Question

Work-energy bar charts for a person going downstairs and upstairs are shown in the figure below. The bar charts show the average energy conversion across several steps. The system is the person, Earth, and the stairs. (a) Describe the differences in the bar charts. How do these differences explain why we are less tired going downstairs? (b) How do you explain that when we walk upstairs lLVthl < IAUchl, but when we walk downstairs AUhl>JAUchl?

Answer 1

In the first bar chart we are going down stairs - 1) Initially we will have some KE and some gravitational Potential Energy. There are no external forces doing work, so the work done will be zero.

2) Finally, when we reached the ground, our speed will be same as we started walking so the KE bar will remain the same as before. Since the height is zero, so there will not be any potential energy. Change in chemical energy Uch will be negative because initially your body metabolism was not doing any work but now since you are moving downstairs your body metabolism will work (even slightly) and you will consume energy. Also, there will be a positive change in the Uth because your body will get heat up because of the activity.

In the second bar chart, we are going upstairs, the argument for the kinetic energy remains the same. Now we will reach a height so the gravitational potential energy will be positive.

1) Change in Uch will be more negative because your body is working against gravity so the body will require more metabolic energy and hence you will consume more energy and Uch will be more negative than when you were moving downstairs.

2) Change in Uth will also be more because your body will get more heated because of the large chemical metabolism and more energy consumption by the body.

hence we will get more tired of going upstairs because the internal energy demand of the body is higher when we go upstairs.

b) when we go upstairs, Uch is greater than Uth because the chemical energy change due to metabolism will be equivalent to the heat energy generated plus the potential energy gained. However, when we go downstairs, our body don't have to perform much metabolic activities because we are going along with gravity and hence losing potential energy in the process. hence the Uch will be less than Uth. Body will anyway get heated, whether you move upstairs and or downstairs.