Calculating Force and Area Ratios for Piston Homework | 464lb Weight Support

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AI Thread Summary
To calculate the necessary force F to support a 464 lb weight using two pistons, the area ratio of the pistons is crucial. The formula used is based on the relationship between force and area, specifically A1/A2 multiplied by the weight. The mechanical advantage is then determined by the ratio of the distances from the pivot point, integrating the smaller distance over the total distance. The final calculations yield the required force F to lift the weight, confirming the application of both the area ratio and mechanical advantage principles. Understanding these concepts is essential for solving similar hydraulic problems.
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Homework Statement



Piston 1 in the figure has a diameter of 0.27 in and is attached to a lever arm a distance 1.8 in from the pivot point. Piston 2 has a diameter of 1.3 in. An external force F acts on the
lever arm at a distance 20 in from piston 1 as shown below. In the absence of friction, find the force F necessary to support the 464 lb weight. Assume the height difference between the pistons is negligible.
Answer in units of lb.

Homework Equations



Forcein/Areain = Forceout/Areaout

The Attempt at a Solution



The picture is #1 on the attached files.
I'm not even sure you're supposed to use this formula, but I have no clue how to solve it. Can someone please guide me in the right direction. Thanks



 

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hi, I was trying to solve the problem with the bernoulli's equation on your other post, and saw that you said you need help with this one, and i happened to just solved it, so i thought i'll stop by, hope it's not too late for your quest thing...


I did (A1/A2)*464lb
so, [pi*(0.27/2)^2]/[pi*(1.3/2)^2] times 464lb = x

then you have to do the mechanical ratio thing.. sooo

(shorter distance/ (shorter distance + longer distance) ) times the above answer you just found = what you need

[1.8/ (1.8+20)]*x = what you need

and I'm still having problem with the bernoulli's equa :(
 
and here's all the technical stuff:

x i mentioned above is force of small piston produced... fyi

technical stuff on the 2nd step:
+F1d1 - Fd = 0
+F1d1 = Fd
so F = (d1/d)*F1
 
and nvm i got the bernoulli's equ :)
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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