Wibiscms/modWibis/view.php?id 3161019 3/5/2017 12:55 AM 18.1/100 Gradebook Print

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Wibiscms/modWibis/view.php?id 3161019 3/5/2017 12:55 AM 18.1/100 Gradebook Print Calculator Periodic Table c 16 Map A Sapling Learning As a city planner, you receive complaints from local residents about the safety of nearby roads and streets. One complaint concerns a stop sign at the corner of Pine Street and 1st Street, Residents complain that the speed limit in the area (55 mph) is too high to allow vehicles to stop in time. Under normal conditions this is not a problem, but when fog rolls in visibility can reduce to only 155 feet. Since fog is a common occurrence in this region, you decide to investigate. The state highway department states that the of friction between a rolling wheel and asphalt ranges between whereas the effective and asphalt of friction between skidding between 0.450 and 0.617.Vehicles of all types travel the road, from small VW bugs weighing 1050 lb tolarge trucks weighing 8580 lb. the miminim that some drivers wil brake property down and others will skid to stop, calculate limit can stop maximum braking distance needed to ensure that all vehicles traveling at the posted speed before reaching the intersection. O Given that the goal is to allow all vehicles to come safely to a stop before reaching the intersection, calculate the maximum desired speed limit. Soroll down for more questions) mph O Previous Check Answer o Next Exit

Explanation / Answer

55 mph = 80.7 ft/s

trucks:

Ek = 1/2mv^2

Ek = 1/2*(8580lb / 32.2 ft/s^2)*(80.7ft/s)^2

Ek = 867658 ft·lb

worst case friction: Ffw = µmg = 0.45 * 8580lb = 3861 lb

stopping distance d = Ek / Ffw = 224.7 ft

best case friction: Ffb = 0.617 * 8580lb = 5294 lb

stopping distance d = Ek / Ffb = 164 ft

bugs:

Ek = 1/2*(1050lb / 32.2ft/s^2) * (80.7ft/s)^2 = 106182 ft·lb

worst case friction: Ffw = 0.45 * 1050lb = 472.5 lb

stopping distance d = 224.7 ft

best case friction: Ffb = 0.617 * 1050lb = 647.85 lb

stopping distance d = 164 ft

Given that the maximum allowable distance is 155 ft, we've got to reduce the maximum allowable Ek of the vehicles,

and it appears not to matter which one we analyze.

worst case friction for bug over 155 ft entails Work = 472.5lb * 155ft = 73237.5 ft·lb

This corresponds to Ek = 73237.5 ft·lb = 1/2*(1050lb / 32.2ft/s^2) * v^2

v = 67 ft/s = 45.68 mph maximum desired speed limit

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