I carry my bag horizontally across a room and I get tired, but the answer key says I did zero work on the bag. That feels wrong.
In physics, work is force times displacement times the cosine of the angle between them: W = F·s·cosθ. When you carry a bag at constant height across a room, the force you apply to support it is vertical (upward, against gravity), but the displacement is horizontal. The angle between the upward force and the horizontal motion is 90 degrees, and cos 90 = 0, so the work done by your supporting force on the bag is zero. You feel tired because your muscles keep contracting and using up chemical energy to hold the bag, but that is a biological cost, not physics work on the bag. To do positive work you would need a force component along the direction of motion, such as when you lift the bag upward.
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