A car with a mass of 900.0 kg climbs a 20.00° incline at a steady speed of 60.00 km/hr. If the total dissipative force acting on the car (due to air resistance and internal friction) add to 500.0 N, what is the power output of the car in watts?
A car with a mass of 900.0 kg climbs a 20.00° incline at a steady speed of 60.00 km/hr. If the total dissipative force acting on the car (due to air resistance and internal friction) add to 500.0 N, what is the power output of the car in watts?
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![**Problem Statement:**
A car with a mass of 900.0 kg climbs a 20.00° incline at a steady speed of 60.00 km/hr. If the total dissipative force acting on the car (due to air resistance and internal friction) adds to 500.0 N, what is the power output of the car in watts?
**Solution Explanation:**
To find the power output of the car, we need to calculate the work done against gravity and the dissipative forces. The power output is the rate at which work is done, given by:
\[ \text{Power} = \text{Force} \times \text{Velocity} \]
1. **Convert the Velocity:**
- Convert 60.00 km/hr to meters per second (m/s):
\[ 60.00 \, \text{km/hr} = \frac{60.00 \times 1000}{3600} = 16.67 \, \text{m/s} \]
2. **Calculate the Gravitational Force Component:**
- The gravitational force component acting down the incline is:
\[ F_{\text{gravity}} = m \cdot g \cdot \sin(\theta) \]
where \( m = 900.0 \, \text{kg} \), \( g = 9.81 \, \text{m/s}^2 \), \( \theta = 20.00° \).
3. **Calculate Total Force:**
- Total force exerted by the car to maintain a steady speed is the sum of force to overcome gravity and the dissipative force:
\[ F_{\text{total}} = F_{\text{gravity}} + 500.0 \, \text{N} \]
4. **Calculate Power Output:**
- Power is given by the product of the total force and velocity:
\[ P = F_{\text{total}} \times 16.67 \, \text{m/s} \]
This calculation will give the power output required to maintain the steady speed up the incline.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8084badb-1caf-4ac3-abaa-e998705ca4db%2F410177de-ff06-4b40-a945-69a9e449e865%2Fmazyxvv_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A car with a mass of 900.0 kg climbs a 20.00° incline at a steady speed of 60.00 km/hr. If the total dissipative force acting on the car (due to air resistance and internal friction) adds to 500.0 N, what is the power output of the car in watts?
**Solution Explanation:**
To find the power output of the car, we need to calculate the work done against gravity and the dissipative forces. The power output is the rate at which work is done, given by:
\[ \text{Power} = \text{Force} \times \text{Velocity} \]
1. **Convert the Velocity:**
- Convert 60.00 km/hr to meters per second (m/s):
\[ 60.00 \, \text{km/hr} = \frac{60.00 \times 1000}{3600} = 16.67 \, \text{m/s} \]
2. **Calculate the Gravitational Force Component:**
- The gravitational force component acting down the incline is:
\[ F_{\text{gravity}} = m \cdot g \cdot \sin(\theta) \]
where \( m = 900.0 \, \text{kg} \), \( g = 9.81 \, \text{m/s}^2 \), \( \theta = 20.00° \).
3. **Calculate Total Force:**
- Total force exerted by the car to maintain a steady speed is the sum of force to overcome gravity and the dissipative force:
\[ F_{\text{total}} = F_{\text{gravity}} + 500.0 \, \text{N} \]
4. **Calculate Power Output:**
- Power is given by the product of the total force and velocity:
\[ P = F_{\text{total}} \times 16.67 \, \text{m/s} \]
This calculation will give the power output required to maintain the steady speed up the incline.
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The steady speed of a car is,
The total resistive or dissipative force acting on a car is,
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