Figure 5-47 shows a section of a cable-car system. The...

Figure $5-47$ shows a section of a cable-car system. The maximum permissible mass of each car with occupants is $2750 \mathrm{~kg}$. The cars, riding on a support cable, are pulled by a second cable attached to the support tower on each car. Assume clined 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 $0.81 \mathrm{~m} / \mathrm{s}^{2}$ ?

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Key Concepts

Force Resolution on an Incline

This concept involves decomposing forces into components parallel and perpendicular to the inclined surface. For a mass on an incline, the gravitational force is split into a component that acts to pull the mass down the slope and a component that acts perpendicular to the surface, which is essential when calculating the net force acting along the incline.

Tension in Cable Systems

Tension refers to the pulling force transmitted along a cable when forces are applied. In cable systems, especially those involving multiple connected sections, understanding how tension differs between segments is crucial for analyzing system performance under acceleration, as the tension must overcome both gravitational components and provide the necessary net force for motion.

Newton's Second Law

This principle states that the net force acting on an object is equal to the product of its mass and its acceleration (F = ma). It is fundamental in analyzing any dynamics problem where forces and acceleration are involved, particularly when determining the additional force required to accelerate a system along an incline.

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