(II) Drag-race tires in contact with an asphalt surface have a very high coefficient of static friction. Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 1.0 km in 12 s, starting from rest.
Solution 44P: We have to calculate the value of coefficient of static friction whose value depends upon the nature of the surface in contact and independent to applied force, as per the given situation. Step 1 of 3 Concept: Newton’s second law: The net force F acting on an object of mass m produces an acceleration a in that object. Mathematically, F= ma. Frictional force also acts on the surface of the bodies in contact whenever their is relative motion between between the two bodies. Step 2 of 3 Distance covered by the racer, s = 1000 m Time taken, t = 12 s Initial velocity of car, u = 0 m/s For determining acceleration, using second kinematical equation, we get, 1 2 s = ut + 2t 2 1000 = 0×12 + 0.5×a×12 1000 × 2 2 a = 12×12 m/s 2 a = 13.89 m/s 2 Therefore tyre was moving with constant acceleration of a = 13.89 m/s .