Free-falling body subject to air resistance

In summary, if a free-falling body is not subject to air resistance, there is a linear relationship between velocity and time, with a constant slope representing the increase in velocity over time. However, when air resistance is taken into account, the acceleration will decrease until the terminal velocity is reached, resulting in a curve with a decreasing slope that eventually flattens out to a constant velocity. This is correct for heavy objects with large surface areas, but may look different for lighter objects such as feathers. The difference in air resistance for different objects can be represented by different equations, such as f= -mg or f= -mg+ kv2.
  • #1
polyperson
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If a free-falling body is not subject to air resistance, there is a linear relationship between v and t giving a line with constant slope (g) showing velocity increasing with time.

If air resistance is taken into account, my guess is that acceleration will decrease until the terminal velocity is reached (i.e. where air resistance = weight of body) giving a curve with decreasing slope which flattens out to constant velocity.

Is this correct or am I barking up the wrong tree? I made certain assumptions i.e that the body is heavy with a large surface area. I know that the curve for a feather would look different!
 
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  • #2
polyperson said:
If a free-falling body is not subject to air resistance, there is a linear relationship between v and t giving a line with constant slope (g) showing velocity increasing with time.
If air resistance is taken into account, my guess is that acceleration will decrease until the terminal velocity is reached (i.e. where air resistance = weight of body) giving a curve with decreasing slope which flattens out to constant velocity.
Is this correct or am I barking up the wrong tree? I made certain assumptions i.e that the body is heavy with a large surface area. I know that the curve for a feather would look different!
Yes, that's correct. You can't be a whole lot more precise. For small objects, the air-resistance is reasonably close to being proportional to the speed: instead of f= -mg you have f= -mg- kv. For larger objects, such as your feather, it's closer to being proportional to v2: f= -mg+ kv2. (The difference in sign is to keep the air resistance upward. If a body is falling downward, v is negative but v2 is positive.)
 
  • #3
Many thanks for that
 

1. What is a free-falling body?

A free-falling body is an object that is only under the influence of gravity and is not experiencing any other external forces, such as air resistance or propulsion. In this state, the only force acting on the object is its weight, causing it to accelerate towards the ground at a constant rate of 9.8 m/s².

2. How does air resistance affect a free-falling body?

Air resistance, also known as drag, is a force that opposes the motion of an object through air. As a free-falling body moves through the air, it experiences an upward force due to air resistance, which increases as the object's speed increases. This causes the object to reach a terminal velocity, where the force of air resistance is equal to the force of gravity, resulting in a constant velocity.

3. What factors affect the amount of air resistance on a free-falling body?

The amount of air resistance on a free-falling body is affected by several factors, including the shape, surface area, and speed of the object. Objects with a larger surface area or a less streamlined shape will experience more air resistance, while objects with a smaller surface area or a more aerodynamic shape will experience less air resistance. Additionally, the faster an object is falling, the greater the air resistance it will experience.

4. Does air resistance always slow down a free-falling body?

No, air resistance does not always slow down a free-falling body. As mentioned earlier, once a free-falling body reaches its terminal velocity, the forces of air resistance and gravity are balanced, resulting in a constant velocity. Therefore, the object will continue to fall at this constant velocity until an external force acts upon it.

5. How is air resistance calculated for a free-falling body?

The calculation of air resistance on a free-falling body involves various equations and factors, including the object's mass, speed, and surface area, as well as the density and viscosity of the air. This can be a complex calculation and is often simplified for practical purposes, such as in introductory physics classes. However, advanced calculations can be used for more precise measurements in scientific experiments.

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