Estimate the terminal speed of a wooden sphere

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SUMMARY

The terminal speed of a wooden sphere with a density of 0.870 g/cm³, a radius of 8.50 cm, and a drag coefficient of 0.500 is calculated to be 56.8 m/s. The mass of the sphere is determined to be 2.24 kg, and the cross-sectional area is 0.0227 m². The calculations utilize the formula v_t = sqrt(2mg/(Dp_airA)), where Dp_air is the density of air at 1.20 kg/m³. Despite achieving this result, the user Mark reports discrepancies with WebAssign, indicating a potential error in the input or calculation process.

PREREQUISITES
  • Understanding of fluid dynamics principles, particularly terminal velocity.
  • Familiarity with the drag coefficient and its impact on falling objects.
  • Knowledge of basic physics equations related to mass, volume, and area.
  • Ability to perform calculations involving square roots and unit conversions.
NEXT STEPS
  • Review the derivation and application of the terminal velocity formula in fluid dynamics.
  • Explore the effects of varying drag coefficients on terminal speed for different shapes.
  • Investigate the impact of air density on falling objects and terminal velocity.
  • Learn about numerical methods for solving physics problems involving drag and terminal velocity.
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MetallicaFNum
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Homework Statement


(a) Estimate the terminal speed of a wooden sphere (density 0.870 g/cm3) falling through air, if its radius is 8.50 cm and its drag coefficient is 0.500. (The density of air is 1.20 kg/m3.)

(b) From what height would a freely falling object reach this speed in the absence of air resistance?


Homework Equations


m = p_sphere*V
A = pi*r^2
v_t= sqrt(2mg/Dp_airA)


The Attempt at a Solution


m = (870 kg/m^3)(4/3)pi(0.085 m)^3 = 2.24 kg
A = pi(0.085 m)^2 = 0.0227 m^2

v_t = sqrt[2(2.24 kg)(9.80 m/s^2)/(0.500)(1.20 kg/m^3)(0.0227 m^3)] = 56.8 m/s

WebAssign keeps telling me I'm within 10% of the correct answer. What am I doing wrong so that I will get the correct answer?

Thanks,
Mark
 
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I don't know, I get your same result.:confused:
 

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