The average NASCAR race car weighs 3400 lb. At a recent Nascar race the cars wen

Question

The average NASCAR race car weighs 3400 lb. At a recent Nascar race the cars went flying around the banked curves at a raceway. The banking of the turns at the raceway are theta = 27 degree. What is the algebraic expression for the component of the normal force in the vertical direction What is the algebraic expression for the gravitational force on the car in terms of its mass What is the algebraic expression for the component of the normal force in the horizontal direction Use your answer to parts (a), (b), and (c) to eliminate F_N and write an expression for the centripetal force on the car in terms of the mass m of the car and the angle theta. If the car is going around the curve at a speed of 190 mph calculate the centripetal force acting on the car. Suppose the curve was not banked. For the same radius, what centripetal force will be needed to keep the car going around the curve at the same speed of 190 mph

Explanation / Answer

weight of car = 3400 lb = 3400*.4536 = 1542.21 kg

theta = 27 degree

(a)

vertical components of normal force

FNy = FN*cos*(theta)

(b)

Fg = m*g        

where ( m = mass   ,    g = gravitational acceleration)

(c)

horizontal components of normal force

FNx = FN*sin*(theta)

(d)

centripetel force

Fc = FN*sin (theta)

FN = m*g / cos(theta)

Fc = m*g * sin (theta) / cos (theta)

(e)

Fc = 1542.2 * 9.8 * sin(27) / cos (27)

Fc = 7709.49 N

(f)

given that curve is not banked so friction is present

Fc = m*v^2 / r

because velocity and r (radius) both are same so Fc will be same

Fc = 7709.49 N

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