Question

You are told the peak daily wind speed [m / s] for a specific location on the surface of planet Mare4.88 plus/minus 2.51 * m / s To help collect real-time environmental data, you are tasked with selecting anappropriate cable for deploying a weather balloon near a recently designed refuelling station that hasa new sensor suite mounted to it. The equation for drag force F_{D} on the weather balloon is:

Fₔ = 1/2 * rho * v ^ 2 * CₔAWhere
p is the mass density of the Martian atmosphere [Ref. 3];
rho = 0.02 plus/minus 0.005 * [kg / (m ^ 3)]
v is the peak daily wind speed;
Cₔ is the rag coefficient for the weather balloon;
v = 4.88 plus/minus 2.51 * [m / s]
Cₔ = 1.7 plus/minus 0.5 [-]
A is the reference area for the weather balloon;
A = 5.7 plus/minus 1.1 * [m ^ 2]
Calculate the mean drag force Fₔ and the uncertainty in Fₔ for the weather balloon assumingthese multiple variables are all independent

Answer 1

The mean drag force on a weather balloon is calculated using the formula that involves the mass density of the atmosphere, the wind speed, the drag coefficient, and the reference area of the balloon. The mean values of these variables are used to compute the mean force, while the principle of propagation of uncertainty is applied to determine the uncertainty in the force.

Step-by-step explanation:

The question asks us to calculate the mean drag force (FD) on a weather balloon and the uncertainty in that force, given several independent variables with their own uncertainties. The drag force is calculated using the formula FD = (1/2) * ρ * v2 * CD * A, where ρ is the mass density of the atmosphere, v is the peak daily wind speed, CD is the drag coefficient, and A is the reference area of the weather balloon. To find the mean value of FD, we use the mean values of the variables:

• ρ = 0.02 kg/m3
• v = 4.88 m/s
• CD = 1.7
• A = 5.7 m2

Mean FD = (1/2) * 0.02 kg/m3 * (4.88 m/s)2 * 1.7 * 5.7 m2

To calculate the uncertainty in FD, we would use the principle of propagation of uncertainty. However, as we do not provide specific calculations for homework help, we encourage you to apply this principle using the given uncertainties in the variables.