Question

Вагон массы 50т движется со скоростью 12 кмч и встречает стоящую на пути платформу массы 30т. Найти скорость совместного движения вагона и платформы непосредственно после того как сработала автосцепка.Вычислить расстояние пройденное вагоном и платформой после сцепления если сила сопротивления составила 5 проц от веса

Answer 1

v1=12 км/ч=10/3 м/с  <----оставим  в  виде дроби

v2=0

m1=50т =50000 кг

m2=30т =30000 кг

Fc=5%*P

g=10 м/с2

-----------------------

v12-?

L -  ?

 

РЕШЕНИЕ

закон сохранения импульса  

m1v1 + m2v2 = (m1+m2)v12

v12 = (m1v1 + m2v2) /(m1+m2) =

       = (50000*10/3+30000*0)  / (50000+30000)=25/12 = 2.08 м/с =2.1 м/с

после сцепки  началось торможение  

вес вагона и платформы P=(m1+m2)g 

сила сопротивления Fc = P* 5%/100%= 0.05P = 0.05g(m1+m2)

ускорение при торможении   a=Fc/(m1+m2) = 0.05g(m1+m2) / (m1+m2)=0.05g

ускорение с МИНУСОМ  a=-0.05g  - торможение

начальная скорость при торможении Vo=v12=25/12

конечная скорость при остановке V=0

расстояние пройденное вагоном и платформой после сцепления

L= (V^2-Vo^2) / 2a = (0^2-(25/12)^2) / (-2*0.05*10) =4.34 м

ОТВЕТ   

скорость 2.08 м/с =2.1 м/с

расстояние 4.34 м

Answer 2

Calculation of the Combined Velocity of the Wagon and Platform

To find the combined velocity of the wagon and platform after the coupling, we can use the principle of conservation of momentum. According to this principle, the total momentum before the coupling is equal to the total momentum after the coupling.

The momentum of an object is given by the product of its mass and velocity. Therefore, we can write the equation:

Initial momentum of the wagon = Final momentum of the wagon + Final momentum of the platform

The initial momentum of the wagon is the product of its mass (50 tons) and velocity (12 km/h). The final momentum of the wagon and platform is the product of their combined mass (50 tons + 30 tons) and the final velocity we need to find.

Let's calculate the combined velocity of the wagon and platform:

Initial momentum of the wagon = Final momentum of the wagon + Final momentum of the platform

(50 tons) * (12 km/h) = (50 tons + 30 tons) * (combined velocity)

Simplifying the equation:

600 tons * km/h = 80 tons * (combined velocity)

Dividing both sides by 80 tons:

(combined velocity) = (600 tons * km/h) / 80 tons

(combined velocity) = 7.5 km/h

Therefore, the combined velocity of the wagon and platform immediately after the coupling is 7.5 km/h.

Calculation of the Distance Traveled by the Wagon and Platform

To calculate the distance traveled by the wagon and platform after the coupling, we need to consider the force of resistance acting against their motion. The force of resistance is given as 5% of the weight.

The force of resistance can be calculated as:

Force of resistance = 5% * (weight of the wagon + weight of the platform)

The weight of the wagon is 50 tons, and the weight of the platform is 30 tons. Therefore:

Force of resistance = 5% * (50 tons + 30 tons)

Force of resistance = 5% * 80 tons

Force of resistance = 0.05 * 80 tons

Force of resistance = 4 tons

Now, we can calculate the distance traveled by the wagon and platform using the equation:

Distance = (Initial velocity * time) - (0.5 * acceleration * time^2)

Since the force of resistance is acting against the motion, the acceleration will be negative. The equation becomes:

Distance = (Initial velocity * time) + (0.5 * acceleration * time^2)

The initial velocity is the combined velocity we calculated earlier (7.5 km/h), and the acceleration is the force of resistance divided by the combined mass of the wagon and platform.

Let's calculate the distance traveled:

Distance = (7.5 km/h * time) + (0.5 * (-4 tons) * time^2)

Since we don't have the time, we cannot calculate the exact distance traveled without this information.

Please provide the time for which the wagon and platform are in motion, and I will be able to calculate the distance traveled.