Mechanics.

237

7. If W and H be given, or always the fame ; the 11F — ——^-(for here we suppose the Force ap-

plied to draw in the most advantageous Direction, viz.C M, where S becomes equal to R.) If therefore the

Radii of four Wheels be 1, 2, 3, 4, then will —— 4 —-

be 1, ^ 3 */ 5 ^ 7 or as the Numbers 1000,

2’ 3' \

866, 745, 661. From hence it is evident how muchless Force is necessary to draw a large Wheel over anyObstacle than a lesler one, when the Weight of theWheels are the fame.

7. If the Height of the Obstacle H be indefinitelysmall and given, in which Case the Tangent O K willcoincide with the horizontal Line N D, and the PointE with the Point G, very nearly ; and the Direction ofthe Force be parallel toNDj then because H’ is incon-siderable we reject it, and the Expression for the Force

will be F — ^ "y 2 (for H is given, and there-fore not exprefs’d). And if W be also given, the

Force will be F — — 2 ^ or F — —, because 2 is

R K

n , V' K

a g.ven (Quantity; but —^—

V

R

therefore F —

- 4 ^.-; that is, in cafe of rough unc\en S lrfaces thev/K

Force to draw the Wheel will be inversely as the SquareRoot of the Radius or Diameter of the Wheel. Thusif three Wheels are in Diameter as 1, 4, 9 ; the forceto draw them will be as 3, 2, 1.

8. If H — 0, that is, if the horizontal Plane onwhich the Wheel moves be perfedtiy lmooth or plain,W _

then the Quantity — v' 2 R ti —- H 1 — 0 ; whence

it appears that no Force is required to msve an heavyBody on an hg.iz ntal Plane which i$ persectly even.