Question

№ 1 Легковой автомобиль массой м = 1500 кг разгоняется из состояния покоя с постоянным ускорением а = 2 м/с². КПД автомобильного двигателя (коэффициент преобразования тепловой энергии сгорания бензина в механическую) считать постоянным и равным n=30%. Сопротивлением воздуха можно пренебречь. Удельная теплота сгорания бензина g = 46 МДж/кг. Как изменяется расход бензина в процессе разгона по мере увеличения скорости h​

Answer 1

Ответ и объеснение на фото!

Answer 2

Calculation of Fuel Consumption during Acceleration

To determine how the fuel consumption changes during acceleration, we need to consider the power output of the engine and the energy required to accelerate the car.

The power output of the engine can be calculated using the formula:

Power = Force x Velocity

The force acting on the car during acceleration can be calculated using Newton's second law of motion:

Force = Mass x Acceleration

Given: - Mass of the car (m) = 1500 kg - Acceleration (a) = 2 m/s² - Efficiency of the engine (n) = 30% (0.3) - Specific heat of combustion of gasoline (g) = 46 MJ/kg

Let's calculate the power output of the engine during acceleration:

Force = Mass x Acceleration = 1500 kg x 2 m/s² = 3000 N

Power = Force x Velocity

Since the car is accelerating from rest, the velocity is continuously changing. Therefore, we need to integrate the power over time to find the total energy required for acceleration.

The energy required for acceleration can be calculated using the formula:

Energy = ∫(Power x dt)

Integrating the power with respect to time, we get:

Energy = ∫(Force x Velocity x dt)

To solve this integral, we need to express velocity as a function of time. The relationship between velocity and time during constant acceleration can be given by:

Velocity = Initial Velocity + Acceleration x Time

Since the car starts from rest, the initial velocity is 0. Therefore, the equation becomes:

Velocity = Acceleration x Time

Substituting this into the energy equation, we get:

Energy = ∫(Force x (Acceleration x Time) x dt)

Simplifying, we have:

Energy = ∫(Force x Acceleration x Time x dt)

Integrating with respect to time, we get:

Energy = (Force x Acceleration x Time²) / 2

Now, let's calculate the energy required for acceleration:

Energy = (3000 N x 2 m/s² x Time²) / 2

To find the time required for acceleration, we can use the equation:

Time = Final Velocity / Acceleration

The final velocity can be calculated using the formula:

Final Velocity = Initial Velocity + Acceleration x Time

Since the car starts from rest, the initial velocity is 0. Therefore, the equation becomes:

Final Velocity = Acceleration x Time

Substituting this into the time equation, we get:

Time = (Acceleration x Time) / Acceleration

Simplifying, we have:

Time = Time

This means that the time required for acceleration is arbitrary and can be chosen based on the desired final velocity.

Now, let's calculate the fuel consumption during acceleration. The energy required for acceleration is equal to the energy output of the engine, which can be calculated using the formula:

Energy Output = Energy Input / Efficiency

Since the efficiency of the engine is given as 30%, the energy output is:

Energy Output = Energy Input / 0.3

Substituting the energy input value we calculated earlier, we get:

Energy Output = ((3000 N x 2 m/s² x Time²) / 2) / 0.3

To calculate the fuel consumption, we need to divide the energy output by the specific heat of combustion of gasoline:

Fuel Consumption = Energy Output / Specific Heat of Combustion

Substituting the energy output value and the specific heat of combustion of gasoline (46 MJ/kg), we get:

Fuel Consumption = (((3000 N x 2 m/s² x Time²) / 2) / 0.3) / 46 MJ/kg

Therefore, the fuel consumption during acceleration depends on the time chosen for acceleration. The longer the acceleration time, the higher the fuel consumption.

Please note that this calculation assumes ideal conditions and neglects factors such as air resistance. The actual fuel consumption during acceleration may vary in real-world scenarios.