This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1874 Excerpt: ...of the string passing over it: if however the axis be moveable, then, as will be presently seen, a mechanical advantage may be gained. It is sometimes assumed as axiomatic that if a perfectly flexible string passes over a smooth surface the tension of the string will be the same throughout; we shall see, however, in ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1874 Excerpt: ...of the string passing over it: if however the axis be moveable, then, as will be presently seen, a mechanical advantage may be gained. It is sometimes assumed as axiomatic that if a perfectly flexible string passes over a smooth surface the tension of the string will be the same throughout; we shall see, however, in the Chapter on Flexible Strings that this result admits of demonstration. In the present Chapter we shall only require a part of the general proposition. We shall suppose the pullies to be circular, and assume that the tensions of the two portions of any string which are separated by a portion in contact with a pully are equal. And this may be shewn to be necessarily true if we merely admit that the string is a tangent to the circle at the point where it ceases to be in contact with the pully. For since the pully is smooth the directions of all the forces which it exerts on the string must pass through the centre of the pully; hence if we take the moments with respect to this point of the forces which act on the string we see that the string cannot be in equilibrium unless the tensions of the two portions are equal. 159. To find the ratio of the power and weight in the single moveable Ftdly. I. Suppose the parts of the string divided by the pully are parallel. Let the string ABP have one extremity fixed at A, and after passing under the pully at B suppose it held by the hand exerting a force P, or it may be passed over a fixed pully. The weight W is suspended by a string from the centre C of the pully. Now the tension of the string.42?Pis the same throughout. Hence the pully is acted on by three parallel forces, P, P, and W; hence 2P-W= 0; therefore = 2. II. Suppose the portions of the string are not parallel. Let a and a be the angles which Aa ...
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