A racetrack curve has radius 70.0 m and is banked at an angle of 12.0 ∘. The coefficient of static friction between the tires an
d the roadway is 0.400. A race car with mass 1200 kg rounds the curve with the maximum speed to avoid skidding. consider friction when solving for a, b, and c.
a) As the car rounds the curve, what is the normal force exerted on it by the road?
b) What is the car's radial acceleration?
c) What is the car's speed?
d) In the case of a banked curve with friction, which of the following forces contribute to the centripetal (inward) acceleration: the frictional force, the normal force, and/or the gravity? and why?
a) As the car rounds the curve, what is the normal force exerted on it by the road?
b) What is the car's radial acceleration?
c) What is the car's speed?
d) In the case of a banked curve with friction, which of the following forces contribute to the centripetal (inward) acceleration: the frictional force, the normal force, and/or the gravity? and why?
1 answer:
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Answer:
The coefficient of static friction is : 0.36397
Explanation:
When we have a box on a ramp of angle , and the box is not sliding because of friction, one analyses the acting forces in a coordinate system system with an axis parallel to the incline.
In such system, the force of gravity acting down the incline is the product of the box's weight times the sine of the angle:
Recall as well that component of the box's weight that contributes to the Normal N (component perpendicular to the ramp) is given by:
and the force of static friction (f) is given as the static coefficient of friction () times the normal N:
When the box starts to move, we have that the force of static friction equals this component of the gravity force along the ramp:
Now we use this last equation to solve for the coefficient of static friction, recalling that the angle at which the box starts moving is 20 degrees: