I'm having trouble answering these questions, if anybody could help I'd appreciate it.

Imagine a solid sphere of diameter, d, falling through the air. After its release, the sphere accelerates until it reaches its terminal velocity. The terminal velocity is obtained when the drag force due to air friction, Fd, balances the weight of the sphere, W.

The weight of the sphere is simply its mass, m, times acceleration due to gravity (g = 9.8 m/s2 ),

W = mg

and the drag force can be computed as

Fd = cd*1/2p*(v^2)*A

Where cd is a dimensionless empirical drag coefficient, ρ is the density of the air, v is the velocity of the sphere, and A = π(d^2)/4 is the frontal area of the falling sphere.

A common correlation for the drag aerodynamic drag of smooth spheres is

cd = 24/Re + 6/(1+sqr(Re)) + 0.4

where Re is the Reynolds number,

Re = ρvd/µ

and µ is the dynamic viscosity of the air. Because the properties of air (e.g., ρ and µ) are temperature-dependent, the terminal velocity will vary with temperature. To investigate this dependence, we will assume that air is an ideal gas, giving

ρ(T) = P/RT

where R = 287.0 J/kg-K is the gas constant for air, P is the absolute air pressure in N/m^2 and T is the temperature in Kelvin. For viscosity, use the following correlation,

µ(T) = b1T^3 + b2T^2 + b3T + b4

where the viscosity is given in kg/m-s with respect to temperature given in Kelvin and b1 = 2.156954157×10−14 , b2 = −5.332634033×10−11 , b3 = 7.477905983×10−8 , and b4 = 2.527878788× 10−7 .

1. Assuming standard atmospheric pressure (P = 101300 N/m^2 ), m = 0.5 kg, and d = 15 cm, compute and plot the terminal velocity of the sphere over the temperature range from -60 C to 60 C.

2. Once you have the plots from step 1, you can re-compute a number of intermediate variables to help you rationalize that your solution makes physical sense. In particular, you should also generate a series of curves for ρ vs. T, µ vs. T, Re vs. T, and cd vs. T. Are all of these plots reasonable? Do they help justify the behavior observed for v vs. T? Explain.

[Geoff Hayes]

Steve - please don't post your homework assignments with the expectation that they will be answered for you. Describe the problem that you are facing and be specific with respect to what is preventing you from moving forward, including any error messages that you are observing. Post whatever work you have attempted so that we know exactly what you have tried.