Friction Challenge Problem - Finding Distance Required To Stop.

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I need help finding the answer for this physics problem that I have to do.

A 2,345kg car is travelling down a highway entrance ramp, at an angle of 5.74 degree at 65 miles/hours and slams on its brakes to keep from hitting another car. If the coefficient of friction between the tires and the roads is 0.403, what is the distance required to stop?

According to one of my friend, he found the Applied Force and Normal Force, and then Friction Force. Afterward he did Net Force and he is just stuck.

I'm not completely sure how to do this problem or even know what friction formula to use for it to be correct.
Help. Thanks.


Science Advisor
Easiest way to do this is to have your x coordinate run along the ramp, and y perpendicular. That way, gravity doesn't point along y, but you only have to deal with one constraint. Specifically, sum of all forces in y direction is zero, because the car can neither fall through ground nor fly off.

The two forces along y are the component of gravity perpendicular to road and the normal force. Use this fact to find normal force, and use that to find friction.

That leaves you with two forces in x direction. There is friction and the x component of gravity. Add them together, and you have your acceleration in x direction, which you can use to compute stopping distance.
The speeding car has a certain amount of kinetic energy = 1/2(mv2).
The action of the braking friction needs to "eat up" all that kinetic energy, and it does so by performing work against the car's kinetic energy, so that work is (Frictional Force) x (Distance over which the friction is acting).

Frictional force is related to the weight of the car acting on the pavement x the coefficient of friction. But because there's an incline, you need to do some trigonometry to figure out what the component of the car's weight is acting down the slope. Also you need the trig to figure out the actual vector of the car's weight acting on the pavement so you get the frictional force calculated correctly.

If the car were not on an incline, then you would simply equate the kinetic energy of the car with the work done by the friction and solve for the stopping distance. But because the car is on an incline, some of the car's weight is working to negate some of the frictional force.

I hope that helps.
It's not that hard man!

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