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In "Thinking Physics" there is a question about pushing a barrel up a ramp. The barrel is 100 pounds and the ramp is 3 feet high and 6 feet on the hypotenuse. The question is how much force a person must use to push the barrel up the ramp.

The answer states that the barrel must gain 300 foot pounds of energy, and this can be achieved by pushing the barrel with 50 pounds of force over the 6 feet.

However, doesn't this ignore the fact that gravity is also pushing against the barrel and providing a force? The barrel is pushing down the ramp with 50 pounds of force, so don't we need to push with 100 pounds so the total force up the ramp is 50 pounds?

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  • $\begingroup$ "foot pounds"? LOL. Who still uses that? $\endgroup$
    – Gert
    Commented Dec 6, 2020 at 20:31
  • $\begingroup$ Haha fair enough, but it's what's used in the book. $\endgroup$
    – Jeff Bass
    Commented Dec 6, 2020 at 20:57
  • $\begingroup$ @Gert, I was told as a high school junior, in 1973, that we in the U.S. were going to change to the metric system. I'm still waiting. $\endgroup$
    – David White
    Commented Dec 6, 2020 at 21:13
  • $\begingroup$ @DavidWhite And here we're still using the mile, despite having been part of the EU. Old habits... $\endgroup$
    – Gert
    Commented Dec 6, 2020 at 21:33

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This problem is not stated very well. It wants you to consider two forces: the force you exert and the force of gravity. The problem implies you are to neglect the work done by friction, which means either a friction-less surface, or the barrel is rolled (not pushed) without slipping, and for pure rolling the force of friction does no work.

The net work considers the force you exert against the opposing force of gravity; the net work is the change in kinetic energy of the barrel which is zero (assuming the barrel is moving very slowly up the ramp, and neglecting any rotational energy gained by the barrel). The work done by gravity is considered as a change in potential energy.

Use an energy balance considering the work you do and the change in potential energy, with no change in kinetic energy of the barrel.

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  • $\begingroup$ Ahh got it. That actually makes much more sense since a net force up the hill would accelerate the barrel and give it more kinetic energy which isn't really the point of the problem. $\endgroup$
    – Jeff Bass
    Commented Dec 6, 2020 at 23:24
  • $\begingroup$ Yes, it is just a poorly worded problem, in my opinion. Glad I could help. $\endgroup$
    – John Darby
    Commented Dec 7, 2020 at 0:13

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