question archive An automobile tire manufacturer wants to test a new brand of tires to see how well they grip the pavement

An automobile tire manufacturer wants to test a new brand of tires to see how well they grip the pavement

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An automobile tire manufacturer wants to test a new brand of tires to see how well they grip the pavement. For the test a professional driver drives in a circle with a radius of 40 m. The driver steadily accelerates until the car starts to skid. With these new tires, the car reaches a speed of 18 m/s before it starts to skid.

a)  (2 points) What type of friction is involved here (before the car skids), kinetic or static?

b)  (8 points) Draw a free-body diagram. In your diagram, indicate the direction that is towards the center of the circle.

c)  (10 points) Derive an equation for the coefficient of friction between the tires and the road, starting from Newton's Second Law.

d)  (5 points) What is the value of the coefficient of friction between the tires and the road?

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