Physics problem help please. :)?

Question

The Sojourner rover vehicle was used to explore the surface of Mars as part of the pathfinder mission in 1997. Use the data below to answer the question that follow.

Mars Data:
Radius = 0.53 x Earth's radius
Mass = 0.11 x Earth's mass

Soujourner Data:
Mass of Sojourner vehicle = 11.5kg
Wheel diameter = 0.13 m
Stored energy available = 5.4 x 10^5 J
Power required for driving under average conditions = 10W
Land Speed = 6.7 x 10^-3 m/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 the Sojourner's weight on the surface of Mars.

c) Assume that when leaving the pathfinder spacecraft, Sojourner rolls down a ramp inclined at 20r (? I don't know this symbol, it looks like a big r that also looks like v) 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) g = GM/r^2; I'll use _M to indicate Mars and _E to indicate Earth, so we have
g_M / g_E = M_M / M_E * (r_E / r_M)^2
= 0.11 * (1/0.53)^2 = 0.39
So Mars surface gravity is 0.39 g.

b) F = mg = 11.5 (0.39) (9.81) = 44 N.

c) I'm assuming the question should be "... inclined at 20 degrees to the horizontal...". It will be sufficient for the resultant of the gravitational force and the normal force to be directed along the ramp. If you draw this triangle you will see that you get cos 20 degrees = F_normal / F_grav, so the minimum normal force is 44 * cos 20 degrees = 42 N.

d) The net force on anything travelling at constant velocity is zero, by Newton's first law.

e) E = Pt and d = vt, so d_max = v(E/P) = (6.7 x 10^-3 ) (5.4 x 10^5) / 10 = 360 m.

f) P = Fv, so (0.010/100 * 10) = F (6.7 x 10^-3) and thus F = 0.15 N.

Answer 2

Sojourner Rover

Answer 3

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