Homework 12

# Homework 12 - sanchez(ds28677 homework 12 Turner(58220 This...

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sanchez (ds28677) – homework 12 – Turner – (58220) 2 top view R = 40 m 22 rear view μ = 0 . 62 How fast can the car take this curve without skidding to the outside of the curve? Correct answer: 23 . 1426 m / s. Explanation: Let : R = 40 m , θ = 22 , m = 1625 kg , and μ = 0 . 62 . Basic Concepts: (1) To keep an object moving in a circle requires a net force of magnitude F c = m a c = m v 2 r directed toward the center of the circle. (2) Static friction law: |F| ≤ μ N . Solution: Consider the free body diagram for the car. Looking from the rear of the car, we have: N F m g a c Let the x axis go parallel the highway sur- face , to the left and 22 below the horizontal, and let the y axis be perpendicular to the sur- face, 22 leftward from vertically up. The car’s centripetal acceleration is directed hor- izontally to the left, so in our coordinates it
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