Ahighway curve of radius 60m is banked at an 18° angle. what is the maximum speed with which a 1500 kg rubber tired car can take this curve without sliding? assume the coefficient of static friction between the tires and the road is 1.0. hint: you must consider carefully which way friction points, up the incline or down the incline. also, remember that for uniform circular motion problems you always want to use radial, tangential, and z axes.

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Explanation:

To solve this problem we need to apply Newton's Second Law to the uniform circular motion, this means, we are going to take in account the radial forces. The forces we have in the x axiss are:

the horizontal component of the friction ,the horizontal component of normal force ,

(we do not consider the weight here since it is only exerted in the y axiss) so

,

the friction points toward the center of the curve, this is why the car will not slide,

,

now remembering that

we get

,

(this will be eq 1).

Now, for the y axiss we have:

vertical component of the friction ,vetical component of the normal force ,weight .

Where the weight and the vertical component of the friction point downwards.

So

,

,

,

(this will be eq 2).

Now we do eq 1 over eq 2:

,

simplifiying and solving for

,

,

,

,

and finaly

Answertraveling around a circular trackexplanation"traveling around a circular track" is the best answer as you could be traveling around a circular track at a constant speed. your velocity would therefore have the same magnitude but will always be constantly direction. since acceleration is the rate of change of velocity, the rate of change will only involve the direction of velocity and not the magnitude.wrong choices: "an object at rest" does not accelerate at all"increasing speed while traveling around a curve" means that the acceleration will not be constant due to only change in direction; it will be constant due to both magnitude and direction"an object in free fall" does not necessarily change direction