The Elementary Principles of Mechanics volume 3

Cover The Elementary Principles of Mechanics volume 3
The Elementary Principles of Mechanics volume 3
A Jay Augustus Jay Du Bois
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-lbs. We have W= r" r ' ~ Tt, or if W = 1 ft. -lb. , n - r a = r ' .
Taking r 1 = 4000 miles and ri = 240000 miles, we have 240000 X 5280 ~ 4000X4000X5280X5280 240000 X 5280 ~ The Theorem of La Place. If any closed surface in a field of force is divided into small portions, the sum of the products of the areas of these portions by the normal components of the forces exerted at them on unit mass is called the integral normal attraction over the surface.
Thus if V is the potential for any point o
...f the surface, then if p is the dV normal to the surface the normal force or unit mass is JV = . If dA i& dp the small elementary area, the product NdA is the normal attraction over /fdV NdA = I dA is the integral normal i/ dp attraction over the whole surface.
Let A be the area of any closed surface, and m any attracting mass wholly external to A. Then it can be shown that f*(lY mA = J-, iA=0.
114 KINETICS OF A PABTICLE TRANSLATION. [CHAP. VIIL This is known as the theorem of La Place.
Take a particle of mass m at O wholly outside the closed surface S.


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