A Treatise on Elementary Statics, Τόμος 12

Macmillan, 1868 - 86 σελίδες

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Σελίδα 7 - We proceed to establish an important theorem which enables us to determine the resultant of any two forces acting at a point : the theorem is called the parallelogram of forces, and may be thus enunciated. If two forces acting at a point be represented in magnitude and direction by two straight lines drawn from that point, and if a parallelogram be constructed having these two lines for adjacent sides, then that diagonal of the parallelogram which passes through the point of application of the forces...
Σελίδα 44 - Prove that the algebraic sum of the moments of two concurrent forces about any point in their plane is equal to the moment of their resultant about the same point.
Σελίδα 50 - POWERS, are six in number; viz. 1. The Lever; 2. The Wheel and Axle; 3. The Pulley; 4. The Inclined Plane; 5. The Screw; 6. The Wedge.
Σελίδα 12 - IV. // 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 will be in equilibrium.
Σελίδα 15 - The Polygon of Forces. 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.
Σελίδα 3 - Let BC represent the rod, A the middle point of the rod. Draw AD making an angle of 45° with AC. Mark off a portion of the line AD, suppose AP, containing 5 units of length, that is, as many units of length as there are units of force in the given force. Then we may say that AP represents the given force in every particular : (1) In point of application, at A the middle point of the rod. (2) In direction, as being inclined at an angle of 45° to the horizon.
Σελίδα 71 - To every action there is always opposed an equal reaction: or, the mutual actions of two bodies upon each other are always equal and directed to contrary pans.
Σελίδα 63 - The substance to be weighed is placed in one scale-pan, and weights of known magnitude are placed in the other till the beam remains in equilibrium in a perfectly horizontal position, in which case the weight of the substance is indicated by the weights which balance it.
Σελίδα 14 - When three forces acting at a point are in equilibrium, each force is proportional to the sine of the angle between the other two.
Σελίδα 82 - ... and a man in the basket support himself and the basket, by pulling at the free end of the string, find the tension he exerts, neglecting the inclination of the string to the vertical, and assuming the weight of the man and basket to be W. 6. A man, whose weight is 12 stone, raises 3 cwt. by means of a system of pulleys in which the same string passes round all the pulleys, there being 4 in each block, and the string being attached to the upper block; neglecting the weights of the pulleys, find...

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