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A man pushes on a piano with mass 180kg; it slides at constant velocity down a ramp that is inclined at 18.4$^\circ$ above the horizontal floor. Neglect any friction acting on the piano. Calculate the magnitude of the force applied by the man if he pushes (a) parallel to the incline and (b) parallel to the floor.

If we neglect any friction acting on the piano wouldn't it accelerate down the ramp at $g\sin(\theta)$ without the influence of the man?

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  • $\begingroup$ You are right of course. Part b doesn't really make sense either. Who would push a piano non-parallel to the ground?? $\endgroup$
    – Metalbeard
    Sep 2, 2017 at 8:51
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    $\begingroup$ For the question to make sense the man must be pushing up the slope i.e. in the opposite direction to the velocity of the piano. The force the man exerts is then simply equal to the gravitational force on the piano so the net force, and therefore the acceleration, is zero. $\endgroup$ Sep 2, 2017 at 9:01
  • $\begingroup$ Constant velocity $\to$ zero acceleration. $\endgroup$
    – Bill N
    Sep 3, 2017 at 16:50

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The piano would, of course, accelerate down the incline with an acceleration equaling g*SinΘ if the person were not exerting a force on it. The problem conveys that the piano is moving with a constant velocity down the incline, which implies that the person must be exerting a force acting up the incline, because the piano is in equilibrium, ie, not accelerating. I hope this helps. :)

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