Calculate the maximum deceleration of a car that is heading down a 30.0° slope (one that makes
an angle of 30° 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 coefficient of static friction is
involved—that is, the tires are not allowed to slip during the deceleration. Calculate for a car:
(a) On dry concrete. (b) On wet concrete. (c) On ice, assuming that μs = 0.100, the same as for
shoes on ice. (The last answer will be positive; this means that you can't stop the car, you can only
reduce the downhill acceleration.)
To calculate the maximum deceleration of a car on different road conditions, we need to use the concept of friction. Friction is the force that opposes the motion or tendency of motion between two surfaces in contact.
The maximum deceleration can be calculated using the formula: a = μs * g
Where:
a = acceleration (deceleration in this case)
μs = coefficient of static friction
g = acceleration due to gravity (approximately 9.8 m/s^2)
Now we can calculate the maximum deceleration for each road condition:
(a) On dry concrete:
For dry concrete, the coefficient of static friction for a typical car tire is around 0.7. So, μs = 0.7.
a = 0.7 * 9.8
a ≈ 6.86 m/s^2
Therefore, the maximum deceleration on dry concrete is approximately 6.86 m/s^2.
(b) On wet concrete:
For wet concrete, the coefficient of static friction is significantly reduced. Let's assume μs = 0.4.
a = 0.4 * 9.8
a ≈ 3.92 m/s^2
Therefore, the maximum deceleration on wet concrete is approximately 3.92 m/s^2.
(c) On ice:
On ice, the coefficient of static friction is given as μs = 0.100.
a = 0.100 * 9.8
a ≈ 0.98 m/s^2
Therefore, on ice, the maximum deceleration is approximately 0.98 m/s^2. Note that the result is positive, meaning that it is not possible to fully stop the car on icy surfaces, only reduce the downhill acceleration.
Remember that these calculations assume ideal conditions and evenly distributed weight on all four tires. The actual deceleration experienced by a car may vary depending on various factors like tire condition, braking systems, and road surface conditions.