6.9
Fuerza de arrastre y velocidad terminal
Una fuerza interesante en la vida cotidiana es la fuerza de arrastre sobre un objeto cuando se mueve en un fluido. Al igual que la fricción, la fuerza…
La fuerza de arrastre es una fuerza indeseable que se opone al movimiento de un objeto a través de un fluido como el aire o el agua.
Para objetos más pequeños que se mueven lentamente, la fuerza de arrastre es proporcional a la velocidad del objeto.
Para objetos más grandes y que se mueven más rápido, la fuerza de arrastre depende del cuadrado de la velocidad del objeto, la densidad del fluido, el área de la sección transversal del objeto y el coeficiente de arrastre.
Como resultado de la fuerza de arrastre, un objeto que cae libremente en un fluido no exhibe una aceleración constante.
Aplicando la segunda ley de Newton, las fuerzas que actúan sobre el objeto son gravitacionales y de arrastre, ignorando la fuerza de flotación.
A medida que el objeto cae, su velocidad aumenta y, como resultado, la fuerza de arrastre también aumenta hasta que equilibra la fuerza gravitatoria, lo que resulta en una fuerza neta y una aceleración nulas.
La velocidad constante más alta en este punto se denomina velocidad terminal, que depende de la masa, la forma y el área de superficie del objeto y de la densidad del fluido a través del cual cae.
Por esta razón, los objetos más pesados tienen una velocidad terminal más alta y caen más 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.