Safe Curve Radius for A Truck?

[skibum1441]

A pick-up truck with two passengers weighs about 14700 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 26.1 m/s?

 

[FlávioMedeiros]

First, you should consider that the gravity on that place is equal to 10 m/s².

Weight is equal to mass times gravity. (w = mg)

14700 = 10m
m = 1470 kg

Since the friction is numerically equal to the weight, you consider that the force responsible for allowing the car to make the turn safely is equal to the centripetal force (m.v²/r), that is, the friction.

Thus, using the second Newton's law, you can easily figure out the answer.

Fr = m.a
A is the rotational aceleration, which is equal to v²/r (Centripetal aceleration)

14700 = mv²/r
14700 = 1470.(26,1)² / r
Multiplying the denominator of the second member by the numerator of the first member, you will obtain:

14700r = 1470.(681,21)
14700r /1470 = 681,21
10r = 681,21
r = 68,121 m

That's it