Question

A pick-up truck with two passengers weighs about 14000 N. In good driving conditions around a curve, the maximum friction with the road is equal to the truck's weight. What is the minimum safe curve radius that the truck could negotiate at 28.9 m/s

Answer 1

85.14 m

Step-by-step explanation:

Let g = 9.81 m/s2. We can find the truck mass from its weight

m = W/g = 14000 / 9.81 = 1427 kg

So if the maximum friction could be the truck weight, which is F = 14000N, then that would also be the maximum centripetal force it could be. According to Newton 2nd law of motion, the maximum centripetal acceleration the truck can have when traveling at a curve is

a = F / m = 14000 / 1427 = 9.81 m/s2

By applying the following formula we can find the minimum safe radius R of the curve when traveling at speed of 28.9 m/s

`a = (v^2)/(R)`

`R = (v^2)/(a) = (28.9^2)/(9.81) = 85.14 m`