Highway 17 between San Jose and Santa Cruz has many relatively tight turns (for

Question

Highway 17 between San Jose and Santa Cruz has many relatively tight turns (for a
highway). It once was nicknamed the freeway of perilous death because the turns were not
banked at the proper angle for the posted speeds causing a troubling number of accidents
involving cars sliding off the road. Rumor has it that the engineer responsible for this error
took his own life driving too fast around a turn. Fortunately Caltrans has rectified the
situation by regrading the road to have the appropriate banks on the turns.

1. For the turn pictured, what is the magnitude of the acceleration of a car going around
this turn at a steady speed of 45 mph?

2. What angle should the road be banked at so that the car can make it around the turn even when the road is wet and slippery?

RI ..,11 62% ü 12:06 AM Assignment 5.pdf Graded Assignment #5 The one about highway 17 lighway) I ouce was nickuaued ie reway ol pelous dealh because he turs were o took his wn life driving ton fast nmnnd a tirn. 1inrtrmately CaltTnns has Trr:tified the this tun at a stedy spood of 45 mph 2. Wlual auyle sould e wad be bankedal so theaake i aroud te tTn vn hrm thr ro is wrt d slipper

Explanation / Answer

1) Assuming this highway has diameter of 200m I.e radius is 100m and speed 45mph = 20.11m/s then

Centripetal force mv^2/r = m*a

Or acceleration a = v^2/r = 20.11^2/100m = 4.04m/s^2

2) v= sqrt(r*g*tan theta) or tan theta= v^2/r*g

tan theta= 20.11^2/(100*9.8)=.412

Or theta = 22.39 degree

2)

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