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

[yang09]

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

 

[shireoki]

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 :(

 

[shireoki]

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

 

[shireoki]

and nvm i got the bernoulli's equ :)

 

[rwisz]

I would first identify the relevant equations and variables in this problem. From the given information, we know that there are two pistons with different diameters and an external force acting on the lever arm. We also know that the weight being supported is 464 lb.

To solve for the force F, we can use the equation Forcein/Areaout = Forceout/Areaout. This equation relates the force applied to the smaller piston to the force required to support the larger piston. We can rearrange this equation to solve for F:

F = (Forceout/Areaout) * Areain/Areaout

In this case, the forceout is the weight being supported, 464 lb, and the areaout is the area of piston 2, which can be calculated using the formula for the area of a circle:

Areaout = π * (diameter/2)^2

Substituting in the given diameter of piston 2, we get:

Areaout = π * (1.3 in/2)^2 = 1.33 in^2

The areain is the area of piston 1, which can also be calculated using the formula for the area of a circle:

Areain = π * (diameter/2)^2

Substituting in the given diameter of piston 1, we get:

Areain = π * (0.27 in/2)^2 = 0.057 in^2

Substituting these values into the equation for F, we get:

F = (464 lb/1.33 in^2) * (0.057 in^2/1.33 in^2) = 1.96 lb

Therefore, the force F necessary to support the 464 lb weight is approximately 1.96 lb. This may seem like a small force, but it is amplified by the mechanical advantage of the lever arm to support the weight.

In conclusion, as a scientist, I would approach this problem by identifying the relevant equations and variables, and then using those equations to solve for the unknown force. I would also double check my calculations and make sure they make sense in the context of the problem.