Terminal Velocity: Calculate Mass of 22cm Ball

In summary, the conversation discusses the use of the equation v^2 = (4mg)/A to determine the mass of a ball with a given terminal velocity and diameter. The correct formula for the area of a sphere is A= pi r^2, not 4pi r^2. The area of the largest cross section is used in problems with air resistance, and in this case, it is a circle with a radius of 0.11m.
  • #1
StephenDoty
265
0
v^2= (4mg)/A

so if a 22cm diameter ball has a terminal velocity of 85m/s, what would the mass of the ball be?
A = 4pi r^2
22cm= 0.22m
v^2 = (39.2m)/(4pi (.11)^2)
7225= (39.2m)/(pi*.0484)
So I got 28kg for the mass and that is not right. Please help.

Stephen Doty
 
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  • #2
You have incorrectly noted that A=4pi r^2, where of course you meant A= pi r^2.
 
  • #3
I know the area of a circle is pi r^2
but isn't the area of a sphere or a ball 4pi r^2 ?
 
  • #4
In problems with air resistance we use area of the largest cross section of an object with a plane that is perpendicular to its direction of movement. In this case that is a circle with radius r
 

FAQ: Terminal Velocity: Calculate Mass of 22cm Ball

1. What is terminal velocity?

Terminal velocity is the maximum speed that an object will reach when falling through a fluid, such as air or water. It occurs when the gravitational force acting on the object is equal to the drag force exerted by the fluid on the object.

2. How is terminal velocity calculated?

Terminal velocity can be calculated using the equation:
v = √(2mg/ρACd)
where v is the terminal velocity, m is the mass of the object, g is the acceleration due to gravity, ρ is the density of the fluid, A is the cross-sectional area of the object, and Cd is the drag coefficient.

3. What is the drag coefficient?

The drag coefficient is a dimensionless quantity that represents the amount of drag or air resistance on an object. It takes into account the shape, size, and surface roughness of the object, as well as the properties of the fluid it is moving through. A higher drag coefficient means there is more air resistance, resulting in a lower terminal velocity.

4. How does mass affect terminal velocity?

The mass of an object does not directly affect its terminal velocity. However, a heavier object will have a larger gravitational force acting on it, requiring a larger drag force to reach terminal velocity. Therefore, a heavier object will have a higher terminal velocity than a lighter object of the same shape and size.

5. Can terminal velocity be exceeded?

No, terminal velocity is the maximum speed that an object can reach when falling through a fluid. Once an object reaches terminal velocity, the drag force will be equal to the gravitational force, resulting in a constant velocity. Any additional force or weight added to the object will not increase its speed beyond terminal velocity.

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