m)d^2 or v = (k/m)^1/2 x d where v is speed of mass,k is spring constant of spring,m is mass and d is distance the spring is compressed

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