A car weighing 2000 lbs is parked on a hillside in San Francisco at an angle of 55o
(relative to the ground). Approximately what is the minimum coefficient of static friction necessary to keep the car from sliding downhill?
Mc = 2000Lbs * 0.454kg/Lb = 908 kg = Mass of car.
Wc = m*g = 908kg * 9.8N/kg = 8898.4 N. = Wt. of car.
Fc = 8898.4 N @ 55o = Force of car.
Fp = 8898.4*sin55 = 7289 N. = Force parallel to hill.
Fv = 8898.4*cos55 = 5104 N. = Force
perpendicular to hill.
Fs = Force of static friction.
Fp-Fs = m*a.
7289 - Fs = m*0 = 0.
Fs = 7289 N.
Fs = uFv = 7289 N.
u*5104 = 7289
u = 1.43.
To determine the minimum coefficient of static friction required to prevent the car from sliding downhill, we need to analyze the forces acting on the car.
First, let’s break down the gravitational force acting on the car. We can resolve it into two components: the vertical component (mg*cosθ), which is counteracted by the normal force (N), and the horizontal component (mg*sinθ), which contributes to the force trying to slide the car downhill.
Next, consider the forces opposing the car from sliding downhill. We have the static friction force (fs) acting in the opposite direction of impending motion.
At the minimum, the static friction force (fs) must be equal to or greater than the force trying to slide the car downhill (mg*sinθ). Therefore, we can set up an equation:
fs ≥ mg*sinθ
Now, let’s plug in the given information:
fs ≥ (2000 lbs) * g * sin(55°)
To convert the weight from pounds to mass, we need to divide it by the acceleration due to gravity (g = 32.2 ft/s²):
fs ≥ (2000 lbs / 32.2 ft/s²) * (32.2 ft/s²) * sin(55°)
Simplifying:
fs ≥ 2000 * sin(55°)
Calculating:
fs ≥ 1712.4 lbs
Finally, since fs represents the static friction force, we can calculate the minimum coefficient of static friction (µs) required:
µs = fs / N
As the car is parked, the normal force (N) would be equal to the gravitational force (mg). So:
µs = fs / (mg)
Substituting the values:
µs = 1712.4 lbs / (2000 lbs)
Simplifying:
µs = 0.8562
Therefore, the minimum coefficient of static friction necessary to keep the car from sliding downhill is approximately 0.8562.