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Yes the work is done, when the porter is walking along a road or he is climbing up or down.
When he is climbing down also he has to work against falling down for which he has to generate an energy. He has to work against the acceleration due to gravity and manage himself to keep a uniform speed down against gravity every moment.Actually should maintain a zero acceleration against the acceleration due to gravity.The larger the steps the more energy is required as his centere of gravity moves up and down more and the PE difference is high in each step. Also the speed or the number of steps per second also adds to the kinetic energy. So his body works in the walking also.
In walking along a load on his head he appears to move uniformly . But his movement is not uniform but descrete. For every step he pushes the ground to get a reaction which helps to get an instant acceleration from zero to a small per second and rest and repeat the activity of getting this acceleration. During each step his centre of gravity along the load moves smoothly along an arc (whose radius is equal to the length of his leg) up and down. So a potential energy differemce occurs for each step. The more the number of steps, the more the energy consumption or work done.
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