What is the frictional force of a car driving around a curved road?

[canadiantiger7]

Homework Statement

a car drives around a curve with a radius 410 m at a speed of 38 m/s. the road is banked at 5.1 degrees, and the car weighs 1400 kg. what if the frictional force of the car? at what speed could you drive around this curve so that the force of friction is zero?

I tried a few equations and got different answers, but none of them correct. any help is appreciated.

Homework Equations

The Attempt at a Solution

 

[StatusX]

What exactly have you tried? You have to show some work before you'll get any help.

 

[canadiantiger7]

i got the acceleration (V2/R) and then plugged that into get Fnet (m*a). but it did not work. that is what it said to do in the book though.

 

[StatusX]

That is the net force on the car, but you need to determine where its coming from. Gravity always acts vertically with magnitude mg. The other two forces are the normal force of the road, which is perpendicular to the surface of the road, and the force of friction, which is parellel to the surface. These must be such that a) the vertical components add to zero, since there's no vertical acceleration and b) the horizontal components add to the net force, providing the centripetal force that keeps the car moving in a circle.

 

[alexander38]

Hi Canadiantiger7,
I’m not getting what you exactly want. Please provide more details so that I can help you.
Thanks & Regards
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[merryjman]

If you bank a curve steeply enough, the normal force will supply the needed centripetal acceleration rather than the frictional force. This is the principle at work at high speed race tracks - this way, the limited friction between the tires/road can be used strictly for accelerating and braking, and not turning as well.

I would start with a free-body diagram if I were you, and then do what StatusX said above with regard to the horizontal and vertical forces. Note that the normal force does NOT point directly upward, as it would in other problems.