Mechanics of engineering. Theoretical mechanics.. by Weisbach J

Author:Weisbach, J. [from old catalog]
Language: eng
Format: epub, pdf
Publisher: New York
Published: 1875-03-25T05:00:00+00:00

therefore the mass of the same reduced to A is

[§ 295.

more accurately

Gk*

—r, we nave

gtf

= ( P + V~ + tf) : V= < Pa ' + 0 V +GV):ga>

Hence the acceleration of P or of the circumference of the wheel is Qb

motive force * a

P =

_ I

9*

ffa>

mass Pa 2 + Qb 2 + Gk 2

Pa—Qh

~ Pa 2 + QV+ GW hence the acceleration of the rising weight Q or of the circumference of the axle is

b P a- Q

P

.gb.

Pa*+ Qb* + Gfc

The tension of the cord, to which P is attached, is Pp _

g V gl v

and that of the cord, to which Q is attached, is and, therefore, the pressure on the hearings is

76),

S + Sl = P + Q-ll + ^l

P + Q

(Pa-QbY

Pa* + Qb* + G V The pressure on the bearing of a wheel and axle, when in rotation, is consequently less than when it is standing still.

From the accelerations p and q the other relations of the motion can be found; after t seconds the velocity of P is

v = p t and that of Q is

v, = qt; Fig. 492. the space described by P is

s = Ipt* and that by Q,

* = 2 g ?•

Example. —Let the weight upon the wheel, Fig. 492, be P=60 pounds and that on the axle, Q = 160 pounds; let the arm of the former be G A = a = 20 inches and that of the latter 5 5 = 5 = 6 inches, and let the axle be composed of a massive cylinder, weighing 10 pounds,

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