A flatbed truck is transporting a steel cylinder of mass 40 kg . It is observed that the truck can accelerate up to a maximum of 2.5 m s ⁻² on a horizontal road without the cylinder slipping backward on the truck bed. The minimum coefficient of static friction between the cylinder and the truck bed must be : (Take g = 10 m s ⁻² )

Step-by-step solution

In the frame of the accelerating truck, a pseudo force acts on the cylinder in the backward direction. To prevent the cylinder from slipping backward, the static friction between the cylinder and the truck bed must be equal to or greater than this pseudo force. The pseudo force acting on the cylinder is: F_ p = m a The maximum static friction force available is: f_ s, = _s N = _s m g For the cylinder not to slip, we must have: F_ p f_ s, m a _s m g _s a g Substituting the given values ( a = 2.5 m s ⁻² and g = 10 m