Estimate the terminal speed of a wooden sphere

• MetallicaFNum
In summary, the estimated terminal speed of a wooden sphere falling through air is 56.8 m/s with a radius of 8.50 cm and a drag coefficient of 0.500. To reach this speed in the absence of air resistance, the object would need to fall from a height that is not specified.
MetallicaFNum

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

I don't know, I get your same result.

1. What is the equation used to estimate the terminal speed of a wooden sphere?

The equation for estimating the terminal speed of a wooden sphere is Vt = (2mg)/(ρAC), where Vt is the terminal speed, m is the mass of the sphere, g is the acceleration due to gravity, ρ is the density of the fluid, A is the cross-sectional area of the sphere, and C is the drag coefficient.

2. What factors affect the terminal speed of a wooden sphere?

The terminal speed of a wooden sphere is affected by several factors including the mass and density of the sphere, the density of the fluid it is falling through, the cross-sectional area of the sphere, and the drag coefficient of the sphere.

3. How does the shape of the wooden sphere affect its terminal speed?

The shape of the wooden sphere can affect its terminal speed by changing its cross-sectional area and drag coefficient. A more streamlined shape will have a lower drag coefficient and thus a higher terminal speed, while a more irregular shape will have a higher drag coefficient and a lower terminal speed.

4. Is the terminal speed of a wooden sphere affected by air resistance?

Yes, the terminal speed of a wooden sphere is affected by air resistance because air resistance creates drag, which acts against the sphere's motion and ultimately determines its terminal speed.

5. How does the terminal speed of a wooden sphere compare to that of other objects?

The terminal speed of a wooden sphere will be different from that of other objects due to differences in mass, shape, and drag coefficient. For example, a heavier object will have a higher terminal speed because it will experience a greater force of gravity, while a more streamlined object will have a lower terminal speed due to its lower drag coefficient.

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