Work done accelerating up a hill

AI Thread Summary
The discussion focuses on the work done by a hiker carrying a 15.0 kg backpack up a 10.0m hill with constant acceleration versus constant velocity. It highlights that while carrying the backpack at constant velocity involves work against gravity alone, accelerating requires additional force parallel to the displacement, resulting in greater total work. The conversation clarifies that this extra work contributes to an increase in kinetic energy, which is essential in understanding the dynamics of the situation. The role of gravity as a conservative force is acknowledged, but the additional force needed for acceleration is emphasized. Ultimately, the hiker's work is greater when accelerating due to the need to overcome both gravitational and inertial forces.
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Alright so I have a question on the work done with constant acceleration up a hill. I was working an example problem that asked for the work a hiker must do on a 15.0 kg backback to carry it up a hill of height h = 10.0m with the hiker keeping a constant velocity (http://i1298.photobucket.com/albums/ag60/Physics_5/IMG_07961.jpg). I understood the solution when the problem had a constant velocity but not with a constant acceleration.

I reasoned that if the hiker was accelerating up the hill, then a force acting parallel to the displacement was also present in addition to the force the hiker exerts upwards against gravity on the backpack. This would seem to indicate that the total force parallel to the displacement was greater than with constant velocity and that the work in the second situation was greater than the first. I didn't think that made sense because gravity is a conservative force but I don't understand why this explanation would not be valid.
 
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Compared to the first setup, the hiker will reach the top with some velocity (can you calculate it?). You can use this to calculate the required energy. You don't have to care about details of the climbing process. Anyway: To accelerate, the hiker has to apply an additional force along the direction of motion.
 
Ok now I get it. All the extra work he does contributes to a higher kinetic energy. Thank you very much.
 

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