New guy with a question about a car (with velocity v) and a highway

[Mitchell Arnott]

Hi all here is the question I need to justify. Please see the attached file with the question.
I would simply like to use the formula (theta)=tan(^-1)[(v^2)/gr] to solve the angle. This gives the correct answer. Now my teacher however solves it using a different vector method and says in order for me to use this in the exam I will need to provide proof that this is an acceptable solution. I have found some stuff online that says; for any object moving at constant velocity on a horizontal surface the centripetal force will be the same as the force of friction. What else can I say to justify this? (My teacher is very stubborn).

 

[mfb]

I moved the thread to the homework forums, as the problem is homework-like.

for any object moving at constant velocity on a horizontal surface the centripetal force will be the same as the force of friction. What else can I say to justify this?

Where is the relation between this statement and the formula you got?
That is the point you have to show.
There is no friction in your problem.

 

[haruspex]

There is no friction in your problem.

and the surface is not horizontal.

 

[Mitchell Arnott]

I moved the thread to the homework forums, as the problem is homework-like.
Where is the relation between this statement and the formula you got?
That is the point you have to show.
There is no friction in your problem.

Yes I agree there is no friction. This I believe is given in the problem itself.
I spoke to the head of the physics department and he basically told me to envision the highway curve as a bowl with the same angle throughout.
I have attached a paper that I wrote to my teacher trying to explain my reasoning for solving the problem as follows and he would not accept it.
I am unsure how to justify using the force at an angle viewing onto the curvature of the highway as a real life solution.
I do not see how it is possible to explain. In fact when I think about it I do not fully comprehend it.
This being that when the head of the department questioned me thoroughly about it I could not answer all of his questions although I thought I understood the material...
It seems I do not. Can someone help me? My test is on wednesday night and I would really like to be able to solve this problem.

 

[Mitchell Arnott]

and the surface is not horizontal.

Agreed please see my response below and see if you can comment some help.

 

[haruspex]

Yes I agree there is no friction. This I believe is given in the problem itself.
I spoke to the head of the physics department and he basically told me to envision the highway curve as a bowl with the same angle throughout.
I have attached a paper that I wrote to my teacher trying to explain my reasoning for solving the problem as follows and he would not accept it.
I am unsure how to justify using the force at an angle viewing onto the curvature of the highway as a real life solution.
I do not see how it is possible to explain. In fact when I think about it I do not fully comprehend it.
This being that when the head of the department questioned me thoroughly about it I could not answer all of his questions although I thought I understood the material...
It seems I do not. Can someone help me? My test is on wednesday night and I would really like to be able to solve this problem.

The attachment is rather hard to read, and the logic flow unclear. You don't need all that verbiage, just a few comments to provide the basis of your equations and the manipulations.
Explaining what you are doing, write out the $\Sigma F=ma$ equations, as they apply to this problem, in each of the horizontal and vertical directions. Then solve.

 

[Mitchell Arnott]

I use force equals mass times acceleration wouldn't I be just using trigonometry to calculate the angle of the triangles using The horizontal and vertical components? I see what you're saying that the acceleration is gravity . I will try to formulate a paper with those equations soon .

 

[Chestermiller]

Have you drawn a free body diagram of the car yet and shown the forces acting on it? This should be your first step. So please articulate what the forces are that are acting on the car.