How Do You Calculate Forces on a Car Traveling on a Banked Curve?

[nugget]

Homework Statement

car is on a banked curve of angle 18^o, radius 70m. Mass of car = 1020kg and weight is taken as 1.0x10^4 N. Find the resultant force and the normal force N when the car is at the design speed.

Homework Equations

force diagram equations

The Attempt at a Solution

I calculated Normal force to be 10514.6N
I calculated the resultant force to be the component of the normal force towards the centre of the banked curve, and got 3249.2N

I think design speed just means max speed the car can safely travel around the curve at, I calculated this to be approx. 14.9 m/s but i could be quite wrong.

Are there things I'm forgetting to consider? is this exactly what the question asks for?

 

[The Liberator]

I checked your answers and everything, and from what I know, you are completely correct.

By the way, as advice, if you have not already done it in other examples it is good show working on the site, and if possible a vector diagram.

 

[nlightner]

I would first double check my calculations to ensure accuracy. It is important to be precise in scientific calculations to ensure the validity of the results. Additionally, I would consider the forces acting on the car, such as the centrifugal force and the friction force, to get a more complete understanding of the situation.

Furthermore, I would also consider the design of the banked curve and its effects on the car's trajectory. Factors such as the angle of the bank, the radius of the curve, and the speed of the car can all play a role in determining the resultant force and the normal force.

In terms of the design speed, I would also take into account any safety measures or regulations that may affect the maximum speed at which the car can safely travel around the curve. This could include factors such as the road conditions, the driver's skill level, and the weight distribution of the car.

Overall, it is important to approach this problem with a critical and analytical mindset, taking into account all relevant factors and considering potential limitations in the data or assumptions made. This will ensure a thorough and accurate analysis of the situation.