Figure 5-57 shows a section of a cable-car system. The...

Figure $5-57$ shows a section of a cable-car system. The maximum permissible mass of each car with occupants is 2800 $\mathrm{kg}$ . The cars, riding on a support cable, are pulled by a second cable attached to the support tower on each car. Assume that the cables are taut and inclined at angle $\theta=35^{\circ} .$ What is the difference in tension between adjacent sections of pull cable if the cars are at the maximum permissible mass and are being accelerated up the incline at 0.81 $\mathrm{m} / \mathrm{s}^{2} ?$

Figure $5-57$ shows a section of a cable-car system. The maximum permissible mass of each car with occupants is 2800 $\mathrm{kg}$ .
The cars, riding on a support cable, are pulled by a second cable
attached to the support tower on each car. Assume that the cables are taut and inclined at angle $\theta=35^{\circ} .$ What is the difference in
tension between adjacent sections of pull cable if the cars are at
the maximum permissible mass and are being accelerated up the
incline at 0.81 $\mathrm{m} / \mathrm{s}^{2} ?$

Key Concepts

Newton's Second Law

Newton's Second Law relates the net force acting on an object to its mass and acceleration. It is fundamental for setting up the equations of motion for objects being accelerated along an incline, where all forces including gravitational components and applied forces contribute to net acceleration.

Dynamics on Inclined Planes

When analyzing motion on inclined planes, forces are resolved into components that are parallel and perpendicular to the surface. This method helps in understanding how gravity and any additional acceleration affect the motion of objects on slopes, and it is essential for correctly computing net forces in such systems.

Gravitational Force Components

The gravitational force acting on an object can be resolved into a component parallel to the incline, which tends to accelerate the object downwards, and a component perpendicular to the incline, which is balanced by the normal force. This resolution is critical in problems involving motion on slopes, as it directly influences the net force and, hence, the acceleration.

Tension in Cable Systems

In cable systems, tension refers to the force transmitted through the cable as it supports and moves loads. Differences in tension between adjacent cable segments arise due to factors like acceleration and gravitational forces, and analyzing these differences requires applying Newton's laws to each section of the system.

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