Find the value of aerodynamic constant C for this dimpled sphere.

In summary, the conversation discusses the use of a formula to determine the value of the aerodynamic constant C for a falling golf ball. The formula for terminal speed is V=sqrt(2mg/pAC), with units in MKS. The conversation also mentions the importance of consistency in units and clarifies that p (rho) represents density in kg/m3.
  • #1
Sneakatone
318
0
A falling golf ball (mass 45 g, radius 20.0mm) reaches high terminal speed of 42 m/s. what is the value of the aerodynamic constant C for this dimpled sphere?

I tried using mv^2/r -> (0.45 kg)*(42 m/s)/0.2m=94.5 but Its not correct. I don't understand what they mean by constant C.
 
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  • #2
Well, the golf ball is undergoing linear motion. Your formula is for the centripetal force on an object in circular motion. What you need is a formula for terminal speed of an object which is falling.
 
  • #3
V=sqrt(2mg/pAC)
 
  • #4
if this is the right equation should the units of v=km/h and r=m?
in other words what should the units be?
 
  • #5
Sneakatone said:
if this is the right equation should the units of v=km/h and r=m?
in other words what should the units be?
Anything you like as long as you are consistent. Put everything into MKS units and you should be safe.
 
  • #6
would you recommend I convert to km since p is km?
 
Last edited:
  • #7
Sneakatone said:
would you recommend I convert to km since p is km?

Isn't p (rho) the density? That would be kg/m3 in MKS.
 

Related to Find the value of aerodynamic constant C for this dimpled sphere.

1. What is the aerodynamic constant C and why is it important?

The aerodynamic constant C is a coefficient that represents the aerodynamic characteristics of a particular object, in this case a dimpled sphere. It is important because it determines the amount of drag force that will act upon the object when it moves through a fluid medium, such as air or water.

2. How is the value of C calculated for a dimpled sphere?

The value of C for a dimpled sphere is typically determined experimentally through wind tunnel testing. The sphere is placed in the wind tunnel and the resulting drag force is measured at different speeds. The value of C is then calculated using the drag equation, which takes into account the sphere's shape, size, and surface characteristics.

3. Can the value of C change for a dimpled sphere?

Yes, the value of C can change depending on various factors such as the speed of the object, the fluid medium it is moving through, and any changes in the surface characteristics of the sphere. For example, if the sphere is coated with a substance that reduces friction, the value of C may decrease.

4. How does the value of C affect the aerodynamic performance of a dimpled sphere?

The lower the value of C, the better the aerodynamic performance of the dimpled sphere. This is because a lower C means there is less drag force acting on the sphere, allowing it to move more efficiently through the fluid medium. This is why dimpled spheres are often used in sports such as golf and tennis, as the dimples help to reduce the value of C and improve the aerodynamic performance of the ball.

5. Are there any real-world applications for knowing the value of C for a dimpled sphere?

Yes, knowing the value of C for a dimpled sphere can have practical applications in industries such as sports, aviation, and automotive. For example, in sports, understanding the aerodynamics of a dimpled ball can help athletes improve their performance. In aviation, the value of C for aircraft design can impact fuel efficiency and speed. In automotive engineering, the value of C for a car's body shape can affect its fuel efficiency and overall performance.

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