Analytical mechanics for students of physics and engineering . (2) the tensile force in thestring, and (3) the reaction of the sphere. 3. The lengths of the mast and the boom of a derrick are ,; and h respectively. Supposing the hinges at the lower end of the 1 m and the pulley at the upper end to be smooth, find the angle the boom makeswith the vertical when a weight W is suspended in equilibrium. 4. Find the tensile force in the chain ami the compression in the boomof the preceding problem. 6. Two rings of weights lli and U, are held on a smooth circularwire in a vertical plane by means of a
Analytical mechanics for students of physics and engineering . (2) the tensile force in thestring, and (3) the reaction of the sphere. 3. The lengths of the mast and the boom of a derrick are ,; and h respectively. Supposing the hinges at the lower end of the 1 m and the pulley at the upper end to be smooth, find the angle the boom makeswith the vertical when a weight W is suspended in equilibrium. 4. Find the tensile force in the chain ami the compression in the boomof the preceding problem. 6. Two rings of weights lli and U, are held on a smooth circularwire in a vertical plane by means of a string subtending an anglithe center. Show that the inclination of the string to the horizon isgiven by tan0=(l. j 1(jtana. 6. A bridge, Fig. (a), of 60-fool span and 10-foot width has two queen-post trusses 9 feet deep. Each truss is divided into three equal parts by two 28 ANALYTICAL MIXHAXK S posts. What arc the stresses in the different parts of the trusses when,there is a load of 150 pounds per square foot of floor space? -->*—20—>K 20—-»i. Fig. (b). 7. Find the force in one of the members of the truss of figure (b). 8. A weight rests upon a smooth inclined plane, supported by two equalstrings the upper ends of which are fastened to two points of the plane inthe same horizontal line. Find the tensile force in the strings and thereaction of the plane. 9. In the preceding problem suppose the plan^ to be rough. 10. A particle is suspended by a string which passes through a smoothring fastened to the highest point of a circular wire in a vertical other end of the .string is attached to a smooth bead which is movableon the wire. Find the position of equilibrium supposing the bead andthe suspended body to have equal weights. 11. A particle is in equilibrium on a rough inclined plane under theaction of a force which acts along the plane. If the least magnitude of theforce when the inclination of the plane is a equals the greatest magnitude when it is «2,
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