A banked curve is safer than a flat curve because ...

Question

BlackTom AI · Accepted Answer

On a banked curve the normal force has a horizontal component that can provide the required centripetal force.

Relevant concepts:
- Centripetal force: an inward (horizontal) net force m v^2 / r is required for circular motion of radius r at speed v.
- Forces on a car on a banked road: weight mg (vertical downward), normal force N (perpendicular to the road surface), and possibly friction. Decomposing N yields vertical and horizontal components.

Step-by-step reasoning and calculations:
1. Take the banking angle as θ measured from horizontal. Decompose the normal force:
   - Vertical component: N cosθ (upward)
   - Horizontal component: N sinθ (points toward center of the curve)
2. If the car is not accelerating vertically, vertical forces balance:
   N cosθ = mg  ->  N = mg / cosθ
3. The horizontal (centripetal) requirement is:
   m v^2 / r = N sinθ
   Substitute N from step 2:
   m v^2 / r = (mg / cosθ) sinθ = mg tanθ
4. Solve for v^2:
   v^2 = r g tanθ
This shows explicitly that the horizontal component of the normal force (N sinθ) supplies the centripetal force needed for turning without relying entirely on friction.

Why the correct answer is correct:
Because the normal force is tilted on a banked surface, its horizontal component provides inward force, reducing the dependence on friction and allowing safer turns at a given speed.

Why the other options are incorrect:
- a. Speed limits being larger is a policy/engineering choice, not the physical reason; physics explains why higher safe speeds are possible, but the statement as written is not the reason.
- b. Banking does not increase the coefficient of friction; it reduces reliance on friction by providing a horizontal force component.
- d. A centripetal force is still required; banking does not eliminate the need for it, it supplies part of it via N.

Conclusion: The correct answer is (c) the normal force contributes to the centripetal force. This matches the provided answer.

A banked curve is safer than a flat curve because ...单项选择题

类似问题

A 905 kg car is driving in a roundabout on a frictionless banked track as shown in the diagram below.The angle of banking, [math: θ=15.4∘].What is the magnitude of the centripetal force acting on the car?*Hint: Break [math: FN] into components

A 917.4 kg car is driving in a roundabout on a frictionless banked track as shown in the diagram below.The angle of banking, [math: θ=16.2∘].What is the magnitude of the centripetal force acting on the car?*Hint: Break [math: FN] into components

A 965.8 kg car is driving in a roundabout on a frictionless banked track as shown in the diagram below.The angle of banking, [math: θ=14.8∘].What is the magnitude of the centripetal force acting on the car?*Hint: Break [math: FN] into components

A student ties a rock to a string then spins the rock in a vertical circular motion at constant speed. The tension in the string:

A man is moving in a horizontal circular motion in the air. The man is tied by a rope that is angled at 300 to the vertical. The rope provides ..

On a banked curve, the force(s) that provide(s) the centripetal force for a turning car is (are)

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单