(a) When opening a door, you push on it perpendicularly with a force of 55.0 N at a distance of 0.850m from the hinges. What torque are you exerting relative to the hinges? (b) Does it matter if you push at the same height as the hinges?
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Final Answer

a) 46.8 Nm46.8 \textrm{ N} \cdot \textrm{m}

b) The vertical position of the force doesn't matter. Only the perpendicular distance from the axis of rotation matters, which doesn't change when point of application of the force is moved vertically.

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OpenStax College Physics, Chapter 9, Problem 1 (Problems & Exercises)

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I'm confused about your answer to part b). On page 319 of the textbook it says " If you apply your force too close to the hinges, the door will open slowly, if at all. Most people have been embarrassed by making this mistake and bumping up against a door when it did not open as quickly as expected. Finally, the direction in which you push is also important. "