Question

Автомобиль с двигателем мощностью N1 = 30 кВт при перевозке груза развивает скорость v1 = 15 м/с. Автомобиль с двигателем мощностью N2= 20 кВт при тех же условиях развивает скорость v2 = 10 м/с. С какой скоростью будут двигаться автомобили, если их соединить тросом?

Answer 1

Ответ:

Дано :

N₁=30 кВт=30 000 Вт

N₂=20 кВт=20 000 Вт

v₁=15 м/с

v₂=10 м/с

___________________

v-?

Решение:

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

F₁=N₁/v₁=30 000/15=2000 H

F₂=N₂/v₂=20 000/10=2000 H

v=(N₁+N₂)/(F₁+F₂)

v=(30 000+20 000)/(2000+2000)=12,5 м/с

Answer 2

Problem Analysis

We are given two cars, one with an engine power of N1 = 30 kW and a speed of v1 = 15 m/s, and another car with an engine power of N2 = 20 kW and a speed of v2 = 10 m/s. We need to determine the speed at which the cars will move if they are connected by a rope.

Solution

To solve this problem, we can use the principle of conservation of energy. The total power output of the two cars combined should be equal to the power required to overcome the resistance of the rope and move both cars at a certain speed.

Let's assume that the combined speed of the two cars when connected by a rope is v. The total power output of the two cars combined can be calculated as follows:

Total Power Output = Power of Car 1 + Power of Car 2

The power of each car can be calculated using the formula:

Power = Force × Velocity

Since the force required to move the cars is the same, we can equate the power of each car:

Power of Car 1 = Power of Car 2

Using the formula for power, we can rewrite this equation as:

Force × Velocity of Car 1 = Force × Velocity of Car 2

Since the force is the same, we can cancel it out:

Velocity of Car 1 = Velocity of Car 2

Therefore, the speed at which the cars will move when connected by a rope is equal to the average of their individual speeds:

v = (v1 + v2) / 2

Substituting the given values:

v = (15 m/s + 10 m/s) / 2 = 25 m/s / 2 = 12.5 m/s

So, when the cars are connected by a rope, they will move at a speed of 12.5 m/s.

Answer

When the cars are connected by a rope, they will move at a speed of 12.5 m/s.