By Ivan, V. Meshchersky, N.M. Sinelnikova
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Extra resources for Collection of Problems in Theoretical Mechanics
141). The cylinder weighs Q kgf. The plane of contact of both halves of the cylinder is vertical. Determine the minimum value of P for which both halves of the cylinder will be in equilibrium on a horizontal plane. Ans. P=—£~Q- kgf. 3 TE 158. A system consists of a hemisphere with a cylinder of equal density and radius r mounted on the flat side (Fig. 142). Assuming that the system rests in stable equilibrium with the hemisphere on a smooth horizontal plane, determine the maximum height h of the cylinder.
Also find the equation of the hodograph of the velocity. Ans. rncm/sec, vy=O; when x=l5 cm, y=O vx=O, vy==— ? — rncm/sec. %%§n”. 169. A particle describes Lissajous’ figure given by the equations: x=2 cos t, y=4 cos 2t (x, y are measured in centimetres 61 and t in seconds). Determine the magnitude and direction of the ve·locity of the particle when it is on the axis Oy. Ans. (1) v=2 cm/sec; cos (v,x)=—l. (2) v=2 cm/sec; cos (v,x)=l. 170. Find the velocity of the centreM A of a connecting rod of the slider crank ggd mechanism and the velocity of the slider M for r=l=a and cp=mt, where m=const .
122). The side AB is horizontal. The lamina rests on the spike at the point E. A force F-= 10 kgf acts parallel to AB at the point H. CE=ED, BH=10 cm. The angle or between the plate and the horizontal surface equals 30° Find the reactions at the points A, B and E. Ans. 17 kgf. _°‘ D 138. Determine the forces in the 6 sup- 6 E orting rods which hold the square plate " BCD when a horizontal force P acts I F ’/M long the side AD. The dimensions are _ U hown in Fig. 123. Fig. 122 Ans. -=——P; S,=P}/2; 139.
Collection of Problems in Theoretical Mechanics by Ivan, V. Meshchersky, N.M. Sinelnikova