As a city planner, you receive complaints from local residents about the safety

Question

As a city planner, you receive complaints from local residents about the safety of nearby roads and stree 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 friction between and asphalt ranges between 0.689 0.770, whereas the effective coefficient between a skidding small wheel and asphalt ranges between 0.450 and 0.617. Vehicles of all types travel on the road, from VW bugs weighing 1210 lb to large trucks weighing 9420 lb. Considering that some drivers will brake properly when slowing down and others will skid to stop, calculate the miminim and maximum braking distance needed to ensure that all vehicles traveling at the posted speed limit can stop before reaching the intersection Minimum Maximum Number Number 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. (Scroll down for more questions.) Number mph Give up & view solution Check Answer Previous

Explanation / Answer

trucks:

Ek = 1/2mv^2

Ek = 1/2 * (9420lb / 32.2 ft/s^2) * (80.7ft/s)^2

Ek = 952603 ft·lb

worst case friction: Ffw = µmg = 0.450 * 9420lb = 4239 lb

stopping distance d = Ek / Ffw = 224.72 ft

best case friction: Ffb = 0.689 * 9420lb = 6490 lb

stopping distance d = Ek / Ffb = 146.77 ft

bugs:

Ek = 1/2 * (1210lb / 32.2ft/s^2) * (80.7ft/s)^2

Ek = 122362 ft·lb

worst case friction: Ffw = 0.55 * 1210lb = 665.5 lb

stopping distance d = 183.86 ft

best case friction: Ffb = 0.770 * 1210lb = 931.7 lb

stopping distance d = 121.33 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 = 665.5lb * 155ft = 103153 ft·lb

This corresponds to Ek = 103153 ft·lb = 1/2 * (1210lb / 32.2ft/s^2) * v^2

v = 74.1 ft/s = 50 mph maximum desired speed limit

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