Final answer:
To find the needed power output for the car to climb the slope, we calculate the force needed to overcome both gravity and resistive forces, then multiply by velocity. The total power required is approximately 28 kW.
Step-by-step explanation:
To calculate the power output needed for a 950-kg car to climb a 2.00° slope at a constant 30.0 m/s, we follow these steps:
- Identify the known values: mass (m) = 950 kg, slope angle (θ) = 2.00°, velocity (v) = 30.0 m/s, and resistive forces (f) = 600 N.
- The unknowns include the power (P) required by the car, and the force (F) applied by the car parallel to the incline.
- To solve for power, we use the formula P = Fv, where F is the total force the car must exert to oppose both gravity and resistive forces, calculated as F = f + mg sin θ.
- Insert the known values into the equation to get P = (600 N + 950 kg × 9.80 m/s² × sin 2°) × 30.0 m/s.
- Solving this gives a power output of approximately 27.7 × 10⁴ W, or about 28 kW.
This amount of power output is reasonable for a car engine to climb a gentle incline.