Final answer:
The maximum braking force of a race car can be calculated using the coefficient of static friction and the normal force, which leads to calculations for acceleration both with and without additional forces like wings or while skidding. The example showcases the effect of static vs. kinetic friction on stopping distances.
Step-by-step explanation:
Calculating Braking Force and Acceleration for a Race Car The problem involves physics concepts, such as friction, acceleration, and force. We are given that the race car has a mass of 500 kg and a coefficient of static friction (μs) of 1.8, which will allow us to calculate the braking force and acceleration. a. The maximum braking force (Static Friction) is found by multiplying the coefficient of static friction by the normal force, which is the weight of the car (mg). So, Fmax = μs × mg = 1.8 × 500 kg × 9.8 m/s2 = 8820 N. b. The acceleration (a) of the car during braking can be calculated using Newton's second law (F = ma). Therefore, a = Fmax / m = 8820 N / 500 kg = 17.64 m/s2. c. When wings add an additional downward force of 4000 N, the total normal force increases to the weight of the car plus the downward force from the wings (N = mg + 4000 N). The new maximum braking force is μs × (mg + 4000 N) = 1.8 × (500 kg × 9.8 m/s2 + 4000 N) = 16020 N. The new acceleration is 16020 N / 500 kg = 32.04 m/s2. d. If the car skids, we use the coefficient of Kinetic Friction (μk), which is 1.2. The kinetic frictional force is F k = μk × mg = 1.2 × 500 kg × 9.8 m/s2 = 5880 N, and the acceleration during skidding is 5880 N / 500 kg = 11.76 m/s2. This explains the importance of avoiding skidding, as higher acceleration (and therefore a higher force) can be applied when the tires do not skid, leading to a shorter stopping distance