Answer: Alice & Bill Do Same Work Climbing Mountain

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SUMMARY

Alice and Bill, both with the same mass, climb a mountain using different paths: Bill takes a steep route while Alice chooses a longer, winding path that is eight times the distance. Despite Alice reaching the summit in one-third of the time it takes Bill, the work done by both climbers is equivalent when considering gravitational potential energy, as their initial and final positions are the same. However, in practical scenarios, Alice's path involves additional work due to horizontal movement. Thus, while the theoretical work is identical, real-world factors can influence the total work done.

PREREQUISITES
  • Understanding of gravitational potential energy
  • Familiarity with the work-energy principle (W = ΔK)
  • Basic knowledge of kinetic energy concepts
  • Awareness of the effects of different path lengths on work done
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  • Explore the work-energy theorem in detail
  • Investigate the impact of path length on work done in physics
  • Learn about gravitational potential energy calculations
  • Examine real-world applications of work in varying terrains
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This discussion is beneficial for physics students, educators, and anyone interested in understanding the principles of work and energy in gravitational fields.

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Homework Statement



Alice and Bill, who happen to have the same mass, both want to climb to the top of a mountain. Bill wants to take the steep path straight up, but Alice wants to take the path that gently winds around the mountain, even though it is 8 times longer than the steep path. They both eventually reach the top of the mountain, but Alice reaches the top in 1/3 the time that Bill takes using the steep route. How does the work that Alice did in climbing the mountain compare with the amount that Bill did?


Homework Equations


W= delta K


The Attempt at a Solution


They both do the same amount of work, correct? Since there KE at the bttom and top are the same?
 
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Answer depends a little bit on the context. If you are expected to treat it as an idealized case of work in gravitational filed then yes, amount of work depends only on the initial and final position, so if they start and stop at the same places amount of work is identical. But in reality it is not, as you do work even when walking horizontal surface.
 

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