15. A car is navigating a banked turn. As shown below, the road surface is tilted at an angle from the horizontal; the car's path is a portion of a horizontal circle. Overhead View From Behind Car R If the car's speed is v1₁, the car can navigate a turn with radius R without requiring friction to keep it from slipping; at this speed the normal force acting on the car has a magnitude is n₁. If the car's speed is smaller than v₁ and it navigates the turn with radius R without slipping, the friction force acting on the car and the normal force (Choose the answer that best fills in both blanks; hint: consider the case in which the new speed is much smaller than v₁.) A) has a magnitude of zero ... is smaller than ₁ B) is directed down the slope... is larger than 1 C) is directed up the slope... is larger than ₁ D) is directed up the slope... is smaller than ₁ Exis directed down the slope... is smaller than ₁ Sxis Car would tend to slide down 149 50 up the slope
15. A car is navigating a banked turn. As shown below, the road surface is tilted at an angle from the horizontal; the car's path is a portion of a horizontal circle. Overhead View From Behind Car R If the car's speed is v1₁, the car can navigate a turn with radius R without requiring friction to keep it from slipping; at this speed the normal force acting on the car has a magnitude is n₁. If the car's speed is smaller than v₁ and it navigates the turn with radius R without slipping, the friction force acting on the car and the normal force (Choose the answer that best fills in both blanks; hint: consider the case in which the new speed is much smaller than v₁.) A) has a magnitude of zero ... is smaller than ₁ B) is directed down the slope... is larger than 1 C) is directed up the slope... is larger than ₁ D) is directed up the slope... is smaller than ₁ Exis directed down the slope... is smaller than ₁ Sxis Car would tend to slide down 149 50 up the slope
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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could explain the answer, and what happens when if car's speed is greater than v1, what happen to friciton force and the normal force
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**Topic: Physics of Banked Turns**
A car is navigating a banked turn. As illustrated in the accompanying diagrams, the road surface is tilted at an angle \( \theta \) from the horizontal, and the car's path forms part of a horizontal circle.
**Diagram Explanation:**
- **Overhead View:** Shows the car moving along a curved path with velocity \( v \) at a radius \( R \).
- **Side View:** Displays the car on a slope inclined at angle \( \theta \).
**Problem Statement:**
If the car's speed is \( v_1 \), it can navigate a turn with radius \( R \) without needing friction to prevent slipping. At this speed, the normal force on the car is \( n_1 \). If the car's speed is less than \( v_1 \) and it travels the turn with radius \( R \) without slipping, we need to determine the direction and magnitude of the friction force and how the normal force changes.
**Options (select the best for both blanks):**
- **A:** The friction force has a magnitude of zero ... normal force is smaller than \( n_1 \).
- **B:** The friction force is directed down the slope ... normal force is larger than \( n_1 \).
- **C:** The friction force is directed up the slope ... normal force is larger than \( n_1 \).
- **D:** The friction force is directed up the slope ... normal force is smaller than \( n_1 \). *(Correct Answer)*
- **E:** The friction force is directed down the slope ... normal force is smaller than \( n_1 \).
**Explanation:**
When the car's speed is smaller than \( v_1 \), it tends to slide down the slope, so the frictional force must act up the slope to prevent this slipping. Therefore, the normal force is reduced since the centripetal force needed is less. The correct option is D, as noted: "Car would tend to slide down so \( f_s \) is up the slope."
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