An Elementary Treatise on MechanicsHarper & Brothers, 1883 |
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Common terms and phrases
accelerating force action angle applied apsis axes axis axle base beam body moves center of gravity center of oscillation centrifugal force circle circumference co-ordinates components concurring forces condition of equilibrium constant force cord couple curve density descend determine displaced fluid distance earth elastic equation feet fixed point fluid force of gravity force varies forces acting friction fulcrum given Hence horizontal impact inclined plane inertia Integrating length lever magnitude mass moment of inertia motion orbit P₁ P₂ parallel forces particle pendulum perpendicular point of application polygon position pressure PROP pulley radius of gyration ratio reaction represent resolved respectively resultant SCHOL seconds sides space described specific gravity square Substituting supposed surface tension tion triangle uniform v₁ versin vertical line vessel vibration virtual velocities weight wheel
Popular passages
Page 227 - The squares of the periods of revolution of any two planets are proportional to the cubes of their mean distances from the sun.
Page 184 - TT is constant, or, the time of vibration of a pendulum varies directly as the square root of the length, and inversely as the square root of the accelerating force.
Page 129 - A beam, 30 feet long, balances itself on a point at one-third of its length from the thicker end ; but when a weight of 10 Ibs. is suspended from the smaller end, the prop must be moved 2 feet towards it, in order to maintain the equilibrium. Find the weight of the beam.
Page 171 - Find the straight line of quickest descent from a given point to a given straight line, the point and the line being in the same vertical plane.
Page 9 - If any number of forces acting at a point can be represented in magnitude and direction by the sides of a POLYGON taken in order, they are in equilibrium.
Page 159 - Ex. 7. The space described by a body in the fifth second of its fall was to the space described in the last second but 4, as 1 to 6. What was the whole space described ? Ans.
Page 295 - ... to a height which is equal to the difference of level between the surface of the water in the...
Page 169 - ... sin. a, (73) in (55), we have v'=2gs sin. a, (74) from which all the circumstances of the motion may be determined. 276. PROP. The velocity acquired by a body in falling down an inclined plane is equal to that acquired in falling freely through the height of the plane. If s=AC, the length of the plane, and h=EC, the height, by (74), DYNAMICS. which, by (53'), is the velocity due to h, the height of the plane. 277. PROP. The times of descent down different inclined planes of the same height vary...
Page 152 - Two bodies m, and ma, whose elasticity is \, mo.ing in opposite directions with velocities 25 and 16 respectively, impinge directly upon each other. Find the distance between them 4£ seconds after impact. Ex. 9. At what angle must a body whose elasticity is .J. be incident on a perfectly hard plane, that the angle made by its path before and after impact may be a right angle? Ex. 10. A ball whose elasticity is e, projected from a given point in the circumference of a circle, after two reflections...
Page 234 - The quantity \i which enters into the results of the preceding investigations is the value of the accelerating force at the unit of distance from the center of force. Now the attractive forces of the sun and planets vary directly as their masses, and if M be the number of units of mass of the sun, and m the same of any planet, and if we assume for the unit of force the attraction of a unit of mass at a unit of distance, M will express the attractive force of the sun at the unit of distance, and m...