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I was wondering, if we had an inclined beam, as shown below, and a ball rests on top of it, how could I set up the toque equation for equilibrium conditions? I mean, would the ball exert a vertical force down on the beam (the weight)?

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I am basing myself off of the classic "man on a ladder" problem.

enter image description here

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  • $\begingroup$ Depends on how your ball stays on the ramp. $\endgroup$ – JMac Apr 24 '17 at 16:04
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A ball can only apply force perpendicular to the tangent of the contact point. You would need to derive the component of force from the acceleration of gravity that is perpendicular to the slope; sin60 * 196N = F.

The man on the ladder is standing on a rung and can be at rest, a ball on a slope will tend to roll unless a moment or other force is acting on it. For your ball to stay steady you will need to find the component of force the ball has acting parallel to the slope and counter it with a moment calculated from the radius of the ball. You can use the 196N and the F you calculated and the Pythagorean theorem to find the force parallel to the slope.

Drew K

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  • $\begingroup$ Oh, okay, I understand. What if it was still the man standing on the ramp? $\endgroup$ – Bee Apr 24 '17 at 18:59
  • $\begingroup$ If the man were standing on the ramp, it would be the same as the ball without the moment to keep him from rolling. There would have to be sufficient friction forces opposite the downward force parallel to the slope. $\endgroup$ – Gwydionforge Apr 24 '17 at 22:19

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