Question

Поезд массой М=2000т трогаясь с места с ускорением а=0,2м/с^2, достигает нужной скорости через t=1мин ,после чего движется равномерно . Определить мощность тепловоза при установившемся движении ,если коэффицент сопротивления k=0,005

Answer 1

• определим скорость тепловоза спустя t = 60 c с допущением, что начальная скорость равна нулю

v = a t = 0.2*60 = 12 м/c

• теперь определим мощность

N = A/t = (F S)/t = F v

так как движение равномерное, то сила тяги F численно равна силе трения Fтр = u N = u mg. тогда

N = u mg v = 0.005*2*10^(7)*12 = 1200000 Вт или 1.2 МВт

Answer 2

Problem Analysis

We are given the mass of a train, the acceleration it experiences while starting, the time it takes to reach a certain speed, and the coefficient of resistance. We need to determine the power of the locomotive when it reaches a steady state of motion.

Solution

To solve this problem, we can break it down into two parts: the initial acceleration phase and the steady-state motion phase.

# Initial Acceleration Phase

During the initial acceleration phase, the train is accelerating with an acceleration of 0.2 m/s^2. We can use the equation of motion to find the final velocity of the train during this phase.

The equation of motion for constant acceleration is:

v = u + at

Where: - v is the final velocity - u is the initial velocity (which is 0 in this case) - a is the acceleration - t is the time

In this case, the initial velocity is 0, the acceleration is 0.2 m/s^2, and the time is 1 minute (which is equal to 60 seconds).

Substituting the values into the equation, we can find the final velocity during the initial acceleration phase.

# Steady-State Motion Phase

After reaching the desired speed, the train moves with a constant velocity. During this phase, the net force acting on the train is zero. The net force can be calculated using the equation:

F_net = F_applied - F_friction

Where: - F_net is the net force - F_applied is the applied force (which is the force exerted by the locomotive) - F_friction is the frictional force

The frictional force can be calculated using the equation:

F_friction = k * m * g

Where: - k is the coefficient of resistance - m is the mass of the train - g is the acceleration due to gravity (approximately 9.8 m/s^2)

Since the net force is zero during steady-state motion, the applied force is equal to the frictional force. Therefore, we can calculate the power of the locomotive using the equation:

Power = F_applied * v

Where: - Power is the power of the locomotive - F_applied is the applied force (which is equal to F_friction) - v is the velocity of the train during steady-state motion

# Calculation Steps

1. Calculate the final velocity during the initial acceleration phase using the equation of motion. 2. Calculate the frictional force using the equation F_friction = k * m * g. 3. Calculate the power of the locomotive using the equation Power = F_applied * v, where F_applied is equal to F_friction and v is the final velocity during steady-state motion.

Let's perform the calculations now.