Incorrect Ratio Calculation

[as1092]

Hello! I have trouble getting an accurate calculation for the ratio of my masses for Division C. Here is a picture of my lever w/ two masses (100g and 200g) attached: https://drive.google.com/file/d/1uSsoP6 ... sp=sharing

So, the calculated ratio is 2:1. However, when I use my compound lever, it reaches static equilibrium when the calculated ratio is close to 3:1. I was wondering what I can do to correct this. I already have a permanent mass attached to the first-class lever on the very left to keep the levers in static equilibrium when no masses are attached, and I still receive very inaccurate mass ratios. Any help would be appreciated. Thank you!

[Umaroth]

I think it would help if you posted the equation you're using as well. I have a bunch that your equation doesn't account for the fact that you didn't place the connection perpendicular to both lever arms, but we will have to look at your equation to verify. Basically putting the lever arm connection diagonal like that would mess up your calculations because the torque exerted would be less than if it were perpendicular to the arms.

[as1092]

I think it would help if you posted the equation you're using as well. I have a bunch that your equation doesn't account for the fact that you didn't place the connection perpendicular to both lever arms, but we will have to look at your equation to verify. Basically putting the lever arm connection diagonal like that would mess up your calculations because the torque exerted would be less than if it were perpendicular to the arms.

I haven't been using equations; I am just trying to calculate the ratio using the distances of the masses from the fulcrum. Also, I have seen many designs that work even with the connection not perpendicular to the lever arm (https://www.youtube.com/watch?v=qIEbVXtrMT0). I am genuinely so confused because in this video it works perfectly, but mine is nowhere near perfect.

[Fizzile]

Make sure that your levers are balanced before you put the masses on.

[thehuntfornedoctober]

It's probably one or both of these two things:

1) As someone already pointed out, the levers have to be balanced before you put the masses on. I don't see a counterweight in the picture you posted. If you don't already have a counterweight and the levers aren't at equilibrium when there aren't any masses hanging, you need to add a counterweight.

2) The mass ratio isn't just the ratio of the distances the masses hang from the fulcrum. You also have account for the ratio of the lever arms. It makes the most sense when you look at the equations.

M1 = Mass on the upper lever
M2 = Mass on the lower lever
x = Distance from M1 to the fulcrum of the upper lever
y = Distance from M2 to the fulcrum of the lower lever
A = Distance from the fulcrum to the connection on the upper lever
B = Distance from the fulcrum to the connection on the lower lever
T = Tension force in the connection

When the upper lever is at equilibrium:
Net torque = 0
M1 * g * x = A * T
(M1 * g * x)/A = T

When the lower lever is at equilibrium:
Net torque = 0
M2 * g * y = B * T
(M2 * g * y)/B = T

Substitute the left side of the first equation in for T

(M1 * g * x)/A = (M2 * g * y)/B

With a little algebra we get this:

M1/M2 = (y/x) * (A/B)

From your picture, it seems like your A/B ratio is about 7/11, so you have to multiply your distance ratio of 3/1 by 7/11 which gives you 21/11 which is about 2.

Hope that clears it up.