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

In summary, the question is asking for the total resistive force acting on a car traveling at a constant speed on a stretch of highway where the elevation decreases by h for every segment of length L. The attempt at a solution involved breaking down the forces into components and using trigonometry, but it was initially incorrect. After re-examining the problem, it was determined that the correct angle to use was arcsin instead of arctan.
  • #1
robbondo
90
0

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 alot.
 
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  • #2
robbondo said:
the elevation decreases an amount h for each segment of road of length L.

Read once again.
 
  • #3
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?
 
  • #4
nm... thanks radou. I see know that the hypotenuse is length l, not the adjacent side. I should be using arcsin not arctan. THANKS!
 

1. What is friction force?

Friction force is a force that opposes the motion of an object. It is caused by the interaction between two surfaces in contact with each other.

2. How does friction force affect a car rolling down an incline at constant velocity?

Friction force acts in the opposite direction of the car's motion, slowing it down. In the case of a car rolling down an incline at constant velocity, the friction force will be equal in magnitude to the force pulling the car down the incline, resulting in a net force of zero and allowing the car to maintain a constant velocity.

3. What factors affect the friction force of a car rolling down an incline?

The friction force of a car rolling down an incline is affected by the weight of the car, the angle of the incline, and the type and condition of the surface the car is rolling on.

4. How can the friction force of a car rolling down an incline be calculated?

The friction force can be calculated using the formula F = μN, where F is the friction force, μ is the coefficient of friction between the two surfaces, and N is the normal force exerted by the car on the surface it is rolling on.

5. Can the friction force of a car rolling down an incline be eliminated?

No, it is not possible to completely eliminate friction force. However, it can be reduced by using smoother surfaces, reducing the weight of the car, or decreasing the angle of the incline.

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