Name: friction on a banked road
Uploaded: 2026-06-24T13:03:27.731Z
Duration: 1 min 17 s
Channel: JoVE

Consider a bus of mass 3 megagrams, having its center of mass at G, traveling along a straight shoulder of the road at a constant velocity. The coefficient of static friction between the tires and the road is 0.5.What is the maximum angle the shoulder can have without causing the bus to slip or tip over?Drawing the free-body diagram, the gravitational, frictional, and normal forces are denoted.The frictional forces at the two contacts are expressed, and the weight of the bus is resolved into its components.Consider the condition for no slipping. Since the bus travels with constant velocity, it satisfies the equilibrium conditions, and the resultant forces acting on it in both directions are zero.Solving the two equations gives the maximum angle for no slipping.When the bus starts tipping, it loses contact with the uphill tires, and no normal or frictional force acts at this point.To prevent tipping, the resultant moment about the downhill tires must be zero. Solving the equation gives the maximum angle for no tipping.

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.
<img alt="Figure 1" src="/files/ftp_upload/14316/14316_PT_Figure_1v2.svg" style="text-align: center; height: 350px;" />
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.
<img alt="Equation 1" src="/files/ftp_upload/14316/14316_PT_Equation_1v2.svg" style="text-align: center; height: 13px;" />
<img alt="Equation 2" src="/files/ftp_upload/14316/14316_PT_Equation_2v2.svg" style="text-align: center; height: 13px;" />
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.
<img alt="Equation 3" src="/files/ftp_upload/14316/14316_PT_Equation_3v2.svg" style="text-align: center; height: 13px;" />
<img alt="Equation 4" src="/files/ftp_upload/14316/14316_PT_Equation_4v2.svg" style="text-align: center; height: 13px;" />
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.

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 ...

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Mechanical Engineering

Unit 1

Friction

KEY TERMS AND CONCEPTS

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friction on a banked road

Friction on a banked road affects whether a bus stays steady while it moves at constant speed. In this problem, a bus with a mass of three megagrams travels on a sloped road. The coefficient of static friction between the tires and the road is 0.5. The goal is to find the maximum bank angle where the bus will not slip or tip.

To solve the motion part, the forces on the bus must be shown first. These include gravity, the normal force, and friction. The normal force is the push from the road, and static friction is the grip that prevents sliding. The bus is then analyzed at the two tire contact points so the force balance can be checked.

Because the bus moves at a constant speed, it is in equilibrium. That means the vertical and horizontal forces cancel each other. Using the bus weight and the road angle, the maximum angle for no sliding can be determined from these balanced forces.

The tipping condition must also be checked. When tipping starts, the bus loses contact at the upper tire contact point. At that point, no reaction force or frictional force acts there. To avoid toppling, the moment about the lower contact point must be zero. That balance gives the largest safe bank angle without tipping.

Friction on a Banked Road

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Friction on a banked road affects whether a bus stays steady while it moves at constant speed. In this problem, a bus with a mass of three megagrams travels on a sloped road. The coefficient of static friction between the tires and the road is 0.5. The goal is to find the maximum bank angle where the bus will not slip or tip. To solve the motion part, the forces on the bus must be shown first. These include gravity, the normal force, and friction. The normal force is the push from the road,...

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key terms and concepts

Find the maximum bank angle for a bus on a banked road by balancing gravity, normal force, static friction, and tipping moments.

Friction on a Banked Road | JoVE K12

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mechanical engineering

Friction on a Banked Road

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