A 2970.9-lbf truck rounds an unbanked curve on the highway at a speed of 57.3 mp

Question

A 2970.9-lbf truck rounds an unbanked curve on the highway at a speed of 57.3 mph. If the maximum frictional force between the surface of the road and all four of the tires is 1273.8 lbf, calculate the minimum radius of curvature for the curve to prevent the truck from skidding off the road.

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CHEGG,

Please start with (show how you derive from) simple formulas (i.e. ac = (Vt2)/R = wVt = w2R and F = (mV2)/r and [arc length] = [angle in radians]/[t] etc.), and please show ALL your work. Thank you!

Explanation / Answer

in horizontal there is only friction force that keeps it from skidding,

in horizontal using newton's 2nd Law, F = ma

so friction force f = m * a_c

a_c =centripetal force

so f = mv^2 / R

I am converting given values in MKS system

mass of truck m = 2970.9 x 0.454 kg = 1348.79 kg

v = 57.3 x 1609 m / 3600sec = 25.61 m/s

friction force = 1273,8 x 4.448 = 5666.14 N

so 5666.14 = 1348.79 x 25.61^2 / R

R = 156.13 m

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