Two crates of mass m₁= 15 kg and m₂= 25 kg are connected by a cable that is strung over a pulley of mass m_pulley= 20 kg as shown in Figure P8.58. There is no friction between crate 1 and the table.

(a) Make a sketch showing all the forces on both crates and the pulley.

(b) Express Newton???s second law for the crates (translational motion) and for the pulley (rotational motion). The linear acceleration α of the crates, the angular acceleration α of the pulley, and the tensions in the right and left portions of the rope are unknowns.?

(c) What is the relation between α and α??

(d) Find the acceleration of the crates.?

(e) Find the tensions in the horizontal and vertical portions of the rope.

Figure P8.58

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Transcribed Image Text:

mpulley m1 m2