The Calculus for Engineers

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E. Arnold, 1897 - Calculus - 378 pages
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Page 81 - Show that the moment of inertia of a body about any axis is equal to the moment of inertia about a parallel axis through the center of mass plus the product of the mass of the body and the square of the distance between the axes.
Page 60 - Show that the most economical dimensions for a rectangular tank to hold a given volume are a square base and a depth equal to one half the side of the b&se.
Page 95 - Curvature. — The curvature of a circle is the reciprocal of its radius ; and of any curve, it is the curvature of the circle which best agrees with the curve. The curvature of a curve is better given as " the angular change (in radians) of the direction of the curve per unit length.
Page 118 - MECHANICS. is /'/2N .... (7), and by adding we can therefore find its total amount for the whole beam. By equating the strain-energy to the loads multiplied by half the displacements produced by them we obtain interesting relations. Thus in the case of a beam of length I, of rectangular section, fixed at one end and loaded at the other with a load w ; at the distance x from the end, M — wx, and the energy due to bending is ____ (8).
Page 20 - ... in the differential calculus, it will be well to point out its obvious geometrical meaning. This is simply that, if the curve APE (see Fig.
Page 95 - When y and z are the principal axes of the section, /, cos2 0+7, sin2 /3 is the moment of inertia of the cross section about a line that passes through the centroid and the axis of rotation.
Page 26 - Perry — Calculus for Engineers. Page 26. In Practical Dynamics one second is the unit of time, one foot is the unit of space, one pound (what is called the weight of one pound in London), is the unit of force. To satisfy the college men who teach engineers, I would say that "The unit of mass is that mass on which the force of 1 Ib. produces an acceleration of 1 ft. per sec. per sec.
Page 85 - I0 the Moment of Inertia about an axis through the centre of gravity, and...
Page 166 - ... but a short time, as in the case of dynamos. Good average values for working tensions of leather belts are: Cemented joints, 400 pounds per square inch. Laced joints, 300 " " " Metal joints, 250 " " " " Horse-Power Transmitted by Belting. If P is the driving force in pounds at the rim of the pulley, and V is the velocity of the belt in feet per minute, the theoretical horse-power transmitted is evidently : It is evident from the above that the horse-power of a belt depends upon two things, the...

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