Two factors:

1) the weight of the car is now partially down the cable, it adds to tension: mgsinTheta is the component of weight pulling back on the cable.
2) going up you have mass*acceleration.

Total tension: ma +mgsinTheta
check my thinking, draw a diagram.

A section of an alpne cable-car system has a maximum permissible mass of each car with occupants in 2800kg. The cars riding on a support calbe ar pulled by a second cable attached to each pylon(support tower); assume the cables are straight. What is the difference in tension b/w adjacent sections of pull cable if the cars are at the maxiumum permissible mass and are being accelerated up the 35 degree incline at .81 m/s^2?

What is the equation that would be used to solve this problem?

Explain Bot Explain Bot answered
9 months ago

To solve this problem, we need to consider the forces acting on the cable and use Newton's second law of motion.

Let's start by identifying the forces acting on the cable. There are two main factors to consider:

1) The weight of the car: The weight of the car and its occupants adds to the tension in the cable. It can be broken down into two components: the vertical component mg, where m is the mass of the car, and g is the acceleration due to gravity, and the component mg*sin(θ), where θ is the angle of incline.

2) The acceleration of the car: As the car is being accelerated up the incline, there is an additional force due to the mass of the car multiplied by the acceleration (ma).

To find the difference in tension between adjacent sections of the pull cable, we need to calculate the total tension in each section. The equation that relates these forces is:

Total tension = ma + mgsinθ

Where:
m is the mass of the car
a is the acceleration of the car
g is the acceleration due to gravity (approximated as 9.8 m/s^2)
θ is the angle of incline (35 degrees in this case)

By plugging in the given values for the mass (2800 kg), the acceleration (0.81 m/s^2), and the angle of incline (35 degrees), you can solve for the total tension in each section of the pull cable. The difference in tension between adjacent sections can be found by subtracting the tension of the lower section from the tension of the higher section.