Deriving atwood's gravity formual

[foo_fighter@hotmail.]

I have always been curios to how Atwood derived his formula a=g(m2+m1)/(m2-m1) to get gravity. Does anyone know how he did it? I have read that he used Netwons f=ma but I personally could not find a way to do this using Newtons f=ma.

Thanks.

 

[jcsd]

The formula is:

g = a(M₁ + M₂)/(M₁- M₂)

using F = ma and F = mg

Gravity is acting on both the weights therefore:

F₁ = M₁g

F₂ = M₂g

The total force acting down is given by:

F = F₁ - F₂

which is:

F = g(M₁ - M₂)

As the force is pulling both weights we can view the two weights as one single weight being acted on with a mass of M₁ + M₂, so using F = ma

F = a(M₁ + M₂)

We,ve now got two terms for the same force so we can subsitue in for F:

a(M₁ + M₂) = g(M₁ - M₂)


changing this around:

g = a(M₁ + M₂)/(M₁- M₂)

Q.E.D.