part a) consider the banking of the surface of the segment of a road,which is cu

Question

part a)

consider the banking of the surface of the segment of a road,which is curved with a radius r. The banking angle is ?. Theequation of motion of the car at a certain speed is given by ?+mg + f =mac =Fc

where ? is the normal force vector exerted bythe surface on the car, mg the gravitational forcevector on te car, and f the friction force vector which is pointingdownhill. Fc to be the magnitudes of thecorresponding force vectors, the x- component equation is givenby

1. -N sin ? + f sin ?= Fc

2. N cos ? + f cos ? = Fc

3. -N cos ?+ f sin ?= Fc

4. N sin ? + f sin ?= Fc

5.-N sin ? + f cos ? = Fc

6. N sin ? + f cos ?= Fc

7. N cos ? +f sin ?= Fc

8. -N cos ?+ f cos ?= Fc

The y-component equation is given by

1. N cos ? - f sin ?- mg= 0

2. N sin ?+ f cos ? - mg = 0

3. N cos ? + f sin ? - mg= 0

4. N sin ? - f sin ? - mg = 0

5. N cos ?+ f cos ?- mg= 0

6. N sin ? - f cos ? - mg = 0

7. N sin ? + f sin ? - mg = 0

8. N cos ? - f cos ? - mg = 0

Part c

Let the radius of the circular segment be 109 m, the mass ofthe car 1863 kg, and the coeffient of the static frictionbetween the road and the tire 0.7. The banking angle is not given.find the magnitude of the normal force N which the roadexerts on the car at the optimal speed (the speed at whichthe frictional force is zero) of 86 km/h. Answer in units ofN.

Explanation / Answer

(a) Look at the forces that affect the slide. They are parallel to the direction of the road surface. These are

1) The component of car weight along the surface, pulling the car down the bank;
2) the component of centrifugal force along the surface, pulling the car up the bank
3) the frictional force acting in the direction of the weaker force and equal to

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