What Speed Causes a Truck to Tip Over on a Banked Curve?

[mengo]

Homework Statement

A truck is traveling around a 3 degree banked turn at a given constant speed with a given radius of curvature. The weight and center of gravity of the truck are also given. The question asks to determine at which speed the truck will tip over.

Homework Equations

The Attempt at a Solution

I'm unsure what the condition is for tipping. At first I figured that if the truck tips towards the outside, tipping will just begin when the reaction forces on the inner wheels are zero. I then set the set the moment of the weight equal to the moment of the centripedal acceleration times mass about the outside set of wheels. The answer I got differed from that given in the texbook.

I'm unsure how else to solve this problem since I am unable to find the normal and friction forces and so I am asking for some help. Thank you.

 

[anathema]

Dear fellow scientist,

Thank you for your question. The condition for tipping in this scenario is when the centrifugal force (which acts towards the outside of the turn) exceeds the combined weight and frictional force acting towards the inside of the turn. This can be calculated by using the formula Fc = mv^2/r, where Fc is the centrifugal force, m is the mass of the truck, v is the speed, and r is the radius of curvature.

To find the normal and frictional forces, you can use the equations Fc = mgsinθ and Ff = μN, where g is the acceleration due to gravity, θ is the bank angle, μ is the coefficient of friction, and N is the normal force. By setting the centrifugal force equal to the combined weight and frictional force, you can solve for the speed at which tipping will occur.

I hope this helps in solving your problem. If you need any further assistance, please don't hesitate to ask. Best of luck with your calculations!

 

[m2003]

As a scientist, it is important to approach problems with a clear understanding of the concepts and variables involved. In this case, the problem involves a truck traveling on a banked curve, with a given speed, radius of curvature, weight, and center of gravity. The question is asking for the speed at which the truck will tip over.

To solve this problem, we must first understand the forces acting on the truck. The truck is experiencing a centripetal force due to its circular motion, and this force is provided by the friction between the tires and the road. The banked curve also provides a normal force to counteract the weight of the truck, keeping it on the road.

To determine the speed at which the truck will tip over, we must consider the balance of forces and moments. The tipping point will occur when the normal force becomes zero, meaning that the truck is no longer able to stay on the road and will tip over. This can be represented mathematically by setting the normal force equal to zero and solving for the velocity.

It is important to note that the normal force and friction force are dependent on the angle of the banked curve. As the angle increases, the normal force decreases, and the friction force increases. Therefore, the tipping speed will also vary depending on the bank angle.

In order to accurately solve this problem, it is necessary to know the exact values of the normal force and friction force. This information can be obtained through the equations for circular motion and the laws of physics. It may also be helpful to create a free body diagram to visualize the forces acting on the truck.

In conclusion, to determine the speed at which the truck will tip over on a banked curve, we must consider the balance of forces and moments, specifically the normal force and friction force. With the appropriate equations and understanding of the concepts involved, we can accurately solve for the tipping speed.