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The Fundamental Equation of Dynamics

Problem 1.63

The following parameters of the arrangement of Fig. 1.11 are available: the angle α\alpha which the inclined plane forms with the horizontal, and the coefficient of friction kk between the body m1m_{1} and the inclined plane. The masses of the pulley and the threads, as well as the friction in the pulley, are negligible. Assuming both bodies to be motionless at the initial moment, find the mass ratio m2/m1m_{2} / m_{1} at which the body m2m_{2} (a) starts coming down; (b) starts going up; (c) is at rest.

Reveal Answer
 (a) m2/m1>sin⁡α+kcos⁡α; (b) m2/m1<sin⁡α−kcos⁡α ;  (c) sin⁡α−kcos⁡α<m2/m1<sin⁡α+kcos⁡α\text { (a) } m_{2} / m_{1}>\sin \alpha+k \cos \alpha; \text { (b) } m_{2} / m_{1}<\sin \alpha-k \cos \alpha \text { ; }\text { (c) } \sin \alpha-k \cos \alpha<m_{2} / m_{1}<\sin \alpha+k \cos \alpha
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