What is the solution to the cow tipping problem?

[asadpasat]

So I saw the cow tipping problem and I am having trouble figuring out how they got to the final equation.
Imagine making a rectangle around a cows body. Making a diagonal across the rectangle and center of mass being in center of the diagonal. One half of the diagonal is "a", and second is "b". Angle between the ground and the diagonal is theta. Drawing a F_g from center of mass divides the bottom line of rectangular in half (x/2)
From lever equation: (F_e)(d_e)=(F_l)(d_l)
Transforming it: (F)(a+b)= (F_l)(d_l)
(F)(a+b)= mg a cosθ [ I don't understand why is "a" necessary]
cosθ= (x/2)/a
(F)(a+b)= mg a ((x/2)/a)
(F)(a+b)= mg (x/2)
(F)= (mg (x/2)) / (a+b)

 

[Doc Al]

OK, I'll bite. What's the "cow tipping problem"? A diagram and statement of the problem would be nice.

 

[lightgrav]

The cow-tipper is pushing with strength Fe , applied to the cow at the top corner, pushing in the optimal direction (perp. to the diagonal).
in line 3, the "lever-arm" for the gravity Force (that is, distance from pivot perp. to the weight vector) is x/2

 

[Doc Al]

The cow-tipper is pushing with strength Fe , applied to the cow at the top corner, pushing in the optimal direction (perp. to the diagonal).
in line 3, the "lever-arm" for the gravity Force (that is, distance from pivot perp. to the weight vector) is x/2

Got it. Thanks!

 

[Doc Al]

(F)(a+b)= mg a cosθ [ I don't understand why is "a" necessary]

You need the perpendicular distance between mg and the pivot, which is "a cosθ". (Or x/2.) Without the "a" the equation would be dimensionally inconsistent.

 

[asadpasat]

You need the perpendicular distance between mg and the pivot, which is "a cosθ". (Or x/2.) Without the "a" the equation would be dimensionally inconsistent.

It seems like a long way from solving for (x/2) by cos, and then substituting cos, just to get (x/2).

 

[Doc Al]

It seems like a long way from solving for (x/2) by cos, and then substituting cos.

I would have went directly to x/2, since you were given that up front.

 

[asadpasat]

I would have went directly to x/2, since you were given that up front.

ok, great. Thanks