In an obscure location in the South Pacific an explorer in a small sail boat cla

Question

In an obscure location in the South Pacific an explorer in a small sail boat claims to have discovered a tiny volcanic island she calls the Isle of Abstract us. The volcano is shiny and seems to be made of obsidian which is a glass-like substance. The map she made has 50 meter contour lines. The rim of the volcano crater happens to be one of the contour lines and the explorer estimates that the island is 250 m long from west to east and 100 meters wide from North to South Assume friction forces can be ignored as the explorer climbs up and down on the mountain. How high above sea level is the volcano crater? How much physical work does the explorer do in following a direct path A rightarrow B if her mass is 55 kg? How much physical work does she do in going from A rightarrow C by following a direct path from A rightarrow B and then a direct path from B rightarrow C? Where is the steepest slope on the mountain (to the N, W, S, or E)? Which direction (N, W, S, or E) is a ball most likely to roll in if it is released from the rim at point B but doesn't fall into the crater?

Explanation / Answer

b)Hmax = 200m as shown in graph

c)Ha=100 m

Hb=200 m

Work done=mg(change in H)=55*9.81*100=53955 J

d)since Hc=Ha

change in H is same therefore no work done for A-->C

hence work done same as (b)

e)steepest slope is where contour lines are most close therfore Western part of the mountain(as seen in map)

f) and g)

Western part will have steepest slope hence highest angle of inclination(theta) hence highest gravitational force parallel to the surface(which is = m.g.sin(theta))

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