Finding cross-sectional area from terminal velocity.

Click For Summary
SUMMARY

The discussion centers on calculating the cross-sectional area of a person based on their terminal velocity of 56 m/s and the relationship between aerodynamic drag and velocity. The drag force (D) is proportional to the product of the cross-sectional area (A) and the square of the velocity (v^2). To estimate A, one must equate the drag force to the gravitational force (mg), but the lack of specific values for mass and drag coefficient complicates the calculation. The textbook answer provided is 0.6 m², suggesting that additional parameters such as the density of air and the drag coefficient are essential for an accurate estimation.

PREREQUISITES
  • Understanding of terminal velocity and its implications in physics.
  • Familiarity with the drag force equation D = Av².
  • Knowledge of gravitational force and its relation to mass (mg).
  • Basic concepts of drag coefficients for various shapes.
NEXT STEPS
  • Research the drag coefficient for different body shapes and its impact on calculations.
  • Learn about the relationship between mass, density, and cross-sectional area in fluid dynamics.
  • Explore the effects of air density on terminal velocity calculations.
  • Study the principles of estimating parameters in physics problems with limited information.
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and fluid dynamics, as well as educators seeking to clarify concepts related to terminal velocity and drag forces.

mgsk
Messages
3
Reaction score
0

Homework Statement



The aerodynamic drag on an object moving through air is proportional to Av^2, where A=cross-section, and v=velocity. The terminal velocity of a person without a parachute falling through the air is about 56m/s. Estimate the area of the cross-section of a person seen from the front.

Homework Equations


The Attempt at a Solution



I'm quite flummoxed by this one. We're told only that drag is propotional to Av^2. Anyway, I began by saying that for terminal velocity to be reached, the drag-force must equal the gravity-force, i.e. D = mg. But, I'm unsure how to proceed from there. I'm not told the mass of the person, nor the drag coefficient, so I really don't know how to find A. I'm sure the use of the word "estimate" here is significant. Maybe I'm expected to find the average human mass, and use that, but then that leaves me still without a complete equation, as I'm told the two are proportional.

The answer given in the textbook is 0.6m^2.

Help?
 
Physics news on Phys.org
You certainly have not been given enough information. As it happens, the drag coefficient for an arbitrary convex body tends to be about 1, but you still need to bring in the mass of the person and the density of the air.
I suppose you could relate the mass of the person to the cross-sectional area, assuming the person's density to be that of water, but that isn't quite straightforward.
This link might help: http://en.wikipedia.org/wiki/Drag_coefficient
 
Cheers, haruspex. I'll have to speak with my physics tutor and see if there's something I'm overlooking. Damn the holidays.
 

Similar threads

Final Velocity of a car with a opposing decreasing drag force
  • · Replies 57 ·
2
Replies
57
Views
3K
Calculate terminal velocity when given cross sectional area
  • · Replies 6 ·
Replies
6
Views
4K
How do I find the terminal speed of a body in water?
  • · Replies 13 ·
Replies
13
Views
4K
Effect of Surface Area on the Drag Coefficient of a Parachute
  • · Replies 6 ·
Replies
6
Views
4K
Can terminal velocity be determined from the information given?
  • · Replies 7 ·
Replies
7
Views
721
Terminal velocity of a skier using a Momentum Balance
  • · Replies 1 ·
Replies
1
Views
2K
How come "terminal velocity" and "final velocity" are different?
  • · Replies 1 ·
Replies
1
Views
2K
Terminal Velocity's Relationship to Mass
  • · Replies 2 ·
Replies
2
Views
3K
High School How to find the objects' areas in this photo in mm^2?
  • · Replies 14 ·
Replies
14
Views
3K
Estimated terminal velocity significantly less than estimated impact velocity
  • · Replies 6 ·
Replies
6
Views
4K