A 1500-kg car coast in neutral down a 2.0degrees hill. The car attains a terminal speed of 20.0 m/s. The question is:how much power must the engine deliver to drive the car on a level road at 20.0 m/s?? Help me out please!!
m g = 1500* 9.81
m g sin theta = 1500 * 9.81 * sin 2 = 514 N propulsive force
Power = force * speed
= 514 N * 20 m/s = 10.27 KW
To determine the power required to drive the car on a level road at 20.0 m/s, we can start by calculating the gravitational force acting on the car as it goes down the hill.
The gravitational force can be calculated using the formula:
Force = mass * acceleration due to gravity
where mass = 1500 kg and acceleration due to gravity = 9.8 m/s².
Force = 1500 kg * 9.8 m/s² = 14,700 N
Next, we need to calculate the force required to overcome air resistance when the car is moving at a constant speed of 20.0 m/s. This force is known as the drag force.
The drag force can be calculated using the formula:
Drag force = 0.5 * air density * velocity² * drag coefficient * frontal area
where air density = 1.2 kg/m³ (typical value), drag coefficient and frontal area are specific to the car. Since these values are not provided, we cannot calculate the exact drag force.
However, we can assume that on a level road at a constant speed of 20.0 m/s, the drag force is equal to the force required to overcome air resistance.
Setting the drag force equal to the gravitational force:
Drag force = 14,700 N
Now, we can solve for the power required to overcome drag force:
Power = Drag force * velocity
Power = 14,700 N * 20.0 m/s = 294,000 W or 294 kW
Therefore, the engine must deliver approximately 294 kW of power to drive the car on a level road at 20.0 m/s.
To determine how much power the engine must deliver to drive the car on a level road at 20.0 m/s, we need to consider the forces acting on the car.
When the car is coasting down the hill, the only force acting on it is the force of gravity, which can be calculated using the formula:
F_gravity = m * g * sin(θ)
Where:
m = mass of the car (1500 kg)
g = acceleration due to gravity (9.8 m/s^2)
θ = angle of the hill (2.0 degrees)
Next, we need to calculate the gravitational force acting on the car:
F_gravity = 1500 kg * 9.8 m/s^2 * sin(2.0 degrees)
Now, we can calculate the power required to overcome this gravitational force. Power is the rate at which work is done, which can be calculated using the formula:
Power = Force * Velocity
Since the car is attaining a terminal speed of 20.0 m/s, we can use this velocity to calculate the power:
Power = F_gravity * 20.0 m/s
Therefore, to determine the power required to drive the car on a level road at 20.0 m/s, we need to plug in the calculated F_gravity value into the power formula:
Power = (1500 kg * 9.8 m/s^2 * sin(2.0 degrees)) * 20.0 m/s
Calculating this will give you the answer to the power required by the engine to drive the car on a level road at 20.0 m/s.