Friction force of a car rolling down an incline at constant velocity.

[robbondo]

Homework Statement

At a certain part of your drive from home to school, your car (mass m) will coast in neutral at a constant speed of v if there is no wind. Examination of a topographical map shows that for this stretch of straight highway the elevation decreases an amount h for each segment of road of length L. What is the total resistive force (friction plus air resistance) that acts on your car when it is traveling at velocity v?

Homework Equations

The Attempt at a Solution

well I broke the forces down into components. I drew the diagram as a triangle with height h and length L. So, the angle of the hill is arctan(H/L). so then I found the x component of the downward force should be the hypotenuse, mg times sin of the angle of the hill which is arctan(H/L). Well, with this i got mgsin(arctan(h/L) as the force down the hill. So since the total force is zero the resistance must be equal to it in the negative. Well, I'm wrong. I was told "check your trigenometry". I hope someone can explain to me what the flaws in my reasoning were. Thanks a lot.

 

[radou]

the elevation decreases an amount h for each segment of road of length L.

Read once again.

 

[robbondo]

I don't undersand. Is there a mistake in the way that I drew my diagram. If it decreases h for every l then shouldn't that equate to a triangle with the height being H and the length L?

 

[robbondo]

nm... thanks radou. I see know that the hypotenuse is length l, not the adjacent side. I should be using arcsin not arctan. THANKS!