When Should Air Resistance Be Considered in Free-Fall Calculations?

  • Thread starter hainam0101
  • Start date
In summary, when solving free-fall problems near Earth, it is important to remember that air resistance may play a significant role. To determine when it is valid to ignore the effects of air resistance, realize that air resistance increases with increasing speed. Thus, as an object falls and its speed increases, its downward acceleration decreases. Under these circumstances, the object's speed will approach a limit, a value called its terminal speed. This terminal speed depends upon such things as the mass and cross-sectional area of the body. Upon reaching its terminal speed, its acceleration is zero.
  • #1
hainam0101
2
0

Homework Statement


When we solve free-fall problems near Earth, it's important to remember that air resistance may play a significant role. If its effects are significant, we may get answers that are wrong by orders of magnitude if we ignore it. How can we tell when it is valid to ignore the effects of air resistance? One way is to realize that air resistance increases with increasing speed. Thus, as an object falls and its speed increases, its downward acceleration decreases. Under these circumstances, the object's speed will approach a limit, a value called its terminal speed. This terminal speed depends upon such things as the mass and cross-sectional area of the body. Upon reaching its terminal speed, its acceleration is zero. For a "typical" skydiver falling through the air, a typical terminal speed is about 51.6 m/s (roughly 116 mph). At half its terminal speed, the skydiver's acceleration will be about 3/4 g. Let us take half the terminal speed as a reasonable "upper bound" beyond which we should not use our constant acceleration free-fall relationships.

(a) Assuming the skydiver started from rest, estimate how far, and for how long, the skydiver falls before we can no longer neglect air resistance.

Homework Equations



v2=v1 + a*(delta)t

The Attempt at a Solution


Still trying.
 
Physics news on Phys.org
  • #2
Your v2 equation looks great! Use it to find out when the velocity reaches 51.6/2.

It might be possible to get a more accurate answer by guessing how the acceleration changes, possibly saying a = 9.81 - kt and finding what value of k gives you that 3/4g value. But I doubt if you are expected to get into this "2nd order approximation" business.
 
  • #3
the acceleration is decreasing. so what a value should i use to apply into that v2 equation.
 
  • #4
I would just use 9.81.
I mentioned how you would go about making a better estimate, but doubt if you are expected to do that.
 

FAQ: When Should Air Resistance Be Considered in Free-Fall Calculations?

What is the problem you need help with?

The first and most common question when someone asks for help is to identify the specific problem that they need assistance with. This helps to provide a clear understanding of the issue at hand and allows others to provide targeted help.

What have you already tried to solve the problem?

Knowing what steps have already been taken to address the problem can help others provide more efficient and effective assistance. It also prevents others from suggesting solutions that have already been attempted.

What type of help do you need?

Some people may need guidance or advice, while others may need someone to physically help them solve the problem. Clarifying the type of help needed can aid in finding the right resources or individuals to assist.

What are the specific details of the problem?

Providing specific details about the problem, such as error messages or specific symptoms, can help others understand the problem better and provide more targeted solutions.

What is the urgency of the problem?

Understanding the urgency of the problem can help prioritize and expedite the assistance. If the problem is time-sensitive, it may require immediate attention, while less urgent problems can be addressed at a later time.

Similar threads

Back
Top