Question

The mass density of air on Mars is ρ=0.016 kg/m³. The gravity on Mars is gMars= 3.7 m/s². The mass density of air on earth under standard pressure and temperature conditions is ρ=1.225 kg/m3. A NASA mars probe weighs 1000 N on Earth. At terminal velocity, the weight of a falling object is equal to the drag force. Assume that the drag coefficient of the parachute used is constant, and has the same value on both Earth or Mars, and is CD=0.8.

a. What diameter parachute will give a terminal velocity of V=10 m/s on Earth under standard air pressure and temperature conditions? Ans. Approximately 5 m.

b. What is the terminal velocity on Mars if the same sized parachute is used? Ans. Approximately 50 m/s. Hint, is the weight of the probe the same on Mars?

c. What diameter of parachute is needed to land the this probe on Mars at a terminal velocity of V=10 m/s?

Answer 1

Drag coefficient on Earth as well as om Mars,

a. Mass density of air on earth,

Weight of object on earth, W = 1000 N

Terminal velocity, V = 10 m/s

Drag force

Where A = Reference Area

If D = diameter of parachute

The object aquires terminal velocity when its weight becomes equal to drag force

b. If m = mass of probe

then its weight on earth, W = mg

Acceleration due to gravity on Mars,

Weight on Mars,

Let = Terminal velocity on Mars

Density of air on Mars,

c. In this case,

Diameter of parachute required in this case is 27.4 m