4. The curves at NASCAR racetracks are banked so that a race car traveling at the correct speed can negotiate the turn without friction. Assume the track is banked at an angle 0 and the radius of the turn is R. a. What is the speed at which the car can negotiate the turn without friction? Think carefully about the direction of the acceleration.

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Author:Raymond A. Serway, Chris Vuille
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**Problem 4: NASCAR Racetrack Curves and Car Dynamics**

The curves at NASCAR racetracks are banked so that a race car traveling at the correct speed can negotiate the turn without friction. Assume the track is banked at an angle \( \theta \) and the radius of the turn is \( R \).

a. What is the speed at which the car can negotiate the turn without friction? *Think carefully about the direction of the acceleration.*

- **Diagram**: A car is shown on a banked curve with the angle of banking marked as \( \theta \) and the radius of the curve as \( R \).

b. Let the coefficient of static friction be \( \mu_s \). What is the maximum speed the car can negotiate this banked turn with such that it does not slip?

- **Diagram**: Another car diagram is similar to part (a) showing a banked turn with implied consideration of friction, denoted by \( \mu_s \).

**Explanations for Diagrams:**

- **Diagram for (a)**: Depicts a race car on a banked track without the influence of friction, showing the angle \( \theta \) and the curve radius \( R \).
- **Diagram for (b)**: Illustrates the scenario where friction plays a role, with the car still on a banked track, emphasizing the effect of static friction on the speed.
Transcribed Image Text:**Problem 4: NASCAR Racetrack Curves and Car Dynamics** The curves at NASCAR racetracks are banked so that a race car traveling at the correct speed can negotiate the turn without friction. Assume the track is banked at an angle \( \theta \) and the radius of the turn is \( R \). a. What is the speed at which the car can negotiate the turn without friction? *Think carefully about the direction of the acceleration.* - **Diagram**: A car is shown on a banked curve with the angle of banking marked as \( \theta \) and the radius of the curve as \( R \). b. Let the coefficient of static friction be \( \mu_s \). What is the maximum speed the car can negotiate this banked turn with such that it does not slip? - **Diagram**: Another car diagram is similar to part (a) showing a banked turn with implied consideration of friction, denoted by \( \mu_s \). **Explanations for Diagrams:** - **Diagram for (a)**: Depicts a race car on a banked track without the influence of friction, showing the angle \( \theta \) and the curve radius \( R \). - **Diagram for (b)**: Illustrates the scenario where friction plays a role, with the car still on a banked track, emphasizing the effect of static friction on the speed.
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