Answer :
Final answer:
The car's acceleration during braking is 17.64 m/s^2. When wings increase the downwards force by 4000 N, the maximum braking force is 16020 N, giving an acceleration during braking of 32.04 m/s^2.
Explanation:
The problem can be approached using Newton's second law of motion and the equation of Friction. The car's weight (force due to gravity) is the mass (500 kg) multiplied by the acceleration due to gravity (9.8 m/s^2), giving 4900 N. The maximum force of static friction, Fmax, can be calculated as the coefficient of static friction (1.8) multiplied by the normal force, which is the weight of the car. Therefore, Fmax = 1.8 * 4900 = 8820 N. This is the force that is responsible for the acceleration during braking. Applying Newton's second law, F = ma, where F is the force and m is the mass, the acceleration a = F/m = 8820N / 500kg = 17.64 m/s^2.
When the car has wings increasing the downward force by 4000 N, the total downward force becomes 4900N + 4000N = 8900N. The maximum braking force can then be calculated as the coefficient of static friction multiplied by this new normal force, 1.8 * 8900N = 16020N. The deceleration during braking with the wings is then 16020N / 500kg = 32.04 m/s^2.
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