A car (m = 1540 kg) is parked on a road that rises 18.9 ° above the horizontal. What are the magnitudes of (a) the normal force and (b) the static frictional force that the ground exerts on the tires?
Wc = mg = 1540kg * 9.8N/kg = 15,092 N. = Wt of car.
Fc = 15092N. @ 18.9 Deg.
Fp = 15092*sin18.9 Deg. = 4889 N. = Force parallel to road.
a. Fv = 15092*cos18.9 = 14,278 N. = Force perpendicular to road = The normal.
b. Fn = Fp - Fs = 0,
4889 - Fs = 0,
Fs = 4889 N. = Force of static friction.
To find the magnitudes of the normal force and the static frictional force exerted on the car, we will use the concepts of inclined planes and Newton's laws of motion.
(a) The normal force (N) is the perpendicular force exerted by the ground on the car. It acts in the vertical direction and prevents the car from sinking through the ground. In this case, the normal force will be less than the weight of the car due to the inclined road.
To calculate the normal force, we can use the relation:
N = mg * cos(θ)
where m is the mass of the car (1540 kg), g is the acceleration due to gravity (approximately 9.8 m/s²), and θ is the angle of the inclined road (18.9°).
Substituting the given values into the equation:
N = (1540 kg) * (9.8 m/s²) * cos(18.9°)
Calculating this expression will give you the magnitude of the normal force exerted on the car.
(b) The static frictional force (f_s) is the force that acts parallel to the inclined road's surface, preventing the car from sliding down the hill. It is determined by the coefficient of static friction (μ_s) and the normal force (N). The equation is given by:
f_s ≤ μ_s * N
where μ_s is the coefficient of static friction.
In this case, we need to find the maximum value possible for the static frictional force since the car is parked and not sliding. This maximum value occurs when the static friction is at its limit, which is when the car is about to slide.
Given that the car is not sliding, the static frictional force (f_s) equals the maximum static frictional force (f_s_max). Therefore, we can rewrite the equation as:
f_s_max = μ_s * N
To find the magnitude of the maximum static frictional force, substitute the calculated value of N from part (a) into this equation and multiply it by the coefficient of static friction (μ_s).
By following these steps, you will be able to find the magnitudes of both the normal force and the maximum static frictional force exerted on the car.