II The century-old ascensores in Valparaiso, Chile, are...

II The century-old ascensores in Valparaiso, Chile, are small cable cars that go up and down the steep hillsides. As FIGURE P7. 43 shows, one car ascends as the other descends. The cars use a two-cable arrangement to compensate for friction; one cable passing around a large pulley connects the cars, the second is pulled by a small motor. Suppose the mass of both cars (with passengers) is $1500 \mathrm{kg},$ the coefficient of rolling friction is $0.020,$ and the cars move at constant speed. What is the tension in the (a) the connecting cable and (b) the cable to the motor?

Key Concepts

Pulley Systems and Tension in Cables

Pulley systems are used to change the direction of applied forces and in some cases to provide mechanical advantage. Tension in the cables of a pulley system is the force transmitted along the rope or cable, which is critical in keeping the system in equilibrium. In such systems, understanding how tension distributes and reacts to additional factors like friction is key to analyzing and solving for unknown forces.

Force Equilibrium

In scenarios where systems move at constant velocity, the sum of forces in any direction equals zero. Understanding force equilibrium helps in setting up equations where opposing forces, such as friction and gravitational or applied tensions, cancel each other out. This concept is central to solving problems that involve balancing different forces in a mechanical system.

Newton's Second Law of Motion

This fundamental law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. When an object moves at constant speed, the net force is zero, meaning all the forces acting on the object balance each other. This principle is crucial in problems where forces such as gravity, friction, and applied tensions are in equilibrium.

Friction (Rolling Friction)

Friction is a resistive force that opposes motion, and in the context of rolling objects, the rolling friction coefficient defines the resistance between the rolling object and the surface. This concept is especially important when calculating the total opposing force that must be counteracted by other forces, such as tension, to maintain constant speed.

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