Solution K2 Var. 20, reshebnik termehu Targ SM 1982


Meeting the challenge of K2 Option 20 Reshebnik on theoretical mechanics to Taskbook Targ SM 1982.
Subject objectives K2 - Research rotational rigid body motion around a fixed axis.
Check the condition of the task K2 (Pages 35-37, Manuals Targ SM 1982):
The mechanism consists of a stepped wheels 1-3 are connected or meshed transmission belt, the toothed rack 4 and the load 5, the end tied yarn wound on one of the wheels (Fig K2.0 -. K2.9, K2 Table.). The radii of the wheels of stages equal to respectively the wheel 1 - r1 = 2 cm, R1 = 4 cm, the wheel 2 - r2 = 6 cm, R2 = 8cm, the wheel 3 - r3 - 12 cm, R3 = 16 cm on the rim. wheels arranged points A, B and C.
In the column "Dano" Table Set law of motion, or the law of change of the driving gear unit speed, where φ1 (t) - the law of rotation of the wheel 1, s2 (t) - the law of motion of the rack 4, ε2 (t); - The law of variation of the angular velocity of the wheel 2, v5 (t) -.. The law of variation load speed 5, and so on (all φ is expressed in radians, s - in centimeters, t - in seconds). The positive direction for φ and ω counterclockwise for s4, s5 and v4, v5 - down.
Determine at time t1 = 2 shown in the table in the column "Find" speed (v - linear, ω - angular) and acceleration (a - line, e - angle) corresponding points or bodies (v5 - load speed 5, and so on. d.).

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