Two masses m1 and m2 are connected by a rope that runs over a pulley with a stat

Question

Two masses m1 and m2 are connected by a rope that runs over a pulley with a stationary axle as in the figure below. A second rope is attached to the rope between the masses m1 and m2 and to the wall such that it makes the angle ? with the wall and ? as shown; this rope has tension T. The system is stationary.

Calculate the masses m1 and m2 as a function of the tension T, the angles ? and ?, and the acceleration due to gravity g.

Ignore the friction between the pulley and the rope, and the masses of the pulley and the ropes.

Explanation / Answer

T' be the tention in the rope 1 at Mass m2 T' = M2g T'' be the tention in the rope 1 at Mass m1 T'' = M1g Applying newton's laws of motion at the joining of rope 1 and 2 T'' = T cos ? - T' cos(180 - ? ) T'' = T cos ? + T'cos ? M1g = T cos ? + M2g cos ?..........1 T sin ? = T' sin(180 - ?) T sin ? = T' sin ? T sin ? = M2g sin ?............2 Solving equation 1 and 2 M2 = T sin ?/g sin ? M1 = T cos ?/g + T sin ?/g tan ?

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