Question

Даю 60 баллов. Мне нужно четкое, понятное, развернутое решение через закон сохранения энергии или с его использованием. Поезд массой 1500 т движется со скоростью 57,6 км/ч и при торможении останавливается пройдя путь 200 м. Какова сила торможения? Как она должна изменится, чтобы тормозной путь уменьшился в 2 раза ?

Answer 1

Через закон сохранения энергии:
Поезд обладает кинетической энергией.$E_k= \frac{m*V^2}{2}$;  Ek=(1500000*(57.6/3.6)^2)/2=192000000=192*10^6 Дж; После полной остановки поезд эту энергию теряет(колеса и рельсы нагреваются, кинетическая энергия переходит в тепловую). В данном случае сила торможения поезда совершила отрицательную работу. A=F*S; A=Ek; Ek=F*S; F=Ek/S; F=192*10^6/200=960000 Н=960*10^3 Н; F(при 100 метрах торможения)=192*10^6/100=1920000 Н=1.92*10^6 Н. 
Ответ: F=960 кН; F(при уменьшенном тормозном пути)=1.92 МН

Answer 2

Problem Analysis

To solve this problem, we can use the principle of conservation of energy. According to this principle, the total mechanical energy of a system remains constant if no external forces are acting on it. In this case, the mechanical energy of the train is converted into work done by the braking force to bring the train to a stop.

Solution

Let's break down the problem into steps:

Step 1: Calculate the initial kinetic energy of the train using the formula: - Kinetic energy (KE) = (1/2) * mass * velocity^2

Given: - Mass of the train (m) = 1500 tons = 1,500,000 kg - Velocity of the train (v) = 57.6 km/h = 16 m/s

Substituting the values into the formula: - KE = (1/2) * 1,500,000 * 16^2

Simplifying the equation: - KE = 1,500,000 * 256

Calculating the value: - KE = 384,000,000 J

Step 2: Calculate the work done by the braking force using the formula: - Work (W) = force * distance

Given: - Distance traveled by the train (d) = 200 m

We need to find the force (F).

Rearranging the formula: - F = W / d

Substituting the values into the formula: - F = 384,000,000 / 200

Simplifying the equation: - F = 1,920,000 N

Therefore, the force of braking is 1,920,000 N.

Step 3: Calculate the new force required to reduce the braking distance by 2 times.

Given: - New distance traveled by the train (d_new) = 200 m / 2 = 100 m

We need to find the new force (F_new).

Using the formula: - F_new = W / d_new

Substituting the values into the formula: - F_new = 384,000,000 / 100

Simplifying the equation: - F_new = 3,840,000 N

Therefore, the new force of braking required to reduce the braking distance by 2 times is 3,840,000 N.

Conclusion

The force of braking required to stop the train after traveling a distance of 200 m is 1,920,000 N. To reduce the braking distance by 2 times, the force of braking needs to be increased to 3,840,000 N.

Please note that the above solution assumes ideal conditions and does not take into account factors such as friction, air resistance, and other external forces that may affect the actual braking force required.