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, you 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 595 kg to large trucks with mass 4095 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. Minimu =? Maximum=?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. = kmh?.

Answer 1

The Coefficient of friction between the wheel and the road inidicates the amount of stopping force to the vehicle along the surface of the road and which is in proportion to the normal weight of the vehicle.

We would need to calculate an appropriate speed limit for both ends of the spectrum.

For a VW bug: Coefficient = 0.550 Weight = 595 Kg

Stopping force = 595 X 0.550 X Gravitational constant (9.8)

Energy expended in stopping = stopping force X Visibility Distance=47meters

Kinetic Energy of Moving Vehicle = 0.5 X mv²

Equating both sides we have:

595 X 0.55 X 9.8 X 47= 0.5 X 595 X v²

Hence v=22.5 m/s or 81 Km/Hr

For a Truck: Coefficient = 0.754 Weight = 4095 Kg

Stopping force = 4095 X 0.754 X Gravitational constant (9.8)

Energy expended in stopping = stopping force X Visibility Distance=47meters

Kinetic Energy of Moving Vehicle = 0.5 X mv²

Equating both sides we have:

4095 X 0.754 X 9.8 X 47= 0.5 X 4095 X v²

Hence v=26.35 m/s or 94 Km/Hr

Hence the speed limits would need to be modified to read as 81 Kmph for small vehicles and 94 kmph for heavy vehicles