6.9
항력과 종단 속도
일상생활에서 흥미로운 힘은 물체가 유체 속에서 움직일 때 물체를 끄는 힘입니다. 마찰과 마찬가지로 항력은 항상 물체의 움직임에 반대됩니다. 단순한 마찰과 달리 항력은 해당 유체에 있는 물체의 속도의 일부 함수에 비례합니다. 이 기능은 복잡하며 물체의 모양, 크기, 속도…
항력은 공기나 물과 같은 유체를 통해 물체의 움직임에 반대되는 바람직하지 않은 힘입니다.
작고 느리게 움직이는 개체의 경우 드래그 힘은 개체의 속도에 비례합니다.
더 크고 빠르게 움직이는 물체의 경우 항력은 물체 속도의 제곱, 유체 밀도, 물체의 단면적 및 항력 계수에 따라 달라집니다.
항력의 결과로, 유체 속에서 자유롭게 떨어지는 물체는 일정한 가속도를 나타내지 않습니다.
뉴턴의 제2법칙을 적용하면 물체에 작용하는 힘은 부력은 무시하고 중력과 항력입니다.
물체가 떨어지면 속도가 증가하고 결과적으로 중력의 균형을 이룰 때까지 항력도 증가하여 알짜 힘과 가속도가 0이 됩니다.
이 지점에서 가장 높은 등속을 말단 속도라고 하며, 이는 물체의 질량, 모양, 표면적, 떨어지는 유체의 밀도에 따라 달라집니다.
이러한 이유로 무거운 물체는 단자 속도가 더 빠르고 더 빨리 떨어집니다.
View the full transcript and gain access to JoVE Core videos
Q1: What is drag force and how does it differ from friction?
Drag force is an undesirable force that opposes an object's motion through a fluid like air or water. Unlike simple friction, drag force is proportional to some function of the object's velocity rather than being constant. For larger, faster-moving objects, drag force depends on the square of speed, fluid density, cross-sectional area, and drag coefficient.
Q2: Why does an object eventually stop accelerating when falling through a fluid?
As a falling object accelerates, drag force increases until it balances gravitational force, resulting in zero net force. At this equilibrium point, acceleration stops and the object reaches constant velocity. Applying second law motion under same acceleration principles, the forces become balanced, preventing further speed changes.
Q3: What is terminal speed and what factors determine it?
Terminal speed is the highest constant velocity an object reaches when falling through a fluid, occurring when drag force balances gravitational force. It depends on the object's mass, shape, surface area, and the density of the fluid. Heavier objects have higher terminal speeds and fall faster than lighter objects.
Q4: How does an object's shape and size affect its terminal velocity?
An object's shape and cross-sectional area significantly influence terminal velocity. A skydiver in a pike position minimizes area and reaches about 350 km/h, while spreading out increases drag and reduces terminal velocity to about 200 km/h. Smaller objects like squirrels reach terminal velocity quickly, protecting them from injury during short falls.
Q5: Why is drag force proportional to the square of speed for large, fast-moving objects?
For larger and faster-moving objects, drag force depends on the square of the object's speed, along with fluid density, cross-sectional area, and drag coefficient. This quadratic relationship means that doubling speed quadruples the drag force. This is why at highway speeds, over 50% of a car's power is used to overcome air drag.
Q6: How do athletes and engineers reduce drag force to improve performance?
Athletes and engineers seek to reduce drag force through aerodynamic shaping and minimizing cross-sectional area. Aerodynamic automobile design reduces drag and increases fuel efficiency, with the most fuel-efficient cruising speed around 70-80 km/h. Skydivers adjust body position to control drag and terminal velocity during descent.
Q7: Why does drag force depend differently on speed for small versus large objects?
For smaller, slowly moving objects, drag force is proportional to speed directly. For larger and faster-moving objects, drag force depends on the square of speed. This difference arises from the complex relationship between object shape, size, velocity, and fluid properties, making drag behavior fundamentally different across scales.