The Physics Behind Walking Up the Dreadful Colgate Hill

  

            When physics class used to be in the chapel, walking up the hill right near the library was always an ungodly experience as I would always be out of breath and sweating by the time I reached the top. The move of physics class to TIA downtown has made walking to physics class much less of a struggle. Why is it such a tiring experience to walk up a hill versus flat land one may ask? The answer is not simple, but with a basic knowledge of physics one will be able to understand the feeling of shortness of breath as you near the top of a hill. 

            When walking on flat land, similar to my walk to TIA, without knowing it you are applying a force to your foot which applies a force to the ground. Surprisingly, the ground applies an equal and opposite force onto your foot which in turn pushes you forward. This agrees with Newton’s third law that states “for every action (force) in nature there is an equal and opposite reaction” (Source 1). In the case of walking, the applied force is one’s foot and the equal and opposite reaction force is the force that the ground exerts back onto you causing a movement forward. The force of gravity is also a key component because without this force acting in the downwards direction, one would not stay on the ground. Related to the downwards vertical force of gravity is the normal force which acts in the upwards direction vertically. The normal force is responsible when walking on flat land, for balancing out the downwards force of gravity. In the case of flat land, the normal force fully compensates for the gravitational force therefore one does not need to work against gravity when walking on level ground. However, on a hill the normal force does not act entirely in the vertical direction it acts in the vertical direction of the object, therefore when walking up a hill the normal force is acting in an upwards diagonal direction in which it cannot entirely balance out the force of gravity (Figure 1). The normal force on a hill only compensates for a part of the downwards gravitational pull, making the gravitational pull on a person walking up a hill stronger compared to one walking on level ground as gravity is no longer fully canceled out. On a hill, the force of gravity is acting upon you therefore, pulling you downwards. In order to move up the hill, this downwards force of gravity must be opposed, when walking on level ground it does not because gravity is fully compensated by the normal force. The steeper the hill is, the larger the force of gravity is on someone, pulling them down the hill harder making it more difficult to move as one needs to do work and exert energy. When walking up the library hill you need to climb as well as move forward in which energy is being exerted and work is being done. If you are walking on a flat ground level road, you stay at the same level in Earth’s gravitational pull or force in which the normal force and gravitational force cancel each other out because they act in equal but opposite directions. However, when walking up hill the normal force is not vertical to the gravitational force and cannot ‘cancel’ it out, therefore one must oppose a portion of the force of gravity on a hill themselves by exerting more energy and doing more work. For every elevation raise, like climbing up a hill, the more energy it takes to oppose the force of gravity. For every degree of incline, at a constant distance you are putting in extra work hence why one becomes out of breath walking up to campus. Walking uphill takes work while walking on a flat level does not. 

Below are the free body diagrams of a person walking up a hill and the forces acting on him/her versus the forces acting on somebody on flat land (Figure 1). Through the diagrams it is evident that the main reason why it is so much more difficult to walk uphill is due to the normal and gravitational forces. One must do more work when trying to walk up a hill therefore exert more energy to overcome the gravitational force as you are working against gravity. In order to move or walk in this case the force of gravity must be opposed, while on the other hand when walking on flat land one does not have to overcome gravity to move as the normal force takes care of that for them. This basic knowledge of physics explains why one is usually out of breath by the time they reach the academic quad at Colgate when walking from downtown. 

Figure 1. Free-body diagram. Above are the free-body diagrams for walking up a hill (left) versus down a hill (right).

Sources:

1. https://www.grc.nasa.gov/www/k-12/airplane/newton3.html

2. https://scienceblogs.com/startswithabang/2010/03/10/the-physics-of-an-inclined-tre

3. https://www.physicsforums.com/threads/why-is-there-no-work-for-someone-walking-on-flat-            plane.795810/