Do not round intermediate answers. Give your final answer(s) to three decimal pl

Question

Do not round intermediate answers. Give your final answer(s) to three decimal places. Check your units The flatbed truck starts from rest on a road whose constant radius of curvature is 28 m and whose bank angle is 11°. If the constant forward acceleration of the truck is 2.5 m/sec2, determine the smallest time t after the start of motion at which the crate on the bed begins to slide. The coefficient of static friction between the crate and truck bed is ,-0.8, and the truck motion occurs in a horizontal plane. t= 17.194 × sec

Explanation / Answer

for crate to slide it has to overcome friction force

this friction force can be overcome by the centripetal force

centripetal force = mv^2 / r

so,

mg * sin(11) + k * (mg * cos(11) + mv^2 * sin(11) / r) = mv^2 * cos(11) / r

g * sin(11) + k * (g * cos(11) + v^2 * sin(11) / r) = v^2 * cos(11) / r

9.8 * sin(11) + 0.8 * (9.8 * cos(11) + v^2 * sin(11) / 28) = v^2 * cos(11) / 28

v = 17.975 m/s

by first equation of motion

v = u + at

since the truck started from rest so

17.975 = 0 + 2.5 * t

t = 7.19 sec

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