Calculate the terminal speed of a wooden sphere(density 0.830g/m^3) falling throught air if its radius is 8.00cm and its drag coefficient is 0.500? From what height would a freely falling object reach this speed in the absence of air resistance?
http://hyperphysics.phy-astr.gsu.edu/HBASE/airfri2.html#c3
Calculate cross sectional area, and use the formula.
To calculate the terminal speed of a wooden sphere falling through air, we need to use the following formula:
v = sqrt((2 * m * g) / (ρ * A * Cd))
Where:
- v is the terminal speed
- m is the mass of the sphere (which can be calculated using the density and volume of the sphere)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- ρ is the density of air (approximately 1.2 kg/m^3)
- A is the cross-sectional area of the sphere (π * r^2, where r is the radius of the sphere)
- Cd is the drag coefficient
Let's calculate the values step by step:
1. Calculate the mass (m) of the sphere:
Mass = density * volume
Given that the density of the wooden sphere is 0.830 g/m^3 and the sphere's radius is 8.00 cm, we need to convert the radius to meters:
Radius = 8.00 cm = 0.08 m
Volume = (4/3) * π * r^3
Volume = (4/3) * π * (0.08 m)^3
Mass = density * volume
Mass = 0.830 g/m^3 * [(4/3) * π * (0.08 m)^3]
2. Calculate the cross-sectional area (A) of the sphere:
A = π * r^2
A = π * (0.08 m)^2
With these values, we can now calculate the terminal speed (v):
v = sqrt((2 * m * g) / (ρ * A * Cd))
Given that the drag coefficient (Cd) is 0.500, you can substitute the calculated values into the formula to find the terminal speed (v).
To find the height from which the object would reach this speed in the absence of air resistance, we need to calculate the time it takes for the object to reach the terminal speed and then use that time to calculate the height.
Let's say the initial velocity of the object is 0 m/s. The time it takes for the object to reach the terminal speed (t) can be calculated as:
t = v / g
Where v is the terminal speed and g is the acceleration due to gravity.
Once you have the time (t), you can calculate the height (h) using the formula:
h = (1/2) * g * t^2
Substitute the values of g and t into the formula to find the height.