Question 18 of 23 Map A Sapling Learning macmillan leir a city planner, you rece

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Question 18 of 23 Map A Sapling Learning macmillan leir a city planner, you receive complaints from local residents about the safety of nearby roads and streets ne 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 1 55 feet. Since fog is a common occurrence in this region, you decide to investigate. The state highway department states that the effective coefficient of friction between a rolling wheel and asphalt ranges between 0.689 and 0.770, whereas the effective coefficient of friction between a skidding (locked) wheel and asphalt ranges between 0.450 and 0.617. Vehicles of all types travel on the road, from small VW bugs weighing 1210 lb to large trucks weighing 7770 lb. Considering that some drivers will brake properly when slowing down and others wi 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 A O Previous Check Answer 0 Next H Ext Hint

Explanation / Answer

55 mph 80.7 ft/s

trucks:
Ek = ½mv² = ½ * (7770 / 32.2 ft/s²) * (80.7ft/s)² = 785746.076 ft·lb
worst case friction: Ffw = µmg = 0.45 * 7770lb = 3496.5 lb
stopping distance d = Ek / Ffw = 224.72 ft
best case friction: Ffb = 0.77 * 7770lb = 5982.9 lb
stopping distance d = Ek / Ffb = 131.332 ft

bugs:
Ek = ½ * (1210lb / 32.2ft/s²) * (80.7ft/s)² = 122362.002 ft·lb
worst case friction: Ffw = 0.45 * 1210lb = 544.5 lb
stopping distance d = 224.72 ft
best case friction: Ffb = 0.77 * 1210lb = 931.7 lb
stopping distance d = 131.332 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 = 544.5lb * 155ft = 84397.5 ft·lb
This corresponds to Ek = 84397.5 ft·lb = ½ * (1210lb / 32.2ft/s²) * v²
v 67.0216 ft/s 45.69 mph maximum desired speed limit

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