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The century-old ascensores in Valparaiso, Chile, are small cable cars that go up and down the steep hillsides. As (Figure 1) 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 each car (with passengers) is 1700 kg, the coefficient of rolling friction is 0.030, and the cars move at constant speed. The angle is 35 degrees and tension in the cable to the motor is 820 N

We are tasked with analyzing the forces involved in the system described in the image. Specifically, we have two cable cars connected via a pulley system, one ascending and the other descending a slope at an angle of 35°, with the system in constant speed motion. 

Let's break down the key information:
- **Mass of each car**: 1700 kg.
- **Coefficient of rolling friction**: 0.030.
- **Angle of the incline**: 35°.
- **Tension in the cable connected to the motor**: 820 N.
- **Constant speed**: This indicates that the net force on each car is zero.

### Forces acting on the ascending car:
1. **Gravitational force component along the slope**: 
   This force pulls the car downhill and is given by:
   \[
   F_{\text{gravity}} = m g \sin(\theta)
   \]
   where:
   - \( m = 1700 \, \text{kg} \) is the mass,
   - \( g = 9.81 \, \text{m/s}^2 \) is the acceleration due to gravity,
   - \( \theta = 35^\circ \) is the incline angle.

2. **Rolling friction force**: 
   Rolling friction opposes the motion of the car, and is given by:
   \[
   F_{\text{friction}} = \mu m g \cos(\theta)
   \]
   where \( \mu = 0.030 \) is the coefficient of rolling friction.

3. **Tension force from the motor**: 
   The given tension in the cable is 820 N, which assists in pulling the car up.

### Balance of forces:
Since the car moves at a constant speed, the net force along the direction of motion is zero, so we can set up the following equation for the ascending car:
\[
T_{\text{motor}} = F_{\text{gravity}} + F_{\text{friction}}
\]
Substitute the formulas for the forces to solve for any unknown quantities.

Let's calculate the individual forces and verify whether the 820 N of tension balances the forces on the car.

#### 1. Gravitational force component:
\[
F_{\text{gravity}} = 1700 \times 9.81 \times \sin(35^\circ) \approx 9513.56 \, \text{N}
\]

#### 2. Rolling friction force:
\[
F_{\text{friction}} = 0.030 \times 1700 \times 9.81 \times \cos(35^\circ) \approx 409.62 \, \text{N}
\]

#### Total forces acting down the incline:
\[
F_{\text{total}} = 9513.56 + 409.62 \approx 9923.18 \, \text{N}
\]

Since the tension in the cable (820 N) is much smaller than the total downhill force (9923.18 N), it suggests that most of the force to pull the cars comes from the pulley system itself. This indicates the motor's role is mainly supplementary to the pulley.

Would you like a further breakdown of any specific part of the process or clarification on how the system functions?

### Follow-up questions:
1. What additional role does the pulley play in balancing forces between the two cars?
2. How would the forces change if the incline angle were steeper, say 45°?
3. What would be the effect on tension if the mass of each car increased to 2000 kg?
4. How does the constant speed condition simplify the force calculations?
5. How would rolling friction change if a different coefficient were used?

### Tip:
In constant speed problems, focus on balancing forces in the direction of motion to simplify the analysis.

The century-old ascensores in Valparaiso, Chile, are small cable cars that go up and down the steep hillsides. As one car ascends, the other descends. The cars use a two-cable arrangement to compensate for friction; one cable passes around a pulley to connect the cars, and the other is pulled by a small motor. Suppose the mass of each car (with passengers) is 1700 kg, the coefficient of rolling friction is 0.030, the cars move at constant speed, the incline is 35 degrees, and the tension in the cable to the motor is 820 N.

Explore the forces acting on the century-old cable cars of Valparaiso, Chile, as they move up and down steep hillsides. This physics problem involves calculating the gravitational and frictional forces on an inclined plane, with constant speed motion and tension provided by a motor. Suitable for high school students learning about Newton's laws and inclined planes.

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