Final answer:
The maximum deceleration of a car on a slope is influenced by the coefficient of static friction, with different values for dry concrete, wet concrete, and ice. These coefficients are crucial to prevent slipping and to understand the car's behavior under different road conditions.
Step-by-step explanation:
The student's question involves determining the maximum deceleration of a car on a slope with different road conditions, considering the coefficient of friction. To solve this, we must consider the physics concepts of friction, forces on an incline, and Newton's second law of motion. The coefficient of static friction (μs) plays a crucial role as it prevents the tires from slipping while the car decelerates.
Firstly, we identify the forces acting on the car: gravitational force down the slope and the frictional force that opposes this motion due to deceleration. The net force is the component of gravitational force along the slope minus the frictional force. Using the equation Fnet = ma, and noting that the frictional force is μs multiplied by the normal force, we can set up and solve equations to find the maximum deceleration for each surface condition:
- On dry concrete: The friction coefficient is typically between 0.6 and 0.85.
- On wet concrete: This coefficient is lower, commonly around 0.2 to 0.3.
- On ice: Given in the scenario as μs = 0.100, we can proceed with the calculation for this specific value.
By substituting the known values and slope angle into the equations, and solving for the maximum deceleration, we can compare the results for different coefficients of friction to understand how they influence the deceleration on various surfaces. It's important to note that any coefficient of friction greater than 1 is unreasonable, as it implies a frictional force greater than the normal force.