Calculate the maximum deceleration of a car that is heading down a 14.5° slope (one that makes an angle of 14.5° with the horizontal) under the following road conditions. You may assume that the weight of the car is evenly distributed on all four tires and that the static coefficient of friction is involved--that is, the tires are not allowed to slip during the deceleration.
(a) on dry concrete
m/s2
(b) on wet concrete
m/s2
(c) on ice, assuming that µs = 0.100, the same as for shoes on ice
m/s2
Additional Materials
To calculate the maximum deceleration of a car on a slope, we need to consider the forces acting on the car.
The forces acting on the car are:
1. Weight (mg): This force acts vertically downward and is given by the equation F = mg, where m is the mass of the car and g is the acceleration due to gravity (9.8 m/s^2).
2. Normal force (N): This force acts perpendicular to the slope and is equal in magnitude but opposite in direction to the component of the weight that is perpendicular to the slope. It can be calculated using the equation N = mg * cos(θ), where θ is the angle of the slope.
The maximum deceleration is determined by the force of friction between the tires and the road surface. The force of friction can be calculated using the equation F_friction = μs * N, where μs is the coefficient of static friction, and N is the normal force.
Now let's calculate the maximum deceleration for each road condition:
(a) Dry concrete:
The coefficient of static friction for dry concrete is typically around 0.7.
First, calculate the normal force:
N = mg * cos(θ)
= (mass of car) * (acceleration due to gravity) * cos(14.5°)
Then, calculate the maximum deceleration:
Deceleration = F_friction / (mass of car)
= (μs * N) / (mass of car)
= (0.7 * N) / (mass of car)
(b) Wet concrete:
The coefficient of static friction for wet concrete is typically lower than for dry concrete, let's assume it is around 0.5.
First, calculate the normal force (same as in part (a)).
Then, calculate the maximum deceleration as we did above, using the coefficient of static friction of 0.5.
(c) Ice:
The given coefficient of static friction μs = 0.100.
First, calculate the normal force (same as in part (a)).
Then, calculate the maximum deceleration using the coefficient of static friction of 0.100.
Note: The answer will depend on the mass of the car. Make sure to input the correct mass of the car in kilograms when substituting values into the equations.