8.6 : Friction: Problem Solving

Friction is an essential force that influences the motion of objects in daily life. Depending on the situation, it can be either beneficial or problematic. Consider a bus with a mass of three megagrams and its center of mass at a specific point, moving along a banked road at a constant speed. The coefficient of static friction between the tires and the road is 0.5. Find the maximum angle of the banked road at which the bus would not slip or tip.

Initially, a visual representation of the gravitational, frictional, and normal forces acting on the bus needs to be created. These forces are crucial for understanding the balance of the bus on the banked road.

Next, the frictional forces at the two contact points between the tires and the road need to be analyzed. This can be accomplished by considering the weight of the bus and how it interacts with the angle of the banked road.

Since the bus travels at a constant speed, it satisfies the equilibrium conditions. This means that the forces acting on the bus in both the vertical and horizontal directions are balanced, and the bus remains stable on the road.

By investigating these forces and their relationships, one can find the maximum angle that ensures the bus remains stable without sliding down the slope.

Now, the tipping condition should be examined. When the bus starts tipping, it loses contact with the upper point (contact point between the upper tire and the road), and no reaction or frictional force acts at the upper point.

To prevent tipping, the forces acting on the bus need to be balanced in such a way that the resultant moment about the lower point must be zero. This helps to determine the maximum angle for no tipping, ensuring that the bus remains stable without toppling over.