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Question 1 of 15

1. Which of the following variables are known?

Question 1 of 15

Question 2 of 15

2. What type of motion is the one seen in this excercise?

Question 2 of 15

Question 3 of 15

3. What type of acceleration can be studied in this excercise?

Question 3 of 15

Question 4 of 15

4. Why should we use the following coordinate system?

 

Question 4 of 15

Question 5 of 15

5. We want the minimum bank angle for the car not to slide. First, we know that if the car moves in a circle; the car has a centripetal acceleration. Now, consider where the car will go if it has a high speed or a slow speed, up or down the curve? What do you think would happen if there is no bank inclination (the angle is 0\(^o\)) or if it has a bigger angle? Taking all of this process into consideration which of the following statements are true?

Question 5 of 15

Question 6 of 15

6. Which newton laws can be seen in this problem?

Question 6 of 15

Question 7 of 15

7. The prompt states two cases: with no friction and a static friction coefficient of 0.2 between the tires and the pavement. So, let's found a general equation with \(\mu_s\geq 0\); then, (\f_r\geq 0\). Taking this condition, which of the following forces diagram is correct?

Question 7 of 15

Question 8 of 15

8. Take into account the coordinate system. Which of the following equations best describe the force diagram?

Question 8 of 15

Question 9 of 15

9. Take the coordinate system and replace the decomposed values in terms of \(N\) and \(f_r\). Then replace with the definition of the centripetal acceleration and the friction force in the X net forces equation. Which of the following equations is equivalent to yours?

Question 9 of 15

Question 10 of 15

10. We have all the numeric values of the last equation. Then, we can solve for \(\theta\) to find the minimum bank angle necessary for the car not to slide.

Question 10 of 15

Question 11 of 15

11. Take the coordinate system and replace the decomposed values in terms of \(N\) and \(f_r\). Then, replace with the definition of the weight and friction force in the Y net forces equation. Which of the following equations for \(N\) is equivalent to yours?

Question 11 of 15

Question 12 of 15

12. Replace the equation for \(N\) we just found in the Y net force equation. Then, use trigonometric identities to obtain an equation for \(\tan\theta\). Which of the following equations is equivalent to yours? (Hint: Try to convert all the \(\sin\theta\) and \(\cos\theta\) into \(\tan\theta\). Remember that \(\tan\theta=\frac{\sin\theta}{\cos\theta}\)).

Question 12 of 15

Question 13 of 15

13. Taking into account the last equation, which of the following statements are true?

Question 13 of 15

Question 14 of 15

14. Let's remember that the prompt states two cases (a) assuming there is no friction with the pavement and (b) assuming a static friction coefficient between the tires and the pavement of 0.2. We already solve for (b), where we will replace 0.2 for the \(\mu\) value. However, what should we do for part (a)?

Question 14 of 15

Question 15 of 15

15. Replace the numerical values in each case; remember to consider the difference between radians and degrees. The bank angle necessary for the car to not slide, assuming there is no friction with the pavement, is \(^o\). On the other hand, the minimum bank angle necessary for the car to not slide, assuming there is a static friction coefficient between the tires and the pavement, is \(^o\).

Question 15 of 15