Multiple-Concept Example 17 reviews the basic concepts involved in this problem.
ID: 2117675 • Letter: M
Question
Multiple-Concept Example 17 reviews the basic concepts involved in this problem. Air rushing over the wings of high-performance race cars generates unwanted horizontal air resistance but also causes a vertical downforce, which helps cars hug the track more securely. The coefficient of static friction between the track and the tires of a 738-kg car is 0.908. What is the magnitude of the maximum acceleration at which the car can speed up without its tires slipping when a 3000-N downforce and an 1360-N horizontal air resistance force act on it?Explanation / Answer
The coefficient of static friction is 0.908. This means the car will begin to slip when the tangential force is 0.908 times the force normal to the track.
The normal force due to the weight of the car is mg = 738 kg * 9.81 m/s^2 =7249.78N
Add the downward force from the airfoil and we get 10249.78 N.
The car begins to slip when the lateral force is 10249.78N * 0.908 = 9306.8N.
When the car is accelerating, the tires are applying lateral force against the track, which will be a maximum of 9306.8 N. This force, transmitted to the car, is opposed by wind resistance. The net force on the car is thus 9306.8 - 1360 = 7946.8N.
The acceleration of the car is given by a=F/m = 7946.8/738 = 10.76 m/s^2
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