A 1,660 kg car is parked on a hill with a slope of 8.0°. Its brakes and transmission are locked in position to keep the car from rolling. The coefficient of static friction of the rubber tires on the asphalt road is 0.14. What is the force of static friction between the tires and the road?
F(fr) =μ(s) •m•g•cosα
To find the force of static friction between the tires and the road, we need to use the formula for static friction:
Fs = μs * N
Where Fs is the force of static friction, μs is the coefficient of static friction, and N is the normal force.
First, we need to find the normal force. The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the weight of the car is the force that is supported by the road surface.
The weight of the car can be calculated using the formula:
W = m * g
Where W is the weight of the car, m is the mass of the car, and g is the acceleration due to gravity (approximately 9.8 m/s^2).
In this case, the mass of the car is given as 1,660 kg. So, we can calculate the weight of the car as:
W = 1,660 kg * 9.8 m/s^2
Next, we need to calculate the vertical component of the weight due to the slope of the hill. The vertical component of the weight can be calculated using the formula:
W_vertical = W * sin(θ)
Where θ is the angle of the slope of the hill.
In this case, the angle of the slope is given as 8.0°. So, we can calculate the vertical component of the weight as:
W_vertical = W * sin(8.0°)
Now, we can calculate the normal force by subtracting the vertical component of the weight from the weight of the car:
N = W - W_vertical
Finally, we can calculate the force of static friction, using the coefficient of static friction and the normal force:
Fs = μs * N
Substituting the values into the formula, we can find the force of static friction between the tires and the road.