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02-02-2017, 12:40 PM
 citfta Gold Member Join Date: Jun 2008 Posts: 1,296
You are still ignoring a couple of things. Here is a copy and paste from the math guy to better explain it than I could.

Quote:
If the arm y has been bent though an angle theta (in your diagram 2 that is an angle of about 120 degrees) then your force Fs has both a horizontal and a vertical component. Its downward component is Fs*cos(theta). Hence the downward force at the fulcrum is Wm+Fs*cos(theta). If theta was 90 degrees Fs has no downward component, and the downward force at the fulcrum would simply be Wm. However there is a sideways force Fs*sin(theta) and if the fulcrum point is not a fixed bearing (i.e. its is like the knife edge illustrated) then the lever will tend to slide sideways. When Fs*cos(theta)=Wm there is zero force on the fulcrum leaving only the sideways force. Since as illustrated your x is greater than y, and the Force Fs acts at a distance from the fulcrum point slightly less that y, to achieve balance Fs is greater than Wm. At an angle where Fs*cos(theta)>Wm the lever will move off the knife edge and be propelled into space by the applied force. It becomes quite clear if theta is 180 degrees (the lever is bent right back on itself) then Fs acts vertically upwards and the lever takes off in an upward direction, or if the fulcrum is a fixed bearing, there is now an upward force on that bearing, and to prevent take off the bearing needs to connect to ground.

You have not summed your forces vectorally, and that is your mistake. You have just assumed that the balance situation for your bent lever system will apply the same weight at the fulcrum as the case for a straight lever, and that is wrong. End of Quote.

You are also neglecting the fact that as the water pushes against the piston to apply pressure to the fulcrum the fulcrum is also applying an opposite force back to the piston and the water. Equal and opposite reaction.

Carroll
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