Two crates of mass m1 = 15 kg and m2 = 25 kg are connected by a cable that is strung over a pulley of mass mpulley = 20 kg as shown in Figure P8.58. There is no friction between crate 1 and the table.(a) Make a sketch showing all theforces 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 a of the crates, the angular acceleration a(alpha) of the pulley, and the tensions in the right and left portions of the rope are unknowns. (c) What is the relation between a and a(alpha)? (d) Find the acceleration of the crates. (e) Find the tensions in the right and left por- tions of the rope. **Figure P8.57 Explanation**This figure illustrates a simple pulley system. It consists of:- A pulley with mass, labeled as \( m_{\text{pulley}} \).- Two masses, \( m_1 \) and \( m_2 \), each attached to either end of a rope that passes over the pulley.- The rope is assumed to be light and frictionless, just like the pulley.The system demonstrates basic principles of mechanics, where the gravitational force acting on the masses creates tension in the rope, causing the system to either become static or accelerate depending on the relationships between the masses \( m_1 \) and \( m_2 \). This setup is a classic example used to analyze the forces and motions within pulley systems in physics.

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Two crates of mass m1 = 15 kg and m2 = 25 kg are connected by a cable that is strung over a pulley of mass mpulley = 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 a of the crates, the angular acceleration a(alpha) of the pulley, and the tensions in the right and left portions of the rope are unknowns. (c) What is the relation between a and a(alpha)? (d) Find the acceleration of the crates. (e) Find the tensions in the right and left por- tions of the rope.

Two crates of mass m1 = 15 kg and m2 = 25 kg are connected by a cable that is strung over a pulley of mass mpulley = 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 a of the crates, the angular acceleration a(alpha) of the pulley, and the tensions in the right and left portions of the rope are unknowns. (c) What is the relation between a and a(alpha)? (d) Find the acceleration of the crates. (e) Find the tensions in the right and left por- tions of the rope.

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