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 (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 0.689 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 8640 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.

Answer 1

Speed Limit refers to the maximum speed a car can have while travelling. When a car skids, it takes longer to stop than the usual time. The car should come to a stop within 155 feet while skidding. Hence, only on the lowest coefficient of sliding friction between the wheels and the road we need to find the maximum speed as the most distance to stop is required by this condition.

Converting ft to m:

155 ft = =47.24m

Since friction is the force slowing down the car we can write:

ΣF=ma

f=ma

N=ma

mg=ma

g=a

Now we can plug this acceleration into a kinematic equation.

=

= = 20.41 m/s

Convert speed from m/s to miles per hour:

= 45.65 miles/hour

Since speed limit signs are in 5 mph increments the speed limit should be 45 mph.