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saplinglearning.com Blackboard Learn Math 26a PaperCut Logi te University Gmail Apple YouTube NewsESPN Google PHYS 5A -Fall17-0SBORNE: HW: Applications of Forces www.saplinglearning oomiibisessiAccessibl ity.php?text-As% 200%20city%20planner% Jump to... (2) Abdullah Tim University, Sacramento-PHYS 5A-Fall17OSBORNE > Activities and Due Dates HW: Applications of Forces 10/6/2017 11:00 PM 27.3/100 Gradebook Print Calculator Periodic Table 6 of 1 Sapling Learning MapA a city planner, you receive complaints from local residents about the safety of nearby roads and streets. complaint concens 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 effective coefficient of friction between a rolling wheel and asphalt ranges between 0.536 and 0.599, whereas the effective coefficient of friction between a skidding (locked) wheel and asphalt ranges between 0.350 and 0.480. Vehicles of all types travel on the road, from small W bugs weighing 1110 ib to large trucks weighing 9.00 10 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 imit can stop before reaching the intersection Minimum Maximum Number 188.60 Incorrect. Be careful when choosing the proper coefficients of friction. ft 168.76 ft Given that the goal is to allow all vehicles to come safely to a stop before reaching the intersection, calculate the maximum speed limit Number (Scroll down for more questions.) 47.18 mph .O Previous #Try Again ONext ijft | MacBook ProExplanation / Answer
55 mph 80.7 ft/s
trucks:
Ek = ½mv² = ½ * (9000lb / 32.2 ft/s²) * (80.7ft/s)² = 910130.589 ft·lb
worst case friction: Ffw = µmg = 0.35 * 9000lb = 3150 lb
stopping distance d = Ek / Ffw = 288.93 ft
best case friction: Ffb = 0.599 * 9000lb = 5391 lb
stopping distance d = Ek / Ffb = 168.824 ft
bugs:
Ek = ½ * (1110lb / 32.2ft/s²) * (80.7ft/s)² = 112249.439 ft·lb
worst case friction: Ffw = 0.35 * 1110lb = 388.5 lb
stopping distance d = 288.93 ft
best case friction: Ffb = 0.599 * 1110lb = 664.89 lb
stopping distance d = 168.824 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 = 388.5lb * 155ft = 60217.5 ft·lb
This corresponds to Ek = 60217.5 ft·lb = ½ * (1110lb / 32.2ft/s²) * v²
v 59.1075 ft/s 40.3 mph maximum desired speed limit
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