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 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 (89 km/h) 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 47 meters. Since fog is a common occurrence in this region, yo u decide to investigate The state highway department states that the effective coefficient of friction between a rolling wheel and asphalt ranges between 0.842 and 0.941, whereas the effective coefficient of friction between a skidding (locked) wheel and asphalt ranges between 0.550 and 0.754. Vehicles of all types travel on the road, from small VW bugs with a mass of 619 kg to large trucks with mass 3711 kg 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 ITm IIn 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. Number (Scroll down for more questions.) km/ h

Explanation / Answer

89 km/h 27.7 m/s

trucks:
Ek = ½mv² = ½ * 3711* (27.7)² = 1423706.6 J
worst case friction: Ffw = µmg = 0.55 * 3711 * 9.8 = 20002.3 N
stopping distance d = Ek / Ffw = 71.2 m
best case friction: Ffb = 0.941 * 3711*9.8 = 34222.1 N
stopping distance d = Ek / Ffb = 41.6 m

bugs:
Ek = ½ * 619 * (27.7)² = 237476.3 J
worst case friction: Ffw = 0.55 * 619 * 9.8 = 3336.4 N
stopping distance d = 71.2 m
best case friction: Ffb = 0.941 * 619 * 9.8 = 5708.3 N
stopping distance d = 41.6 m

Given that the maximum allowable distance is 47 m, 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 47 m entails Work = 3336.4 * 47 = 156810.8 J
This corresponds to Ek = 156810.8 = ½ * (619) * v²
v 22.5 m/s maximum desired speed limit

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