Question

Грузовой состав движется по ровному участку дороги со скоростью 60 км/ч, электровоз при этом развивает полезную мощность 100 кВт. С какой скоростью (в км/ч) надо подниматься по участку с уклоном 1 м на 200 м пути, чтобы развиваемая мощность равнялась 120 кВт? Сила сопротивления равна 0,01 от силы тяжести состава.

Answer 1

P1=Ft1v1=umgv1; Ft2-ung - mg sin a=0; P2=Ft2v2=v2 разделив Р2 на Р1, выразим v2.
V2=P2/P1•u/u+sin a• V1=48км/ч

Answer 2

Дано P1=100 кВт    V1=60 км/ч    h=1 м   L=200м    P2=120 кВт   V2- ?

при горизонтальном движении P1=Fтяг*V1=Fтр*V1=k*m*g*V1

при подъеме вверх
P2=(m*g*sina +Fтр*соsa)*V2
при малых углах соsa=1   sina=h/L=1/200=0,005
P2=m*g*(sina+k)*V2
P2/P1=(sina+k)*V2/k*V1
V2=P2*k*V1/(sina+k)*P1=120*0,01*60/100*0,015=72/1,5=48 км/ч

Answer 3

Calculation of the Required Speed

To determine the speed at which the train needs to climb a section of the road with a slope of 1 meter over 200 meters in order to develop a power of 120 kW, we can use the formula for power:

Power = Force x Velocity

In this case, the force is the sum of the force of gravity and the force of resistance. The force of gravity can be calculated as the weight of the train, which is equal to the mass of the train multiplied by the acceleration due to gravity. The force of resistance is given as 0.01 times the force of gravity.

Let's calculate the force of gravity and the force of resistance:

Force of Gravity = Mass x Acceleration due to Gravity

The acceleration due to gravity is approximately 9.8 m/s^2.

Force of Resistance = 0.01 x Force of Gravity

Now, let's calculate the force of gravity and the force of resistance:

Force of Gravity = Mass x 9.8

Force of Resistance = 0.01 x Force of Gravity

To calculate the mass of the train, we can use the formula:

Power = Force x Velocity

Since the power is given as 100 kW and the velocity is given as 60 km/h, we can convert the velocity to m/s:

Velocity = 60 km/h = (60 x 1000) / 3600 m/s

Now, let's calculate the mass of the train:

100,000 = (Mass x 9.8) x (60 x 1000) / 3600

Simplifying the equation:

Mass = (100,000 x 3600) / (9.8 x 60 x 1000)

Now that we have the mass of the train, we can calculate the force of gravity and the force of resistance.

Next, we can calculate the force required to develop a power of 120 kW:

Force = Power / Velocity

Since the power is given as 120 kW, we can convert it to W:

Power = 120,000 W

Now, let's calculate the force required:

Force = 120,000 / Velocity

Finally, we can calculate the required velocity to develop a power of 120 kW:

Velocity = Force / (Force of Gravity + Force of Resistance)

Now, let's substitute the values into the equation and calculate the required velocity.