Terminal Speed of 6.5 kg Ball: Calc Error?

In summary, the terminal speed of a 6.5 kg spherical ball with a radius of 3.0 cm and a drag coefficient of 1.50 is being calculated using the formula vt=sqrt((2Fg)/(CpA)), where Fg is force of gravity, C is drag coeff., p is air density, and A is cross sectional area. However, the incorrect answer is obtained due to the use of incorrect values for C, p, Fg, and A. The error is resolved by converting the radius from centimeters to meters and including the mass of the sphere in the calculation of Fg.
  • #1
GingerBread27
108
0
What is the terminal speed of a 6.5 kg spherical ball with a radius of 3.0 cm and a drag coefficient of 1.50? The density of the air through which the ball falls is 1.2 kg/m3.

I used vt=sqrt((2Fg)/(CpA)). Where Fg is force of gravity, C is drag coeff., p is air density , and A is cross sectional area. When I plug in the numbers I get the wrong answer. I used 1.5 as C, 1.2 as p, 9.8 as Fg, and (9*pi) as a (area of circle-pi*r^2). What am I doing wrong.
 
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  • #2
I think you need to convert your radius to meters.
 
  • #3
I forgot to convert lol but that doesn't help, answer is still wrong.
 
  • #4
Never Mind Figured it Out :)
 
  • #5
Your expression hasn't got units of velocity.

I think you have forgotten to include the sphere mass in Fg.
 

What is the terminal speed of the 6.5 kg ball and how is it calculated?

The terminal speed of the 6.5 kg ball is the maximum speed that the ball can reach as it falls through the air. It is calculated using the formula terminal speed = (2mg)/(ρACd), where m is the mass of the ball, g is the acceleration due to gravity, ρ is the density of air, A is the cross-sectional area of the ball, and Cd is the drag coefficient.

How do you measure the mass of the 6.5 kg ball?

The mass of the 6.5 kg ball can be measured using a scale or balance. The ball should be placed on the scale and the reading will indicate its mass in kilograms.

How does air density affect the terminal speed of the ball?

Air density plays a significant role in determining the terminal speed of the ball. The higher the air density, the greater the resistance the ball will experience as it falls through the air. This will result in a lower terminal speed.

Can the terminal speed of the ball be affected by the shape or size of the ball?

Yes, the terminal speed of the ball can be affected by its shape and size. A larger cross-sectional area or a shape that creates more drag will result in a lower terminal speed. A smaller cross-sectional area or a streamlined shape will result in a higher terminal speed.

What are some potential sources of error when calculating the terminal speed of the ball?

Some potential sources of error when calculating the terminal speed of the ball include uncertainties in measuring the mass and dimensions of the ball, assumptions made about air density and drag coefficient, and variations in environmental conditions such as air temperature and humidity. Additionally, human error in performing the calculations can also introduce inaccuracies.

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