Question

The Sojourner rover vehicle shown in the sketch was used to explore the surface of Mars as part of the Pathfinder mission in 1997. Use the data in the tables below to answer the questions that follow.

Mars Data	Sojourner Data
Radius: 0.53 x Earth's radius Mass: 0.11 x Earth's mass	Mass of Sojourner vehicle: 11.5 kg Wheel diameter: 0.13m Stored energy available:  5.4 x 105J Power required for driving under average conditions:  10W  Land speed: 6.7 x 10-3m/s

a. Determine the acceleration due to gravity at the surface of Mars in terms of g, the acceleration due to gravity at the surface of Earth. 

b. Calculate Sojourner's weight on the surface of Mars. 

c. Assume that when leaving the Pathfinder spacecraft Sojourner rolls down a ramp inclined at 20° to the horizontal. The ramp must be lightweight but strong enough to support Sojourner. Calculate the minimum normal force that must be supplied by the ramp. 

d. What is the net force on Sojourner as it travels across the Martian surface at constant velocity? Justify your answer. 

e. Determine the maximum distance that Sojourner can travel on a horizontal Martian surface using its stored energy. f. Suppose that 0.010% of the power for driving is expended against atmospheric drag as Sojourner travels on the Martian surface. Calculate the magnitude of the drag force.

Answer 1

(a) Plug into g = GM_planet /r_planet² lookup earth mass and radius

g_mars = 3.822m/s² to get it in terms of g_earth divide by 9.8 g_mars = 0.39 g_earth

(b) Since on the surface, simply plug into F_g = mg = (11.5)(3.8) = 44N

(c) On the incline, F_n = mgcosθ = (44)cos(20) = 41N