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Question

Solving this question will makes us realize that y-component of tension $T$ of the string satisfies the inequality

$0<T_y<0.671W$

And the y component of the force exerted by pivot $B$ on the rod $BC$ satisfies the inequality

$0<B_y<0.5W$

Which tells us

$$R_a>2W-0.671W-0.5W=0.829W$$

$$R_a<2W-0W=2W$$

$$0.829W<R_a<2W$$

Where $R_a$ is the force exerted by the pivot on the rod $AB$.

My question is how can the pivot exert an upward force on the rod AB? Is the rod glued with the pivot? How can a pivot provide a force in almost any direction to maintain equilibrium?

Fabio Somenzi
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mathnoob123
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  • The reaction forces are really giving you a good deal of work. They seem appear as needed and always are calculated after the cinematic aspect of the problem is solved. It's a good way to see them considering where their name, reaction forces, comes from: they appear due to the impenetrability of bodies. – Rafa Budría May 31 '17 at 04:59
  • So, you have the answer in your question: yes, they work as if they were glued: when glued, the forces between the objects are reaction forces. – Rafa Budría May 31 '17 at 05:05
  • For the record, $T_y = 0.6W$, which means $B_y = 0.4W$. – Fabio Somenzi May 31 '17 at 06:55

1 Answers1

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The definition of a pivot is that it is fixed in location and will provide whatever force is necessary to stay there. If the thing attached to it wants to move down it will provide the upward force to counter that. In this case, the two rods weigh $W$ each and will fall under gravity if unsupported. The pivot has to provide the support, so has to provide an upward force of $2W$. That way the net force on the triangle is zero and the system can be stable.

Ross Millikan
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  • Can you provide a real life example of a pivot? – mathnoob123 May 31 '17 at 07:34
  • @FaiqRaees: Not far from it is an eye bolt screwed into some fixed support, especially if you confine motion to the plane perpendicular to the opening. If the thing that goes through the eye fills it up you can get forces in all directions. There are complicated spherical bearings that do not have the plane restriction. – Ross Millikan May 31 '17 at 13:37
  • I assume even a door hinge will provide the same purpose assuming it does have some internal dodges that prevent rotational movement when a toque is applied. – mathnoob123 May 31 '17 at 13:41