6.9
Força de Arrasto e Velocidade Terminal
Uma força interessante na vida cotidiana é a força de arrasto em um objeto quando ele está se movendo em um fluido. Assim como o atrito, a força de ar…
A força de arrasto é uma força indesejável que se opõe ao movimento de um objeto através de um fluido como ar ou água.
Para objetos menores e que se movem lentamente, a força de arrasto é proporcional à velocidade do objeto.
Para objetos maiores e em movimento mais rápido, a força de arrasto depende do quadrado da velocidade do objeto, da densidade do fluido, da área da seção transversal do objeto e do coeficiente de arrasto.
Como resultado da força de arrasto, um objeto caindo livremente em um fluido não exibe aceleração constante.
Aplicando a segunda lei de Newton, as forças que atuam sobre o objeto são gravitacionais e de arrasto, ignorando a força de empuxo.
À medida que o objeto cai, sua velocidade aumenta e, como resultado, a força de arrasto também aumenta até equilibrar a força gravitacional, resultando em força resultante e aceleração zero.
A velocidade constante mais alta neste ponto é chamada de velocidade terminal, que depende da massa, forma e área de superfície do objeto e da densidade do fluido pelo qual ele está caindo.
Por esse motivo, objetos mais pesados têm uma velocidade terminal mais alta e caem mais rápido.
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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.