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If an air cylinder is pushing two platens apart with a force of $100\: \mathrm{lbs}$, do the platens need to push back at $100\: \mathrm{lbs}$ or $50\: \mathrm{lbs}$ each to keep the cylinder from moving? Assume no friction and both platens are not fixed.

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More on forces and factors of two: physics.stackexchange.com/q/41291/2451 and links therein. –  Qmechanic Oct 21 '12 at 18:19

2 Answers 2

An easy way to answer this question is to assume one of the platens is fixed. If you make the statement that a 100 lb force is pushing the platens apart, then there is a 100 lb force pushing one platen away from the other. Since the other platen is stationary we can imagine a normal force equal to 100 lb is applied to keep the total force at zero. Now just imagine there is a person inside the cylinder, if he braces himself on one side and pushes against the other side with 100 lb of force, there is a normal force at his feet pushing in the opposite direction with a 100 lb of force (and we are making the assumption the cylinder is horizontally aligned in order to neglect gravity). Now the person inside the cylinder is not going to know that one plate is fixed and the other isn't. He has no frame of reference where he can make that determination. So even if in reality both sides are movable in some external reference frame, internally the dynamics are the same. So each of the platens feel 100 lbs of force.

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If the piston was pushing with 100 and the ends react with 50 then the ends would fly appart. Static equilibrium dictates that all parts share the same load of 100 lbs.

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protected by Qmechanic Mar 21 '13 at 19:10

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