Question

Is it safe to drive your 1600-kg car at a speed 27 m/s around a level highway curve of radius 150 m if the effective coefficient of static friction between teh car and the road is 0.40? Use the method outlined below in bold to solve the problem: (Please show all work/explanations)

Visual Representation: Sketch the Situation described in the problem

Physical Situation: Write in words any assumptions made regarding objects and interactions

Physical Representation: Indicate the direction of acceleration

Physical Representation: Draw a free-body diagram of the system. Check for consistency w/the physical situation including direction of $\aa$ and summation of force

Math Representation: Apply Newton's Second Law in radial form. Check for consistency with your physical representation as well as the physical situation

Solve adn Evaluate: Determine the speed of the car for the conditions given. Decide if your answer is reasonable

Answer 1

Answer 2

The centripetal force acting on a car is E_c = mv^2/r = 1600 times 27^2/150 = 7776N The frictionless force acting on the car is f = mu mg = 0.4 times 1600 times 9.8 = 6272 N F_c > f The centripetal force is greater than the frictional force This is a force This is a false.