Question

Электровоз движется с постоянной скоростью 43,2 км/ч, развивая при этом среднюю силу тяги 40 кН. Определите КПД двигателей электровоза, если они работают под напряжением 1,5 кВ и потребляют силу тока 380А

Answer 1

Формулы мощности: N=FV и N=UI

N1=40000*12м/с=48000Вт 

N2=1500*380=57000Вт

КПД = Апол./Аобщ. * 100% = 570000t/1050000t *100%=54%

Answer 2

Calculation of Efficiency (КПД) of the Electric Locomotive

To determine the efficiency (КПД) of the electric locomotive, we need to calculate the input power and the output power.

The input power (P_in) can be calculated using the formula:

P_in = V * I

Where: - V is the voltage (напряжение) at which the motors of the electric locomotive operate, given as 1.5 kV (киловольт) in the question. - I is the current (сила тока) consumed by the motors, given as 380 A (ампер) in the question.

Substituting the given values, we get:

P_in = 1.5 kV * 380 A

To calculate the output power (P_out), we need to consider the force (сила тяги) exerted by the locomotive and the velocity (скорость) at which it is moving.

The force (F) exerted by the locomotive can be calculated using the formula:

F = m * a

Where: - m is the mass (масса) of the locomotive. - a is the acceleration (ускорение) of the locomotive, which is assumed to be zero since the locomotive is moving at a constant speed.

Since the locomotive is moving at a constant speed, the force exerted by the locomotive is equal to the force of resistance (сила сопротивления) opposing its motion.

The force of resistance (Fr) can be calculated using the formula:

Fr = F_drag + F_rolling

Where: - F_drag is the drag force (сила сопротивления воздуха). - F_rolling is the rolling resistance force (сила сопротивления качению).

The drag force (F_drag) can be calculated using the formula:

F_drag = 0.5 * ρ * A * v² * Cd

Where: - ρ is the air density (плотность воздуха). - A is the frontal area (фронтальная площадь) of the locomotive. - v is the velocity (скорость) of the locomotive. - Cd is the drag coefficient (коэффициент сопротивления).

The rolling resistance force (F_rolling) can be calculated using the formula:

F_rolling = C_rr * m * g

Where: - C_rr is the rolling resistance coefficient (коэффициент сопротивления качению). - g is the acceleration due to gravity (ускорение свободного падения).

Once we have the force of resistance (Fr), we can calculate the output power (P_out) using the formula:

P_out = F * v

Finally, we can calculate the efficiency (КПД) of the electric locomotive using the formula:

КПД = (P_out / P_in) * 100%

Let's calculate the efficiency (КПД) of the electric locomotive using the given values.

Calculation Steps:

Step 1: Calculate the input power (P_in): - V = 1.5 kV - I = 380 A

P_in = 1.5 kV * 380 A

Step 2: Calculate the force of resistance (Fr): - Calculate the drag force (F_drag) using the given values of air density (ρ), frontal area (A), velocity (v), and drag coefficient (Cd). - Calculate the rolling resistance force (F_rolling) using the given value of rolling resistance coefficient (C_rr).

Step 3: Calculate the output power (P_out): - F = Fr (since the locomotive is moving at a constant speed) - v = 43.2 km/h (км/ч)

P_out = F * v

Step 4: Calculate the efficiency (КПД): - КПД = (P_out / P_in) * 100%

Let's calculate the efficiency (КПД) using the given values.

Calculation:

Step 1: Calculate the input power (P_in): - V = 1.5 kV - I = 380 A

P_in = 1.5 kV * 380 A = 570 kW

Step 2: Calculate the force of resistance (Fr): - We don't have the specific values of air density (ρ), frontal area (A), drag coefficient (Cd), and rolling resistance coefficient (C_rr) for the electric locomotive. Without these values, we cannot calculate the force of resistance (Fr) accurately.

Unfortunately, without the specific values of air density (ρ), frontal area (A), drag coefficient (Cd), and rolling resistance coefficient (C_rr), we cannot accurately calculate the efficiency (КПД) of the electric locomotive.

Please provide the specific values of air density (ρ), frontal area (A), drag coefficient (Cd), and rolling resistance coefficient (C_rr) for the electric locomotive, or any additional information that may help us calculate the efficiency (КПД) accurately.