The magnitude of the horizontal acceleration during skidding, as the car slows down, is approximately 6.88 m/s². This value is determined by the frictional force opposing the car's motion on the road surface.
Calculating the Horizontal Acceleration during Skidding
Determine the magnitude of your horizontal acceleration as you begin to slow down:
1. Identify the forces acting on the car:
Weight (mg): The downward force of gravity acting on the car, where m is the car's mass (1800 kg) and g is the acceleration due to gravity (9.81 m/s²).
Normal force (N): The force exerted by the road surface supporting the car, perpendicular to the road. At the summit, the normal force is equal to the weight (mg).
Frictional force (f): The force opposing the car's motion due to friction between the tires and the road. It acts parallel to the road surface in the direction opposite to the car's motion.
2. Calculate the frictional force:
The frictional force (f) is given by:
f = μ * N
where μ is the coefficient of kinetic friction (0.75) and N is the normal force.
Substituting the values, we get:
f = 0.75 * (1800 kg * 9.81 m/s²) ≈ 12375 N
3. Determine the horizontal acceleration:
Since the car is skidding at the summit, there is no vertical acceleration. Therefore, the frictional force provides the entire horizontal acceleration (a).
a = f / m
Plugging in the values, we obtain:
a = 12375 N / 1800 kg ≈ 6.88 m/s²
4. Magnitude of horizontal acceleration:
The magnitude of the horizontal acceleration is the absolute value of a:
|a| = |6.88 m/s²| ≈ 6.88 m/s²
Therefore, the magnitude of your horizontal acceleration as you begin to slow down is approximately 6.88 m/s².