Final answer:
a) The speed of the car is 18.9 m/s. b) The friction force acting on the car is 3035 N. c) The gravitational force acting on the car is 12250 N. d) The normal force exerted on the car is 11950 N.
Step-by-step explanation:
a) To calculate the speed of the car, we can use the centripetal force formula:
Fc = (mv^2)/r
Where Fc is the centripetal force, m is the mass, v is the speed, and r is the radius of the curve. Rearranging the formula gives:
v = sqrt((Fc * r)/m)
Substituting the given values, v = sqrt((m * g * tan(theta) * r)/m) where g is the acceleration due to gravity and theta is the angle of the banking. Calculating the values gives:
v = sqrt((1250 kg * 9.8 m/s^2 * tan(14°) * 72 m)/1250 kg) = 18.9 m/s
b) The friction force acting on the car can be calculated using:
Friction force = m * g * sin(theta)
where m is the mass, g is the acceleration due to gravity, and theta is the angle of the banking. Calculating the values gives:
Friction force = 1250 kg * 9.8 m/s^2 * sin(14°) = 3035 N
c) The gravitational force acting on the car can be calculated using:
Gravitational force = m * g
where m is the mass and g is the acceleration due to gravity. Substituting the given value gives:
Gravitational force = 1250 kg * 9.8 m/s^2 = 12250 N
d) The normal force exerted on the car can be calculated using:
Normal force = m * g * cos(theta)
where m is the mass, g is the acceleration due to gravity, and theta is the angle of the banking. Calculating the values gives:
Normal force = 1250 kg * 9.8 m/s^2 * cos(14°) = 11950 N