B Forces between two immovable objects

[Saint.V8]

This is most likely dead simple but my brain has shut down for the day!

Lets say a Hydraulic Jack is placed in a square steel frame so once the jack is operated it acts upon the top and bottom rails which are held in place by the two side rails...

The jack is pumped up to say 10 tonnes - does this mean that the top rail and bottom rail are receiving 5 tonnes each or 10 tonnes each?

My brain for some reason just won't tell me which one is correct and it is most frustrating!

 

[lekh2003]

Since it is a hydraulic jack and the pressure is same everywhere in a hydraulic system, there must be 10 tonnes of force on both the top and bottom rails. It is not halved.

 

[jbriggs444]

The jack is pumped up to say 10 tonnes - does this mean that the top rail and bottom rail are receiving 5 tonnes each or 10 tonnes each?

The top rail is subject to 10 tons upward force. The bottom rail is subject to 10 tons downward force. Those forces are on different objects and in different directions. They do not add to 20 tons.

The jack is subject to 10 tons of downward force from the top rail. The jack is subject to 10 tons of upward force from the bottom rail. Those forces act on the same object. They add - as vectors. Since they are in opposite directions, they add to a net of 0 tons. The jack does not move as a result.

The jack is under a compressive stress of 10 tons. If you were to slice the jack in two at any point, you would find the two halves pushing on each other with 10 tons of force.

 

[lekh2003]

The top rail is subject to 10 tons upward force. The bottom rail is subject to 10 tons downward force. Those forces are on different objects and in different directions. They do not add to 20 tons.

The jack is subject to 10 tons of downward force from the top rail. The jack is subject to 10 tons of upward force from the bottom rail. Those forces act on the same object. They add - as vectors. Since they are in opposite directions, they add to a net of 0 tons. The jack does not move as a result.

The jack is under a compressive stress of 10 tons. If you were to slice the jack in two at any point, you would find the two halves pushing on each other with 10 tons of force.

The fact that our two posts are often seconds within each other is uncanny.

 

[Saint.V8]

You bunch of superstars...now it has been explained, it is dead simple really...

For some unknown reason, my brain couldn't fathom out which side of the argument was correct - I have been working on a simulation model and the results it was giving me just didn't seem right, and it is because I was halving the total load between the rails...rather than ensuring the jack was in equilibrium within the system.

You wouldn't think I am 39 years and been doing this sort of thing for most of my working life...I just had a total brain failure.

Many thanks chaps for keeping me sane!

 

[sophiecentaur]

Newton's third law applies here. If the jack is pushing with 10 tons weight then that is what each rail is getting.
It could be easier if you think in terms of tension. Imagine a string holding up a 2kg mass via a spring balance It will be pulling with the 20N (approx) up on the mass and down on the hook in the ceiling with 20N.
The only time the forces will be less is if the forces at one end are in the same direction and 'shared', say there are two hooks in the ceiling and a Vee in the string - 10N each, then.

 

[A.T.]

The jack is pumped up to say 10 tonnes - does this mean that the top rail and bottom rail are receiving 5 tonnes each...

Only if the jack manufacturer was very cheeky.